ANSYS Workbench 12官方中文培训教程--Dynamic动力学模块教程及实例

ANSYS, Inc. Proprietary

© 2009 ANSYS, Inc. All rights reserved.TOC-1 July 2009

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ANSYS Mechanical

Dynamics

Table of Contents

Training Manual


© 2009 ANSYS, Inc. All rights reserved.TOC-2 July 2009

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Table of Contents1. Introduction to Dynamics 1-1

Definition & Purpose 1-6

Types of Dynamic Analysis 1-9

Basic Concepts and Terminology 1-15

Damping 1-21

Workshop 1 – Flywheel 1-33

2.Modal Analysis 2-1


Terminology & Concepts 2-5

Procedure 2-21

Workshop 2A – Plate with Hole 2-40

Workshop 2B – Prestressed Wing 2-40

3.Harmonic Response Analysis 3-1


Terminology & Concepts 3-5

Procedure 3-17

Workshop 5 – Fixed-Fixed Beam 3-31

4.Response Spectrum Analysis 4-1


Response Calculations 4-8

Mode Combination 4-12

Procedure 4-14

Workshop 4 – Suspension Bridge 4-25

5.Random Vibration Analysis 5-1


Power Spectral Density 5-5

Workbench capabilities 5-9

Procedure 5-10

Workshop 5 – Girder Assembly 5-22

6.Transient Analysis 6-1

Introduction 6-4

Preliminary Modal Analysis 6-7

Including Nonlinearities 6-10

Part Specification and Meshing 6-17

Nonlinear Materials 6-19

Contact; Joints; and Springs 6-20

Initial Conditions 6-27

Loads; Supports; Joint Conditions 6-30

Damping 6-32

Analysis Settings 6-33

Reviewing Results 6-35

Workshop 6 – Caster 6-37


© 2009 ANSYS, Inc. All rights reserved.1-1 July 2009

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ANSYS Mechanical

Dynamics

Chapter 1:

Introduction

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Welcome!

• Welcome to the Workbench Dynamics training course!

• This training course covers the procedures required to perform

dynamic analyses with ANSYS Workbench.

• It is intended for novice and experienced users.

• A related course is ANSYS Rigid and Flexible Dynamic Analysis,

which covers multi-body analysis.

• Several other advanced training courses are available on specific

topics.

– See the training course schedule on the ANSYS homepage:

www.ansys.com under “Training Services”.

Introduction

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Course Objectives

• This course is intended for users already familiar with the procedures

for performing a linear static analysis in Workbench Mechanical

environment.

– Prerequisite is ANSYS Workbench – Mechanical Introduction

• By the end of this course, you will be able to use Mechanical to

define, solve, and interpret the following dynamic analyses:

– Modal

– Harmonic Response

– Response Spectrum

– Random Vibration

– Transient

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Course Material

• The Training Manual you have is an exact copy of the slides.

• Workshop descriptions and instructions are included in the

Workshop Supplement.

• Copies of the workshop files are available (upon request) from the

instructor.

Introduction

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Introduction to Dynamics

A. Define dynamic analysis and its purpose.

B. Discuss different types of dynamic analysis available in Workbench

Mechanical.

C. Cover some basic concepts and terminology.

D. Review the types of damping available in Workbench Mechanical.

E. Do a sample dynamic analysis exercise.

Introduction

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A. Definition & Purpose

• A dynamic analysis is a technique used to determine the dynamic

behavior of a structure or component.

• It is an analysis involving time, where the inertia and possibly

damping of the structure play an important role.

• “Dynamic behavior” may be one or more of the following:

– Vibration characteristics

• how the structure vibrates and at what frequencies

– Effect of harmonic loads.

– Effect of seismic or shock loads.

– Effect of random loads.

– Effect of time-varying loads.

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… Definition & Purpose

• A static analysis might ensure

that the design will withstand

steady-state loading conditions,

but it may not be sufficient,

especially if the load varies with

time.

• The famous Tacoma Narrows

bridge (Galloping Gertie)

collapsed under steady wind

loads during a 42-mph wind

storm on November 7, 1940, just

four months after construction.

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• A dynamic analysis usually takes into account one or more of the

following:

– free vibrations

• natural vibration frequencies and shapes

– forced vibrations

• e.g. crank shafts, other rotating machinery

– seismic/shock loads

• e.g. earthquake, blast

– random vibrations

• e.g. rocket launch, road transport

– time-varying loads

• e.g. car crash, hammer blow

• Each situation is handled by a specific type of dynamic analysis.

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B. Types of Dynamic Analysis

• Consider the following examples:

– An automobile tailpipe assembly could shake apart if its natural frequency

matched that of the engine. How can you avoid this?

– A turbine blade under stress (centrifugal forces) shows different dynamic behavior.

How can you account for it?

• A modal analysis can be used to determine a structure’s vibration

characteristics.

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… Types of Dynamic Analysis

– Rotating machines exert steady,

alternating forces on bearings and

support structures. These forces

cause different deflections and

stresses depending on the speed of

rotation.

• A harmonic-response analysis can

be used to determine a structure’s

response to steady, harmonic loads.

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– Spacecraft and aircraft components must withstand random loading of varying

frequencies for a sustained time period.

A random-vibration analysis can be used to determine how a component

responds to random vibrations.

Courtesy: NASA

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– Skyscrapers, power-plant cooling

towers, and other structures must

withstand multiple short-duration

transient shock/impact loadings,

common in seismic events.

• A response-spectrum analysis can

be used to determine how a

component responds to

earthquakes.

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– An automobile fender should be able to withstand low-speed impact, but deform

under higher-speed impact.

– A tennis racket frame should be designed to resist the impact of a tennis ball and

yet flex somewhat.

• A transient analysis can be used to calculate a structure’s response to time

varying loads.

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• Choosing the appropriate type of dynamic analysis depends on the type of

input available and the type of output desired.

Type Input Output

Modal • none • natural frequencies and

corresponding mode shapes

• stress/strain profile

Harmonic • sinusoidally-varying excitations

across a range of frequencies

• sinusoidally-varying response at

each frequency

• min/max response over frequency

range

Spectrum • spectrum representing the

response to a specific time history

• maximum response if the model

were subjected to the time history

Random • spectrum representing probability

distribution of excitation

• response within specified range of

probabilities

Transient • time-varying loads • time-varying response

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C. Basic Concepts and Terminology

Topics discussed:

• General equation of motion

• Modeling considerations

• Damping

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Equation of Motion

• The linear general equation of motion, which will be referred to

throughout this course, is as follows (matrix form):

• Note that this is simply a force balance:

Basic Concepts & Terminology

FuKuCuM

vectorload applied

nt vectordisplaceme nodalmatrix stiffness structural

vector velocity nodalmatrix damping structural

on vectoraccelerati nodalmatrix mass structural

F

uK

uC

uM

appliedstiffnessdampinginertial FFFF

FuKuCuM

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Equation of Motion

• Different analysis types solve different forms of this equation.

– Modal

• F(t) set to zero; [C] usually ignored.

– Harmonic Response

• F(t) and u(t) assumed to be sinusoidal.

– Response Spectrum

• Input is a known spectrum of response magnitudes at varying frequencies in

known directions.

– Random Vibration

• Input is a probabilistic spectrum of input magnitudes at varying frequencies in

known directions.

– Transient

• The complete, general form of the equation is solved.


FuKuCuM

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Modeling Considerations - Geometry and Mesh

• Generally same geometry and meshing considerations for static

analysis apply to dynamic analysis.

– Include as many details as necessary to sufficiently represent the model

mass distribution.

– A fine mesh will be needed in areas where stress results are of interest. If

you are only interested in displacement results, a coarse mesh may be

sufficient.


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Modeling Considerations - Nonlinearities

• Nonlinearities, such as large deflections, nonlinear contact, material

nonlinearities, etc, are allowed only in a full transient dynamic

analysis with large deflection turned ON.

• All other Workbench dynamic analysis types are linear.

– the initial state of nonlinearities will be maintained throughout the

solution; i.e., [K] = const.

FuuKuCuM

nonlinear


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Modeling Considerations - Material properties

• Mass properties [M]– e.g. density, point mass

– required for all dynamic analysis types

– specify mass density when using metric units, and

– specify weight density when using British units

• Damping properties [C]– e.g. viscous, material (discussed later)

– required for mode-superposition harmonic

– optional but recommended for all other dynamic analysis types

• Stiffness (elastic) properties [K]– e.g., Young’s modulus, Poisson’s ratio, shear modulus

– required for all flexible analysis types

• Note that Mechanical has display (interactive) units and solution units.

FuKuCuM


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D. Damping

• Damping is an energy-dissipation

mechanism that causes vibrations

to diminish over time and eventually

stop.

– e.g. vibrational energy that is

converted to heat or sound

• The amount of damping may

depend on the material, the velocity

of motion, and/or the frequency of

vibration.

• Damping be classified as:

– Viscous damping (e.g. dashpot,

shock absorber)

– Material / Solid / Hysteretic damping

(e.g. internal friction)

– Coulomb or dry-friction damping

(e.g. sliding friction)

– Numerical damping


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Damping

• If the amount of damping in a system

becomes large, the response will no

longer oscillate.

• Critical damping is defined as the

threshold between oscillatory and

non-oscillatory behavior.

• The damping ratio is the ratio of the

damping in a system to the critical

damping, given by


cc

c

nc mkmm

kmc 222

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Damping

• The undamped natural frequency of a

1-DOF system is given by

• The addition of viscous or solid

damping slightly alters the natural

frequency of a system.

• Coulomb damping has no effect on

frequency.


nd 21

m

kn

21

n

d

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Viscous damping

• Viscous damping force is

proportional to the velocity of the

vibrating body.

• Assuming the motion is harmonic,

• This type of damping occurs, for

example, when a body moves

through a fluid.

• For structural systems, a stiffness

multiplier is often used in place of c

for numerical simplicity.


ucFd

uicucF nd

ukiukF

kc

nd

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• The value of c in

can be input directly as element damping

(Details section of Spring connection).

Viscous damping

• The value of in

can be input directly as global

damping value (Details section of

Analysis Settings) or as material-

dependent damping value

(Material Damping Factor material

property).


uicucF nd

ukiukF nd

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Material / Solid / Hysteretic damping

• Solid damping is inherently present

in a material (energy is dissipated

by internal friction), so it is typically

considered in a dynamic analysis.

• Experience shows that energy

dissipated by internal friction in a

real system does not depend on

frequency.

• Not well understood and therefore

difficult to quantify, so again a

stiffness multiplier is used for

numerical simplicity.


kuiFd 2

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Material / Solid / Hysteretic damping

• Damping ratio isn’t available in a transient analysis since

the response frequency is not known in advance.

– The value of can be calculated from a known value of

(damping ratio) and a known frequency :

– Pick the most dominant response frequency to calculate .


• The value of in

can be input directly as global

damping value (Details section

of Analysis Settings) or as

material-dependent damping

value (Constant Damping

Coefficient material property).

n /2

kuiFd 2

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Coulomb or dry-friction damping

• Coulomb damping occurs when a body slides on a dry surface.

• Damping force is proportional to the force normal to the surface.

– m is the coefficient of friction

– m is the mass

– g is the gravitational constant

– sgn(y) is the signum function, defined as

• Not considered in a linear dynamic analysis. Generally requires a

nonlinear transient solution.


)sgn(xmgFdm

0for 0

0for 1

0for 1

)sgn(

y

y

y

y

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Numerical Damping

• Numerical Damping is not true damping.

– Artificially controls numerical noise produced by the higher frequencies of a structure.

• Stabilizes the numerical integration scheme by damping out the unwanted high frequency modes.

• The default value of 10% will damp-out spurious high frequencies and is a sensible value to try initially.

• Use the lowest possible value that damps out nonphysical response without significantly affecting the final solution.


High-frequency

response

Primary

Frequency

undamped

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Damping – Summary

• In summary, Workbench allows the

following four inputs for damping:

– Beta damping (viscous)

• Global or material-dependent.

• Defines the stiffness matrix multiplier

for damping.

– Element damping (viscous)

• Defines the damping coefficients

directly.

– Damping ratio (solid)

• Global or material-dependent.

• Defines the ratio of actual damping to

critical damping.

– Numerical damping (artificial)

• Defines the amplitude decay factor

obtained through a modification of

the time-integration scheme.

• NOTE: The effects are cumulative if

set in conjunction.


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Damping

• Different industries specify damping in different ways:

= Viscous damping factor or damping ratio

h = Loss factor or Structural damping factor

Q = Quality factor or simply

D = Log decrement

D = Spectral damping factor

A = Amplification factor

• The following table provides the conversions (note: U = strain energy)

Measure Damping ratio Loss Factor Log Decrement Quality FactorSpectral

Damping

Amplification

Factor

Damping Ratio h/2 D/2p 1/(2Q) D/(4pU) 1/2A

Loss Factor 2 h D/p 1/Q D/(2pU) 1/A

Log Decrement 2p ph D p/Q D/(2U) p/A

Quality Factor 1/2 1/h p/D Q 2pU/D A

Spectral

Damping4pU 2pUh 2UD 2pU/Q D 2pU/A

Amplification

Factor1/2 1/h p/D Q 2pU/D A


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References & Bibliography

• S. S. Rao, Mechanical Vibrations.

• K. Ogata, Modern Control Engineering.

• B. J. Lazan, Damping of Materials and Members in Structural

Mechanics.

• A. K. Gupta, Response Spectrum Method: In Seismic Analysis and

Design of Structures.

• U.S. Nuclear Regulatory Commission Regulatory Guide 1.92,

Combining Modal Responses and Spatial Components in Seismic

Response Analysis.

• D. E. Newland, An Introduction to Random Vibrations, Spectral &

Wavelet Analysis.

• Military Standard 810E, Environmental Test Methods And

Engineering Guidelines.

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E. Introductory Workshop

• In this workshop, you will run a

sample dynamic analysis of a

flywheel.

• Follow the instructions in your

Dynamics Workshop supplement

WS1: Intro (Flywheel)

• The idea is to introduce you to the

steps involved in a typical dynamic

analysis. Details of what each step

means will be covered in the rest of

this seminar.

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ANSYS Mechanical

Dynamics

Chapter 2:

Modal Analysis

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Modal Analysis

A. Define modal analysis and its purpose.

B. Discuss associated concepts, terminology, and mode extraction

methods.

C. Learn how to do a modal analysis in Workbench.

D. Work on one or two modal analysis exercises.

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Description & Purpose

• A modal analysis is a technique used to determine the vibration

characteristics of structures:

– natural frequencies

• at what frequencies the structure would tend to naturally vibrate

– mode shapes

• in what shape the structure would tend to vibrate at each frequency

– mode participation factors

• the amount of mass that participates in a given direction for each mode

• Most fundamental of all the dynamic analysis types.

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Benefits of modal analysis

• Allows the design to avoid resonant vibrations or to vibrate at a

specified frequency (speaker box, for example).

• Gives engineers an idea of how the design will respond to different

types of dynamic loads.

• Helps in calculating solution controls (time steps, etc.) for other

dynamic analyses.

Recommendation: Because a structure’s vibration characteristics

determine how it responds to any type of dynamic load, it is generally

recommended to perform a modal analysis first before trying any other

dynamic analysis.

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• A “mode” refers to the pair of one

natural frequency and

corresponding mode shape.

– A structure can have any number of

modes, up to the number of DOF in

the model.

mode 1

← {f}1

f1 = 109 Hz

mode 2

← {f}2

f2 = 202 Hz

mode 3

← {f}3

f3 = 249 Hz

Terminology


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• The structure is linear (i.e. constant stiffness and mass).

• There is no damping.

– Damped eigensolvers (MODOPT,DAMP or MODOPT,QRDAMP) may be

accessed using Commands Objects, but will not be covered here.

• The structure has no time varying forces, displacements, pressures,

or temperatures applied (free vibration).

Assumptions & Restrictions

Theory

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• Start with the linear general equation of motion:

• Assume free vibrations, and ignore damping:

• Assume harmonic motion:

FuKuCuM

Development

iiii

iiii

iii

tu

tu

tu

f

f

f

sin

cos

sin

2

0

00

uKuM

FuKuCuM

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• Substitute and simplify

• This equality is satisfied if fi = 0 (trivial, implies no vibration) or if

• This is an eigenvalue problem which may be solved for up to n

eigenvalues, i2, and n eigenvectors, fi, where n is the number of

DOF.

0

0sinsin

0

2

2

ii

iiiiiii

KM

tKtM

uKuM

f

ff

0det 2 MK i

Development

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• Note that the equation

has one more unknown than equations; therefore, an additional

equation is needed to find a solution.

– The addition equation is provided by mode shape normalization.

• Mode shapes can be normalized either to the mass matrix

or to unity, where the largest component of the vector {f}i is set to 1.

• Workbench displays results normalized to the mass matrix.

• Because of this normalization, only the shape of the DOF solution

has real meaning.

1 i

T

i M ff

0det 2 MK i

Extraction & Normalization

Theory

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• The square roots of the eigenvalues

are i, the structure’s natural

circular frequencies (rad/s).

• Natural frequencies fi can then

calculated as fi = i/2p (cycles/s).

– It is the natural frequencies, fi in Hz,

that are input by the user and output

by Workbench.

• The eigenvectors {f}i represent the

mode shapes, i.e. the shape

assumed by the structure when

vibrating at frequency fi.

mode 1

← {f}1

f1 = 109 Hz

mode 2

← {f}2

f2 = 202 Hz

mode 3

← {f}3

f3 = 249 Hz

Eigenvalues & Eigenvectors

Theory

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• The equation

can be solved using one of two solvers available in Workbench Mechanical:

– Direct (Block Lanczos)

• To find many modes (about 40+) of large models.

• Performs well when the model consists of shells or a combination of shells and solids.

• Uses the Lanczos algorithm where the Lanczos recursion is performed with a block of vectors. Uses the sparse matrix solver.

– Iterative (PCG Lanczos)

• To find few modes (up to about 100) of very large models (500,000+ DOFs).

• Performs well when the lowest modes are sought for models that are dominated by well-shaped 3-D solid elements.

• Uses the Lanczos algorithm, combined with the PCG iterative solver.

• In most cases, the Program Controlled option selects the optimal solver automatically.

0det 2 MK i

Equation Solvers

Theory

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Participation Factors (Solution Information)

• The participation factors are calculated by

where {D} is an assumed unit displacement spectrum in each of the global

Cartesian directions and rotation about each of these axes.

– This measures the amount of mass moving in each direction for each mode.

– The “Ratio” is simply another list of participation factors, normalized to the largest.

• The concept of participation factors will be important in later chapters.

DMT

ii f

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Participation Factors (Solution Information)

• A high value in a direction indicates that the mode will be excited by forces in

that direction.

mode 1 mode 3 mode 5

Theory

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Effective Mass (Solution Information)

• Also printed out is the effective mass.

• Ideally, the sum of the effective masses in each direction should equal total

mass of structure, but will depend on the number of modes extracted.

• The ratio of effective mass to total mass can be useful for determining

whether or not a sufficient number of modes have been extracted.

1 if,2

2

, i

T

ii

i

T

i

iieff M

MM ff

ff

Theory

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Prestress Effects

• A prestressed modal analysis can be used to calculate the

frequencies and mode shapes of a prestressed structure, such as a

spinning turbine blade.

– The prestress influences the stiffness of the structure through the stress-

stiffening matrix contribution.

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Prestress Effects

• In free vibration with prestress analyses, two solutions are required.

– A linear static analysis is initially performed:

– Based on the stress state [s] from the static analysis, a stress stiffness matrix [S] is calculated (see Theory Reference for details):

– The free vibration with pre-stress analysis is then solved, including the [S] term:

• Note that the prestress only affects the stiffness of the system.

– i.e. the static prestress will not be added to the modal stress

s FuK

Ss

02 ii MSK f

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• Contact regions are available in modal analysis; however, since this

is a purely linear analysis, contact behavior will differ for the

nonlinear contact types, as shown below:

• Contact behavior will reduce to its linear counterparts.

– It is generally recommended, however, not to use a nonlinear contact

type in a linear-dynamic analysis

Contact Type Static Analysis

Linear Dynamic Analysis

Initially Touching Inside Pinball RegionOutside Pinball

Region

Bonded Bonded Bonded Bonded Free

No Separation No Separation No Separation No Separation Free

Rough Rough Bonded Free Free

Frictionless Frictionless No Separation Free Free

Frictional Frictionalm = 0, No Separation

m > 0, BondedFree Free

Contact Regions

Remarks & Comments

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Unconstrained Systems

• An unconstrained system is one that has no constraints or supports

and can move as a rigid body in at least one direction.

– Rigid-body motion can be considered to be a mode of oscillation with

zero frequency.

– In practice, these modes may not have a frequency of exactly zero.

• Note that a well-connected system can have at most six rigid-body

modes.

– Obtaining more than six rigid-body modes may indicate that assemblies

are not well connected.

“rigid-body”

or

“zero” modes

Remarks & Comments

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Symmetry Boundary Conditions

• Symmetry BC’s will only produce symmetrically shaped modes, so

some modes can be missed.

– It may be necessary to apply several different symmetry conditions to

find all modes.

– The full model below results in the frequencies listed in the tabular view.

– A quarter-symmetry model will require three sets of symmetry boundary

conditions to find all modes (see next slide)...

Remarks & Comments

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Symmetry Boundary Conditions

Symmetry BC

Anti-Symmetry BC

Symm-Asym BC

Full Model

etc

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Procedure:

Modal

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Procedure

• Drop a Modal (ANSYS) system into the project schematic.

Modal

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Procedure

• Create new geometry, or link to

existing geometry.

• Edit the Model cell to bring up the

Mechanical application.

Modal

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Preprocessing

• Verify materials, connections, and mesh settings.

– This was covered in Workbench Mechanical Intro.

Modal

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Preprocessing

• Add supports to the model.

– Displacement constrains must have a magnitude of zero.

Modal

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Solution Settings

• Choose the number of modes to

extract.

• If needed, upper and lower bounds

on frequency may be specified to

extract the modes within a specified

range.

Modal

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Solution Settings

• If the Program-Controlled solver

selection is not appropriate, the

solver type can be changed to

either Direct or Iterative.

• Stress and strain results may be

turned on under Output Controls.

Modal

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Postprocessing

• Total-deformation results may be

quickly inserted by highlighting

multiple rows in the tabular view or

histogram view.

Modal

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Postprocessing

• If stress/strain were requested, these results may also be access from the

Solution Toolbar.

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Procedure:

Prestressed Modal

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Procedure

• The procedure to do a prestressed

modal analysis is essentially the

same as a regular modal analysis,

except that you first need to

prestress the structure by doing a

static analysis.

• The static analysis results in a

stressed structure, which is used as

the initial condition for the modal

analysis.

Prestressed Modal

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Procedure

• Drop a Static Structural (ANSYS) system into the project schematic.

Prestressed Modal

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Procedure

• Drop a Modal (ANSYS) system onto

the Solution cell of the Modal

system.

• Note the circular-ended connector,

indicating a data transfer from the

Static to the Modal analysis.

Prestressed Modal

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Procedure


existing geometry.



Prestressed Modal

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Preprocessing

• In the Static Structural system, insert the loads and supports that will cause

the prestressed-state to occur.

Prestressed Modal

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Postprocessing

• Review the static results before

proceeding.

Prestressed Modal

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Preprocessing

• Workbench will automatically setup

the data transfer between the

systems.

• To verify the data transfer, one can

ensure that

– Future Analysis is set to

Prestressed analysis in the Static

Structural system

– Pre-Stress Environment is set to

Static Structural in the Modal

system

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Postprocessing

• The modal results may be reviewed as described in the previous section.

Prestressed Modal

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Postprocessing

• Note that the prestressed state increased the frequencies of this structure.

– e.g. the first mode in this example increased from 108.3 Hz to 274.6 Hz

Not Prestressed Prestressed

Prestressed Modal

• A prestress may not always increase the natural frequencies; a compressive

load will decrease the frequencies.

– In fact, a sufficiently-high compressive load will result in a natural frequency of

zero, effectively replicating the results of a buckling analysis.

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D. Workshop - Modal Analysis

This workshop consists of two problems:

1. Modal analysis of a plate with a hole

– A step-by-step description of how to do the analysis.

– You may choose to run this problem yourself, or your instructor may

show it as a demonstration.

(WS2A: Modal Analysis - Plate with a Hole).

2. Pre-stressed Modal analysis of a model airplane wing

– This is left as an exercise to you.

(WS2B: Modal Analysis - Model Airplane Wing).

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ANSYS Mechanical

Dynamics

Chapter 3:

Harmonic Response

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Harmonic Analysis

A. Define harmonic analysis and its purpose.

B. Learn basic terminology and concepts underlying harmonic

analysis.

C. Learn how to do a harmonic analysis in Workbench.

D. Work on a harmonic analysis exercise.

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A. Definition & Purpose

What is harmonic analysis?

• A technique to determine the steady state response of a structure to

sinusoidal (harmonic) loads of known frequency.

• Input:

– Harmonic loads (forces, pressures, and imposed displacements) of

known magnitude and frequency.

– May be multiple loads all at the same frequency. Forces and

displacements can be in-phase or out-of phase. Body loads can only be

specified with a phase angle of zero.

• Output:

– Harmonic displacements at each DOF, usually out of phase with the

applied loads.

– Other derived quantities, such as stresses and strains.

Harmonic Analysis

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Harmonic analysis is used in the design of:

• Supports, fixtures, and components of rotating equipment such as

compressors, engines, pumps, and turbomachinery.

• Structures subjected to vortex shedding (swirling motion of fluids)

such as turbine blades, airplane wings, bridges, and towers.

Why should you do a harmonic analysis?

• To make sure that a given design can withstand sinusoidal loads at

different frequencies (e.g, an engine running at different speeds).

• To detect resonant response and avoid it if necessary (by using

dampers, for example).

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B. Terminology & Concepts

Topics covered:

• Assumptions and Restrictions

• Equation of motion

• Nature of harmonic loads

• Complex displacements

• Solution methods

Harmonic Analysis

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• The entire structure has constant or frequency-dependent stiffness,

damping, and mass effects.

• All loads and displacements vary sinusoidally at the same known

frequency (although not necessarily in phase).

• Acceleration, bearing, and moment loads are assumed to be real (in-

phase) only.

Theory

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Development

• Start with the linear general equation of motion:

• Assume [F] and {u} are harmonic with frequency W:

• Note: The symbols W an w differentiate the input from the output:

W = input (a.k.a. imposed) circular frequency

w = output (a.k.a. natural) circular frequency

ti

ti

tii

ti

ti

tii

euiu

eiu

eeuu

eFiF

eiF

eeFF

W

W

W

W

W

W

21

max

max

21

max

max

sincossincos

FuKuCuM

Theory

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Development

• Take two time derivatives:

• Substitute and simplify:

• This can then be solved using one of two methods.

ti

ti

ti

euiuu

euiuiu

euiuu

W

W

W

W

W

21

2

21

21

2121

2

2121

21

21

2

FiFuiuKCiM

eFiFeuiuK

euiuCi

euiuM

FuKuCuM

titi

ti

ti

WW

W

W

WW

W

W

Theory

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Development

• The full method solves the system of simultaneous equations directly

using a static solver designed for complex arithmetic:

– c denotes a complex matrix or vector

• The mode-superposition method expresses the displacements as a

linear combination of mode shapes (see Theory Reference for details).

ccc

FuK

FuK

FiFuiuKCiM

ccc

WW

2121

2

jcjcjjj fyi

FiFuiuKCiM

WW

WW

22

2121

2

2 ww

Theory

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Solution Methods

FULL MSUP

• Exact solution. • Approximate solution; accuracy depends in

part on whether an adequate number of

modes have been extracted to represent

the harmonic response.

• Generally slower than MSUP. • Generally faster than FULL.

• Supports all types of loads and boundary

conditions.

• Does not support nonzero imposed

harmonic displacements.

• Solution points must be equally distributed

across the frequency domain.

• Solution points may be either equally

distributed across the frequency domain or

clustered about the natural frequencies of

the structure.

• Solves the full system of simultaneous

equations using the Sparse matrix solver for

complex arithmetic.

• Solves an uncoupled system of equations

by performing a linear combination of

orthogonal vectors (mode shapes).

• Prestressing is not available in either method in ANSYS Workbench 12.0.

Theory

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Nature of Harmonic Loads

• Multiple loads and boundary

conditions may be input, each with

different amplitude and phase

angles (interpreted as lag angle).

• All loads and displacements, both

input and output, are assumed to

occur at the same frequency.

• Calculated displacements will be

complex if

– damping is specified or

– applied load is complex.

Theory

angle phase

freqency

amplitude where

sin

w

w

X

iii tXx

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Resonance

• When the imposed frequency

approaches a natural frequency in

the direction of excitation, a

phenomenon known as resonance

occurs.

– This can be seen in the figures on

the right for a 1-DOF system

subjected to a harmonic force for

various amounts of damping.

• The following will be observed:

– an increase in damping decreases

the amplitude of the response for all

imposed frequencies,

– a small change in damping has a

large effect on the response near

resonance, and

– the phase angle always passes

through ±90° at resonance for any

amount of damping.

Remarks & Comments

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Contact Regions

• Contact regions are available in harmonic analysis; however, since

this is a purely linear analysis, contact behavior will differ for the

nonlinear contact types, as shown below:

• Contact behavior will reduce to its linear counterparts.

– It is generally recommended, however, not to use a nonlinear contact

type in a linear-dynamic analysis

Contact Type Static Analysis

Linear Dynamic Analysis

Initially Touching Inside Pinball RegionOutside Pinball

Region

Bonded Bonded Bonded Bonded Free

No Separation No Separation No Separation No Separation Free

Rough Rough Bonded Free Free

Frictionless Frictionless No Separation Free Free

Frictional Frictionalm = 0, No Separation

m > 0, BondedFree Free

Remarks & Comments

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Mode Superposition

• The Mode Superposition method will automatically perform a modal

analysis first

– The number of modes necessary for an accurate solution will be

estimated if a frequency range is not supplied.

• the default range is from zero to twice the ending frequency

– The harmonic analysis portion is very quick and efficient, hence, the

Mode Superposition method is usually much faster overall than the Full

method

• Since a free vibration analysis is performed, Mechanical knows what

the natural frequencies of the structure are and can cluster the

harmonic results near them (see next slide)

Remarks & Comments

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… Solution Methods - Mode Superposition

• Cluster option captures the peak response better than evenly-spaced

intervals.

Evenly spaced

frequency points

Clustered frequency

points

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Procedure:

Harmonic Response

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C. Procedure

Four main steps:

• Build the model

• Choose analysis type and options

• Apply harmonic loads and solve

• Review results

Harmonic Analysis

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Build the Model

Model

• Nonlinearities are not allowed.

• See also Modeling Considerations in Module 1.

Harmonic Analysis Procedure

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Choose Analysis Type & Options

Build the model

Choose analysis type and options

• Enter Solution and choose

harmonic analysis.

• Main analysis option is solution

method - discussed next.

• Specify damping - discussed

next.


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… Choose Analysis Type & Options

Analysis options

• Solution method - full or mode

superposition.

• For large models (>1 million

DOF), set Store Results at All

Frequencies to “No”.

Damping

• Choose from beta damping and

damping ratio (constant

damping ratio is most

commonly used).


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Apply Harmonic Loads and Solve

Build the model


Apply harmonic loads and solve

• Structural loads and supports may also be used in harmonic

analyses with the following exceptions:

– Loads Not Supported:

• Gravity Loads

• Thermal Loads

• Rotational Velocity

• Pretension Bolt Load

• Compression Only Support (if present, it behaves similar to a Frictionless

Support)

• Remember that all structural loads will vary sinusoidally at the same

excitation frequency


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… Apply Harmonic Loads and Solve

• A list of supported loads are shown below:

– Not all available loads support phase input. Accelerations, Bearing Load,

and Moment Load will have a phase angle of 0°.

• If other loads are present, shift the phase angle of other loads, such that the

Acceleration, Bearing, and Moment Loads will remain at a phase angle of 0°.


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• Specifying harmonic loads requires:

– Amplitude and phase angle

– Frequency

• Loads are applied all at once in the first

solution interval (stepped).

• Amplitude and phase angle

– The load value (magnitude) represents

the amplitude Fmax.

– Phase angle Y is the phase shift

between two or more harmonic loads.

Not required if only one load is present.

Non-zero Y valid for force,

displacement, and pressure harmonic

loads.

Real

Ima

gin

ary

F1max

F2max


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• Amplitude and phase angle (continued)

– Mechanical allows direct input of amplitude and phase angle into the

Details window.

Real

Ima

gin

ary

F1max

F2max


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• Frequency of harmonic load:

– Specified in cycles per second

(Hertz) by a frequency range and

number of substeps within that

range.

– For example, a range of 0-50 Hz

with 10 solution intervals gives

solutions at frequencies of 5, 10,

15, …, 45, and 50 Hz. Same

range with 1 substep gives one

solution at 50 Hz.


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Review Results

Build the model


Apply harmonic loads and solve

Review results

• Three steps:

– Plot displacement vs. frequency at specific points in the structure.

– Identify critical frequencies and corresponding phase angles.

– Review displacements and stresses over entire structure at the

critical frequencies and phase angles.


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Review Results

Displacement vs. frequency plots

• Pick nodes that might deform the

most, then choose the DOF

direction.

• Then graph the desired frequency

response.


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… Review Results

Identify critical frequencies and phase angles

• Bode plot shows frequency at which highest amplitude occurs.

• The amplitude and phase angle at which the peak amplitude occurs

are shown in the Worksheet tab.


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… Review Results

• Next step is to review displacements and stresses over the entire

model at that frequency and phase angle.

• The frequency and phase angle must be manually entered into the

Details window.


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… Review Results

• A harmonic analysis produces a real and imaginary solution as

separate sets of results.

• Plot deformed shape, stress contours, and other desired results at

a specified frequency and phase angle.


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Harmonic Analysis

• In this workshop, you will examine the harmonic response of a

fixed-fixed beam to harmonic forces caused by rotating

machinery mounted on the beam.

• See your Dynamics Workshop supplement for details

WS3: Harmonic Analysis - Fixed-Fixed Beam

Workshop

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ANSYS Mechanical

Dynamics

Chapter 4:

Response Spectrum

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Response Spectrum Analysis

Topics covered:

• Definition and purpose

• Overview of Workbench capabilities

• Procedure

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• A response-spectrum analysis

calculates the maximum response

of a structure to a transient loading.

• It is performed as a fast alternative

of approximating a full transient

solution.

• The maximum response is

computed as scale factor times the

mode shape.

• These maximum responses are then

combined to give a total response

of the structure.


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Types of Analyses

Types of Response Spectrum analysis:

• Single-point response spectrum

– A single response spectrum excites all specified points in the model.

• Multi-point response spectrum

– Different response spectra excite different points in the model.


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Common Uses

• Commonly used in the analysis of:

– Nuclear power plant buildings

and components, for seismic

loading

– Airborne Electronic equipment

for shock loading

– Commercial buildings in

earthquake zones


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Terminology & Concepts

• Instead of simulating the response of a structure to a full time history,

we could figure out how each mode would respond to the time

history, then combine the responses together.

• In other words, the response of each mode of a structure is similar to

a 1-DOF oscillator, just scaled by some amount.

• If we know the natural frequencies and mode shapes of a structure,

we can simply determine what the displacement would be for a 1-DOF

oscillator, if it were subjected to the same transient loading, and

scale the response by the appropriate amount.

• If there is more than one load, each will have its own spectrum.


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• The structure is linear (i.e. constant stiffness and mass).

• For single-point response spectrum analysis, the structure is excited

by a spectrum of known direction and frequency components, acting

uniformly on all support points.

• For multi-point response spectrum analysis, the structure may be

excited by different input spectra at different support points.

– Up to 20 different simultaneous input spectra are allowed.


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Participation Factors

• A modal analysis must first be completed to determine the natural

frequencies, mode shapes, and participation factors for each mode.

– This procedure was covered in Chapter 2: Modal Analysis.

DM

KM

T

ii

ii

02

mode frequency mode shapespectrum

value

participation

factor

mode

coefficientresponse

1 1 {}1 S1 1 A1 {R}1

2 2 {}2 S2 2 A2 {R}2

3 3 {}3 S3 3 A3 {R}3

… … … … … … …

Theory

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Spectrum Values

• For each natural frequency, the spectrum value can be determined by a

simple look-up from the response-spectrum table.

– When values are needed between input frequencies, log-log interpolation is done

in the space as defined.


value

participation

factor

mode

coefficientresponse

1 1 {}1 S1 1 A1 {R}1

2 2 {}2 S2 2 A2 {R}2

3 3 {}3 S3 3 A3 {R}3

… … … … … … …

Theory

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Mode Coefficients

• The mode coefficients can be determined from the participation factors,

depending on the type of spectrum input.

– Recall: participation factors measure the amount of mass moving in each direction

for a unit displacement.


value

participation

factor

mode

coefficientresponse

1 1 {}1 S1 1 A1 {R}1

2 2 {}2 S2 2 A2 {R}2

3 3 {}3 S3 3 A3 {R}3

… … … … … … …

2

onaccelerativelocityntdisplaceme

i

iii

i

iiiiii

SA

SASA

Theory

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Response

• The response (displacement, velocity or acceleration) for each mode can

then be computed from the frequency, mode coefficient, and mode shape.

• If there is more than one significant mode, the response for each mode must

be combined using some method.

responseon acceleratifor

responsety for veloci

responsent displacemefor

2

iiii

iiii

iii

AR

AR

AR


value

participation

factor

mode

coefficientresponse

1 1 {}1 S1 1 A1 {R}1

2 2 {}2 S2 2 A2 {R}2

3 3 {}3 S3 3 A3 {R}3

… … … … … … …

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Mode Combination

• In general, mode combinations take the form:

where R is the total modal response and RiRj is the entrywise product (a.k.a. Hadamard or Schur product) of modes i and j.

• The modal correlation coefficients, eij, are uniquely defined, depending on the method chosen for evaluating the correlation coefficient.

• The methods for mode combination are SRSS, CQC, and ROSE.

2

1

1 1

N

i

N

j

jiij RRR e

0 and modes correlated eduncorrelatfor

10 and modes correlatedpartially for

1 and modes correlated completelyfor

ij

ij

ij

ji

ji

ji

e

e

e

Theory

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Mode Combination

• The SRSS method is generally more conservative than the other

methods.

– assumes that all maximum modal values are uncorrelated

– for a structures with coupled modes, this assumption overestimates the

responses overall

• The CQC and the ROSE methods providing a means of evaluating

modal correlation for the response spectrum analysis.

– accounting for mode coupling makes the response estimate from these

methods more realistic and closer to the exact time history solution

2

1

1 1

2

1

1 1

2

1

1

2

ROSECQCSRSS

N

i

N

j

jiij

N

i

N

j

jiij

N

i

i RRRRRkRRR ee

ji

ji

ij

ij

for 0.0

for 0.1

e

e

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Procedure:

Response Spectrum

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Procedure


Response Spectrum

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Procedure

• Drop a Response Spectrum system onto the Solution cell of the

Modal system.

Response Spectrum

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Procedure


existing geometry.



Response Spectrum

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Preprocessing



Response Spectrum

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Preprocessing



Response Spectrum

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Solution Settings


extract.




range.

Response Spectrum

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Postprocessing

• Review the modal results before

proceeding.

Response Spectrum

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Preprocessing

• Insert an Acceleration, Velocity, or Direction response spectrum.

• Set the Boundary Condition, Spectrum (Tabular) Data, and Direction.

Response Spectrum

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Postprocessing

• Insert Directional Deformation, Velocity, or Acceleration.

Response Spectrum

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Postprocessing

• Stress (normal, shear, equivalent) and Strain (normal, shear) results

can also be reviewed.

Response Spectrum

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• In this workshop, you will determine the response of a

prestressed suspension bridge subjected to a seismic load.

• See your Dynamics Workshop supplement for details

WS4: Response Spectrum Analysis - Suspension Bridge

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ANSYS Mechanical

Dynamics

Chapter 5:

Random Vibration

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Random Vibration Analysis

Topics covered:

• Definition and purpose

• Overview of Workbench capabilities

• Procedure


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A. Definition and Purpose

What is random vibration analysis?

– A spectrum analysis technique based on probability and statistics.

– Meant for loads such as acceleration loads in a rocket launch that

produce different time histories during every launch .

Reference: Random vibrations in mechanical systems by Crandall & Mark


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• Transient analysis is not an option since the time history is not

deterministic (sample is not repeatable).

• Instead, using statistics the sample time histories are converted to

Power Spectral Density function (PSD), a statistical representation of

the load time history.

… Definition and Purpose

Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.


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Power Spectral Density

• Sample time histories are converted to Power Spectral Density

function (PSD), a statistical representation of the load time history.

Reference: Random vibrations in

mechanical systems by Crandall

& Mark

Image from “Random Vibrations Theory and

Practice” by Wirsching, Paez and Ortiz.


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Statistical Representation

• A Random Vibration analysis computes the probability distribution of

different results, such as displacement or stress, due to some

random excitation

• The analysis follows a modal analysis

• An internal combination is done to compute the combined effect from

each mode and their interactions.

3sGaussian

(normal)

Distribution


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Power Spectral Density

• The Power Spectral Density is the

mean square value of the excitation

for a unit frequency band.

– The area under a PSD curve is

the variance of the response

(square of the standard

deviation).

– The units used in PSD are mean

square/Hz (e.g. an acceleration

PSD will have units of G2/Hz).

– The quantity represented by

PSD may be displacement,

velocity, acceleration, force, or

pressure.

Random Vibration curve by MIL-STD-202


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Common Uses

• Commonly used for

– Airborne electronics

– Acoustic loading of Airframe parts

– Jitter in alignment of optical

equipment

– Relative deformation in large

mirrors


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Workbench Capabilities

• Input:

– Natural frequencies and mode shapes from a modal analysis

– Single or multiple PSD excitations applied to ground nodes

• Output:

– 1s results can be contoured like any other analysis.

– Response PSD at one DOF (one point in one direction)

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Procedure:

Random Vibration

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Procedure


Random Vibration

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Procedure

• Drop a Random Vibration system onto the Solution cell of the Modal

system.

Random Vibration

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Procedure


existing geometry.



Random Vibration

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Preprocessing



Random Vibration

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Preprocessing



Random Vibration

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Solution Settings


extract.




range.

Random Vibration

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Postprocessing

• Review the modal results before

proceeding.

Random Vibration

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• Insert an Acceleration, Velocity, or Direction PSD base excitation.

• Set the Boundary Condition, Load (Tabular) Data, and Direction.

Preprocessing

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Postprocessing

• Insert Directional Deformation, Velocity, or Acceleration.

– the direction and sigma value may be chosen here

– note that results are always reviewed with scaling set to 0.0

Random Vibration

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Postprocessing

• Stress (normal, shear, equivalent) and Strain (normal, shear) results

can also be reviewed.

Random Vibration

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Postprocessing

• Response PSD can be plotted at one DOF (one point in one direction,

either absolute or relative to base excitation).

Random Vibration

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Workshop – Random Vibration

• In workshop 5A, you will determine the displacements and stresses

in a girder assembly due to an acceleration PSD.

WS5A: Random Vibration (PSD) Analysis of a Girder Assembly



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ANSYS Mechanical

Dynamics

Chapter 6:

Transient

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Overview

• Transient structural analysis provides users with the ability to

determine the dynamic response of the system under any type of

time-varying loads.

– Unlike rigid dynamic analyses, bodies can be either rigid or flexible. For

flexible bodies, nonlinear materials can be included, and stresses and

strains can be output.

– Transient structural analysis is also known as time-history analysis or

transient structural

analysis.

– To perform Flexible

Dynamic Analyses, an

ANSYS Structural,

ANSYS Mechanical, or

ANSYS Multiphysics

license is required

Assembly shown here is from an Autodesk Inventor sample model

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Topics Covered

Background Information:

A. Introduction to Transient Structural Analyses

B. Preliminary Linear Dynamic Studies

C. Background Information on Nonlinear Analyses

Procedural Information:

D. Demo – Impact Problem

E. Part Specification and Meshing

F. Nonlinear Materials

G. Contact; Joints; and Springs

H. Initial Conditions

I. Loads; Supports; and Joint Conditions

J. Damping

K. Transient Structural Analysis Settings

L. Reviewing Results

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A. Introduction

• Transient structural analyses are needed to evaluate the response of

deformable bodies when inertial effects become significant.

– If inertial and damping effects can be ignored, consider performing a

linear or nonlinear static analysis instead

– If the loading is purely sinusoidal and the response is linear, a harmonic

response analysis is more efficient

– If the bodies can be assumed to be rigid and the kinematics of the system

is of interest, rigid dynamic analysis is more cost-effective

– In all other cases, transient structural analyses should be used, as it is

the most general type of dynamic analysis

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… Introduction

• In a transient structural analysis, Workbench Mechanical solves the

general equation of motion:

Some points of interest:

– Applied loads and joint conditions may be a function of time and space.

– As seen above, inertial and damping effects are now included. Hence,

the user should include density and damping in the model.

– Nonlinear effects, such as geometric, material, and/or contact

nonlinearities, are included by updating the stiffness matrix.

tFxxKxCxM

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… Introduction

• Transient structural analysis encompasses static structural analysis

and rigid dynamic analysis, and it allows for all types of Connections,

Loads, and Supports.

• However, one of the important considerations of performing transient

structural analysis is the time step size:

– The time step should be small enough to correctly describe the time-

varying loads

– The time step size controls the accuracy of capturing the dynamic

response. Hence, running a preliminary modal analysis is suggested in

Section B.

– The time step size also controls the accuracy and convergence behavior

of nonlinear systems. Background information on the Newton-Raphson

method is presented in Section C.

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B. Preliminary Modal Analysis

• While transient structural analyses use automatic time-stepping,

proper selection of the initial, minimum, and maximum time steps is

important to represent the dynamic response accurately:

– Unlike rigid dynamic analyses which use explicit time integration,

transient structural analyses use implicit time integration. Hence, the

time steps are usually larger for transient structural analyses

– The dynamic response can be thought of as various mode shapes of the

structure being excited by a loading. The initial time step should be

based on the modes (or frequency content) of the system.

– It is recommended to use automatic time-stepping (default):

• The maximum time step can be chosen based on accuracy concerns. This

value can be defined as the same or slightly larger than the initial time step

• The minimum time step can be input to prevent Workbench Mechanical from

solving indefinitely. This minimum time step can be input as 1/100 or 1/1000 of

the initial time step

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… Preliminary Modal Analysis

• A general suggestion for selection of the initial time step is to use the

following equation:

where fresponse is the frequency of the highest mode of interest

• In order to determine the highest mode of interest, a preliminary

modal analysis should be performed prior to the transient structural

analysis

– In this way, the user can determine what the mode shapes of the

structure are (i.e., how the structure may respond dynamically)

– The user can also then determine the value of fresponse

response

initialf

t20

1

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… Preliminary Modal Analysis

Points of Consideration:

• The automatic time-stepping algorithm will increase or decrease the

size of the time step during the course of the analysis based on the

calculated response frequency.

– Automatic time-stepping algorithm still relies on reasonable values of

initial, minimum, and maximum time steps

– If the minimum time step is being used, that may indicate that the initial

time step size was too large. The user can plot the time step size by

selecting “Solution Output: Time Increment” from the Details view of the

Solution Information branch

• When performing a modal analysis to determine an appropriate

response frequency value, it is not sufficient to request a certain

number of modes, then to use the maximum frequency. It is a good

idea to examine the various mode shapes to determine which

frequency may be the highest mode of interest contributing to the

response of the structure.

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C. Including Nonlinearities

• There are several sources of nonlinear behavior, and a transient

structural analysis may often include nonlinearities:

– Geometric nonlinearities: If a structure

experiences large deformations, its

changing geometric configuration can

cause nonlinear behavior.

– Material nonlinearities: A nonlinear stress-strain

relationship, such as metal plasticity shown on

the right, is another source of nonlinearities.

– Contact: Include effects of contact is a type

of “changing status” nonlinearity, where an

abrupt change in stiffness may occur when

bodies come in or out of contact with each other.

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… Including Nonlinearities

• In a linear analysis, the applied force F and

displacement x of the system are related such

that doubling the force would double the

displacement, stresses, and strains

– This assumes that the change in the original and

final deformed shapes is negligible since the same

stiffness matrix [K] is used

• In a nonlinear analysis, the relationship between

the applied force F and displacement x is not

known beforehand

– As the geometry undergoes deformation, so too,

does the stiffness matrix [K] change

– The Newton-Raphson method needs to be

implemented to solve nonlinear problems

K

F

x

F

x

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• Nonlinear analyses require several solution iterations:

– The actual relationship between applied load and deformation (dotted

green line below) is not known a priori

– The Newton-Raphson method, which can be thought of as a series of

linear approximations with corrections, is performed (solid blue lines)

• The load Fa is applied to the structure. Based on the new deformed shape,

internal force F1 is calculated. If Fa ≠F1 then the system is not in equilibrium. A

new stiffness matrix [K] (slope of blue line) is calculated based on the current

conditions.

• This process is repeated until Fa =Fi for iteration i, at which point the solution is

said to be converged

• Oftentimes, the applied load Fa must be

split into smaller increments in order for

convergence to occur. Hence, for a ramped

load, a smaller time step may be needed

to ensure convergence

x

Fa

1

2

34

F1

x1

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• As shown from the previous slides, the time step size will also have

an influence on nonlinear analyses:

– The time step size should be small enough to allow the Newton-Raphson

method to obtain force equilibrium (convergence)

– The user may also need to specify the initial, minimum, and maximum

timesteps based on nonlinear considerations

• Usually, the dynamic considerations for picking a time step size as

discussed in Section B is sufficient.

– Since Workbench Mechanical only uses one set of time steps, resolving

the dynamic response often provides a small enough time step to resolve

nonlinear effects as well.

– Determination of the time step size based on nonlinear considerations is

often not as straightforward as choosing the dynamic time step size.

Hence, the user may rely on automatic time-stepping algorithm to ensure

convergence and accuracy.

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• The automatic time-stepping algorithm takes into account the following nonlinear effects:

– If force equilibrium (or some other convergence criterion) is not satisfied, bisection occurs

– If an element has excessive distortion, bisection occurs

– If the maximum plastic strain increment exceeds 15%, bisection occurs

– Optional: if contact status changes abruptly, bisection occurs

• Bisection is part of the automatic time-stepping algorithm, when the solver goes back to the previously converged solution at time ti and uses a smaller time increment ti.

– Bisections provide an automated means to solve nonlinear problems more accurately or to overcome convergence difficulties.

– Note, however, that bisections result in wasted solver time since the solution returns to the previously converged solution and tries again with a smaller time step. Hence, choosing the right initial and maximum time step can minimize the number of bisections that occur

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• By default, large deformation effects and automatic time-stepping will

be active:

– The user does not need to do anything special to account for

nonlinearities.

• However, as noted before, if nonlinear effects dominate, the time step size may

be dictated by nonlinear considerations rather than dynamic concerns.

• “Large Deflection” can be toggled in the Details view of the “Analysis Settings”

branch

– If the user wants to turn on time step size checks based on contact status,

this can be done in with “Time Step Controls” in the Details view of a

given contact region.

• Using this option may decrease the time step to ensure correct momentum

transfer between parts in impact-type of situations

• Note, however, that the time step may become excessively small, so this is not

recommended in general, especially for preliminary analyses



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Procedure:

Transient

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E. Part Specification

• In a transient structural analysis, parts may be rigid or flexible:

– Under the “Geometry” branch, the “Stiffness Behavior” can be toggled

from “Flexible” to “Rigid” on a per-part basis

– Rigid and flexible parts can co-exist in the same model

• Consideration for flexible parts are the same as in static analyses:

– Specify appropriate material properties, such as density, Young’s

Modulus, and Poisson’s ratio

– Nonlinear materials, such as plasticity or hyperelasticity, can also be

included

• For rigid parts, the following apply:

– Line bodies cannot be set to rigid

– Multibody parts must have all bodies set to rigid

– Density is the only material property needed to

calculate mass properties. All other material

specifications will be ignored.

– An “Inertial Coordinate System” will automatically

be defined at the centroid of the part

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… Part Specification

• For flexible bodies, the mesh density is based on the following:

– The mesh should be fine enough to capture the mode shapes of the

structure (dynamic response)

– If stresses and strains are of interest, the mesh should be fine enough to

capture these gradients accurately

• For rigid bodies, no mesh is produced

– Rigid bodies are rigid, so no

stresses, strains, or relative

deformation is calculated.

Hence, no mesh is required

– Internally, rigid bodies are

represented as point masses

located at the center of its

“Inertial Coordinate System”


On the figure on the right, one can

see flexible bodies (meshed) and

rigid bodies (not meshed) in the

same model.

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F. Nonlinear Materials

• For flexible bodies, nonlinear materials may be defined:

– Metal plasticity:

• Define Young’s modulus and Poisson’s ratio

• Select either isotropic or kinematic hardening law and either bilinear or

multilinear representation of stress-strain curve

– For multilinear stress-strain curve, remember that values should be logarithmic plastic

strain vs. true stress

– Hyperelasticity:

• Select a hyperelastic model based on strain invariants (neo-Hookean,

Polynomial, Mooney-Rivlin, or Yeoh) or principal stretch (Ogden):

– If material constants are not known, enter test data, then select hyperelastic model on

which to perform curve-fit

– If material constants are known, select hyperelastic model and enter constants

• To account for inertial effects, density should also be defined for

both flexible and rigid bodies.

• Material damping, discussed in Section I, may also be input for

flexible bodies.

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G. Contact; Joints; Springs

• Contact, joints, or springs can be defined under the “Connections”

branch in transient structural analyses

– Contact is defined between solid and surface bodies (rigid parts must be

single body). Contact is used when parts can come in and out of contact

or if frictional effects are important.

• Nonlinear contact (rough, frictionless, frictional) may be defined for faces of

solid or surface bodies (flexible or rigid) at v12.

– Joints are defined for 3D rigid or flexible bodies only. Joints can be

defined between two bodies or from one body to ground. Joints are

meant to model mechanisms where the part(s) are connected but relative

motion is possible.

• Joints are defined faces, lines, or keypoints of 3D solid, surface, or line bodies,

both flexible and rigid.

– Springs are defined for 3D rigid or flexible bodies. Springs provide

longitudinal stiffness and damping for the scoped region(s), meant to

represent stiffness/damping effects of parts not explicitly modeled.

• Springs can be defined on vertices, edges, or faces of 3D bodies

• Defined springs cannot have zero length

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… Contact

• Contact regions can be defined between flexible bodies:

– Contact is useful when the contacting area is not known beforehand or if

the contacting area changes during the course of the analysis

– Any type of contact behavior (linear, nonlinear) can be specified,

including frictional effects

• Play Animation

In the animation, some

surfaces of two parts are

initially not in contact, but

as the analysis

progresses, the surfaces

come into contact, as

shown on the right,

allowing for forces to be

transmitted between the

two bodies.

Flexible Dynamic Analysis 3.avi

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… Contact

• In contact, parts are prevented from penetrating into each other. The

different type of contact describe behavior in the separation and

sliding directions:

Normal Direction Tangential Direction

Contact Type Separate Slide

Bonded no no

No Separation no yes

Rough yes no

Frictionless yes yes

Frictional yes yes (when Ft≥mN)

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… Contact

• Different contact formulations allow for establishing the mathematical

relationship between contacting solid bodies:

– For bonded and no separation contact, the contacting areas are known

beforehand based on the geometry and pinball region

• The recommended contact formulation to use is either “Pure Penalty” (default)

or “MPC”

– For rough, frictionless, and frictional contact,

the actual contacting areas are not known

a priori, so an iterative approach is required

• The recommended contact formulation to use

is “Augmented Lagrange”

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… Joints

• Joints can be defined between bodies or from a body to ground:

– Joints define the allowed motion (kinematic constraint) on surface(s)

– Various types of joints can be defined for flexible or rigid bodies:

• Fixed, Revolute, Cylindrical, Translational, Slot, Universal, Spherical, Planar,

or General Joints

– Definition and configuration of joints is covered in a separate training

course named “ANSYS Rigid and Flexible Dynamic Analysis”.

– Unlike rigid dynamic analysis, the actual – not relative – degrees of

freedom are specified.

The animation on the right shows

an assembly using cylindrical and

revolute joints


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… Joints

• In transient structural analyses, the user has an additional option of

specifying the behavior of the joint:

– “Rigid” (default) behavior means that the scoped surface(s) will not

deform but be treated as rigid surface(s). This means that a scoped

cylindrical surface will remain cylindrical throughout the analysis.

– “Deformable” behavior means that while the

joint constraint is satisfied, the scoped

surface(s) are free to deform. This means that

a scoped cylindrical surface may not remain

cylindrical throughout the analysis.

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… Springs

• Springs can be defined between bodies or from body to ground:

– Springs define the stiffness and/or damping of surface(s)

• Refer to Section I for additional details on damping

– Springs can be defined for rigid or flexible bodies

– These are longitudinal springs, so the stiffness or damping is related to

the change in length of the spring

• The spring must not have zero length

• Springs can be defined on vertices, edges, or surfaces

• Definition and configuration of springs is covered in a separate training

course named “ANSYS Rigid and Flexible Dynamic Analysis”.

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H. Initial Conditions

• For a transient structural analysis, initial displacement and initial

velocity is required:

– User can define initial conditions via “Initial Condition” branch or by

using multiple Steps

• Defining initial displacement & velocity with the

“Initial Condition” object:

– Default condition is that all bodies are at rest

• No additional action needs to be taken

– If some bodies have zero initial displacement but

non-zero constant initial velocity, this can be input

• Only bodies can be specified

• Enter constant initial velocity (Cannot specify more

than one constant velocity value with this method)

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… Initial Conditions

• Defining initial displacement & velocity by using multiple Steps:

– This technique is required for all other situations

– Leave “Initial Conditions” to “At Rest.” For “Analysis Settings,” use 2

Steps over a small time interval:

• First Step should have very small “Step End Time” in Details view. Also,

change “Time Integration: Off” and “Auto Time Stepping: Off” only for the first

Step. Modify “Define by: Substeps” with “Number of Substeps: 1”.

– Apply a “Displacement” support with appropriate values (discussed in

next slide) in Step 1. Deactivate this “Displacement” support in Step 2.

– The idea behind such a technique is that the first Step, solved over a

small time interval t1, will provide an initial displacement & velocity

based on an imposed xinitial “Displacement” support.

If the time interval t1 is small enough, the effect on the actual ending

time should be negligible.

1

1

t

xv

initialinitial

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… Initial Conditions

– Initial displacement = 0, initial velocity ≠ 0

• Ramp a very small displacement value over a small time interval to produce the

desired initial velocity. Deactivate it for Step 2.

– Initial displacement ≠ 0, initial velocity ≠ 0

• Ramp the desired initial displacement over a time interval to produce the

desired initial velocity. Deactivate it for Step 2.

– Initial displacement ≠ 0, initial velocity = 0

• Step apply the desired initial displacement over a time interval to ensure that

initial velocity is zero. Deactivate it for Step 2, if necessary.

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I. Loads; Supports; Conditions

• For rigid bodies, just as in a rigid dynamic analysis, only inertial

loads, remote loads, and joint conditions are supported.

– Rigid bodies do not deform, so structural & thermal loads do not apply

• For deformable bodies, any type of load can be used:

– Inertial and structural loads

– Structural supports

– Joint (for defined joints) and thermal conditions

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… Time-Varying Loads

• Structural loads and joint conditions can be input as time-dependent

load histories

– When adding a Load or Joint Condition, the

magnitude can be defined as a constant,

tabular value, or function.

– The values can be entered directly in the

Workbench Mechanical GUI or entered in

the Engineering Data page

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J. Damping

• As noted in Section A, the equations solved for in transient structural

analyses also include a damping term

• Since the response frequency is not known in advance of running the

simulation, are only two types of damping available:

– Viscous damping

• beta damping (optionally material-dependent) or by element damping

– Numerical damping

• See Chapter 1 for more details.

• The effect of damping is cumulative. Hence, if 2% material-

dependent beta damping and 3% global beta damping is defined, that

part will have 5% damping.

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K. Analysis Settings

• Besides damping, there are various other

options the user can set under the “Analysis

Settings” branch.

• It is important that the user specify the solution

times in the “Step Controls” section

– The “Number of Steps” controls how the load

history is divided. As noted in Section G, one

can impose initial conditions with multiple load

steps – use “Time Integration” to toggle whether

inertial effects are active for that step

– The “Step End Time” is the actual simulation

ending time for the “Current Step Number”

– The initial, minimum, and maximum timesteps

should be defined as noted in Sections B & C

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… Analysis Settings

• The “Solver Controls” section allows the user

to choose the equation solver, use of weak

springs, and use of large deflection effects

– Transient structural analyses may typically

involve large deformations, so “Large Deflection:

On” should be used (default behavior).

– “Output Controls” allows users to control how

frequently data is saved to the ANSYS result file.

For multiple step analyses, one can save results

only for the end of the step. Also, one can also

save results at intervals that are as evenly-

spaced as possible (depending on automatic

time-stepping)

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L. Reviewing Results

• After completion of the solution, reviewing transient structural

analysis results typically involves the following output:

– Contour plots and animations

– Probe plots and charts

• Generating contour plots and animations are similar to other

structural analyses

– Note that the displaced position of rigid

bodies will be shown in the contour result,

but the rigid bodies will not show any

contour result for deformation, stress, or

strain since they are rigid entities

– Typically, animations are generated using

the actual result sets, not distributed sets

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… Reviewing Results

• Probes are useful in generating time-history charts

to understand the transient response of the system.

Some useful probe results are as follows:

– Deformation, stresses, strains, velocities, accelerations

– Force and moment reactions

– Joint, spring, and bolt pretension results

• Chart objects, based on probes, can also be added

to include in reports or as independent figures

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D. Workshop – Transient Analysis

• In this workshop, you will determine the dynamic response of a

caster wheel exposed to a side impact such as hitting a curb.

WS6: Transient Analysis of a Caster Wheel

Striker

Tool

Wheel


© 2009 ANSYS, Inc. All rights reserved.WS1-1 July 2009

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ANSYS Mechanical

Dynamics

Workshop 1:

Intro (Flywheel)

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Workshop 1 – Introduction

• In this workshop, the vibration characteristics of a spinning flywheel will be

investigated.

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Workshop 1 – Project Schematic

• Drop a Static Structural system into the Project Schematic.

• In this system, the rotational velocity will be applied.

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• Drop a Modal system onto the Results cell of the Static Structural system.

• In this system, the prestressed modes will be found.

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• Drop a Harmonic Response system onto the Model cell of the Static

Structural System.

• In this system, a harmonic load will be applied to the static flywheel.

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• Import the geometry file

– Flywheel.igs

• Edit the Model cell to open the Mechanical application.

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Workshop 1 – Preprocessing

• Two coordinate systems will be added to align with the center of the shaft.

• The origin of the first coordinate system can easily be located along the shaft

axis by selecting two keypoints.

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Workshop 1 – Preprocessing

• Duplicate the first coordinate system.

– set the type of the newly-created coordinate system to Cylindrical

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Workshop 1 – Static Preprocessing

• Select the symmetry surfaces and insert a Frictionless support.

– Since the geometry is 3D, a frictionless support is the same as applying a

symmetry boundary condition.

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• Insert a Remote Displacement on the flywheel hub.

– select the coordinate system that aligns with the axis of the shaft

– fix the X Component, Z Component, and Rotation Y

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• Insert a Rotational Velocity inertial load.

– select the coordinate system that aligns with the axis of the shaft

– set the Z component to 600 RPM

• Solve the model.

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• Insert a Directional Deformation.

– set the Coordinate System to the Cylindrical Coordinate System that aligns with

the axis of the shaft

• The X-Axis orientation is now the radial component.

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Workshop 1 – Static Postprocessing

• Duplicate the Directional Deformation.

– set the Orientation to Y Axis

• This is now the tangential component of deformation.

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Workshop 1 – Static Postprocessing

• Using the cylindrical coordinate system again, insert radial and tangential

components of stress.

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Workshop 1 – Modal Postprocessing

• Move down to the Modal branch and Solve.

• Insert some total deformation plots to review the mode shapes.

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Workshop 1 – Harmonic Preprocessing

• Drag and drop the Frictionless Support and Remote Displacement from the

Static Structural branch into the Harmonic Response Branch.

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Workshop 1 – Harmonic Preprocessing

• Insert an Acceleration inertial load.

– set the Z component to 2 G (~20000 mm/s^2)

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Workshop 1 – Harmonic Solution Settings

• Modify the Analysis Settings.

– set the Range Maximum to 500 Hz

– set Cluster Results to Yes

– set Constant Damping Ratio to 5%

• Solve the model.

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Workshop 1 – Harmonic Postprocessing

• Insert a Deformation

Frequency Response

result on the outer surface

of the flywheel.

– set the Spatial Resolution

to Use Maximum

– set the Orientation to Z

Axis

• Make note of the

frequency and phase angle

at which the maximum

amplitude occurs.

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Workshop 1 – Harmonic Postprocessing

• Insert a Directional Deformation result.

– set the Orientation to Z Axis

– use the frequency and phase angle for the maximum amplitude, noted from the

previous slide (229.28 Hz @ 92.859°)



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ANSYS Mechanical

Dynamics

Workshop 2A:

Modal Analysis

(Plate with a Hole)

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Workshop 2A - Goals

• Our goal is to determine the first 10 natural frequencies and mode

shapes for the plate with the hole shown.

• The plate is made of Aluminum.

• Assume the plate is fully constrained at the hole.

– As if the plate is tightly bolted down at the hole.

Fixed Center

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Workshop 2A – Project Schematic

• From the project schematic, insert a

new Modal system.

• Import the Geometry file

– plate.iges

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Workshop 2A - Preprocessing

• Edit the Engineering Data cell.

– add Aluminum Alloy from the General Materials library to Engineering Data

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• Return to the Project, and Edit the Model cell to open the Mechanical

application.

– set the plate thickness to 0.1 in

– set the plate material assignment to Aluminum Alloy

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Workshop 2A - Environment

• Constrain the center hole.

– highlight the Modal Branch to >Insert>Fixed Supports.

• Switch to edge selection mode as necessary

• Use Box Select, or drag single-select LMB around the hole to pick all

applicable edge segments (4 edges)..

– Click “Apply” in the Details window

– Reorient model as necessary throughout.

9

8

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Workshop 2A – Modal Solution

• Check the Details of Modal

Analysis Settings.

– set Max Modes to Find to 10

– set Calculate Stress “Yes”

– set Calculate Strain “Yes”

• If you just want frequencies and

shapes, you don’t need to

“calculate” stress or strain. It will

save a little time to skip those

calculations.

• Solve the Modal analysis.

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Workshop 2A - Results

• After the modal solution is completed, review the modal shapes for each

frequency.

• Click on the Modal Solution Branch in the Tree. Then LMB on the top of the

Frequency Column in the “Tabular Data” region, and >RMB>Create Mode

Shape Results

– This will automatically insert “Total Deformation” objects in the Tree for all modes

solved.

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• To get an overall view of the Modal results step thru (LMB) the Total

Deformation result objects for each mode.

– You can also Animate (Play & Stop) the mode from the Timeline window.

– Note: Make a note of your highest natural Frequency mode:

• Max Indicated Freq = _________________Hz.

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Workshop 2A - Comments

• Remember:

– Displacements reported with mode shapes are “relative” and do not reflect the actual max magnitudes of the displacements.

• The actual magnitudes will depend on the energy input to the system (depends on forcing function).

• Sometimes it is challenging to visualize the true mode shape from a simple contour plot.

– Try the Vector Display instead.

• Adjust the Vector Scale slider as desired.

• You can also animate the vector plot too.

Contour

Plot.

Difficult to

determine

deformation

directions

Vector

Plot

Arrows may

be more

intuitive in

some cases.



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ANSYS Mechanical

Dynamics

Workshop 2B:

Modal Analysis

(Model Airplane Wing)

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Workshop 2B - Goals

• Our goal is to determine the first 5 natural frequencies and mode

shapes for the prestressed model airplane wing shown.

• Assume one end of the wing is fully fixed.

• The wing is made of Titanium.

Fixed End

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Workshop 2B – Project Schematic


new Static Structural system.

• Drop a Modal system onto the

Solution cell of the Static Structural.


– wing.iges

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Workshop 2B - Preprocessing

• Edit the Engineering Data cell.

– add Titanium Alloy from the General Materials library to Engineering Data

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Workshop 2B - Preprocessing

• Return to the Project, and Edit the Model cell to open the Mechanical

application.

– set the wing material assignment to Titanium Alloy

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Workshop 2B - Environment

• Constrain the far end of the wing.

– On the >Static Structural branch >Insert>Fixed Supports.

– Switch to face selection mode as necessary

– Use LMB to pick the applicable surface.


– Use “Depth Picking” and/or reorient the model as necessary throughout.

Depth

Picking

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Workshop 2B - Environment

• Apply a pressure load to the underside of the wing.

– On the >Static Structural branch >Insert>Pressure.

– Switch to face selection mode as necessary

– Use LMB to pick the applicable surface.


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Workshop 2B – Static Solution

• Solve the Static Structural model.

• Review the results.

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Workshop 2B – Modal Solution

• Check the Details of Modal Analysis Settings

– set Max Modes to Find to 5

– set Calculate Stress to “Yes”

– set Calculate Strain to “Yes”


5

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Workshop 2B - Results

• After the modal solution is completed we’d like to review the modal

shapes for each frequency.

• Click on the Modal Solution Branch in the Tree. Then LMB on the top

of the Frequency Column in the “Tabular Data” region, and

>RMB>Create Mode Shape Results

– This will automatically insert “Total Deformation” objects in the Tree for

all modes solved.

13

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Workshop 2B - Results

• To get an overall view of the Modal results step thru (LMB) the Total

Deformation result objects for each mode.

– Remember to Animate (Play & Stop) the mode from the Timeline

window.

• You can typically rotate the model during animation too.

– Note: Make a note of your highest natural Frequency mode:

• Max Indicated Freq = _________________Hz.

• Experiment with the Vector Graphics and (vector) scale slider.

Animation and rotation can also be performed on Vector plots.



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ANSYS Mechanical

Dynamics

Workshop 3:

Harmonic Response

(Fixed-Fixed Beam)

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Workshop 3 - Goals

• Our goal is to determine the harmonic response of a fixed-fixed beam

under the influence of two harmonic forces.

– The forces represent rotating machines mounted at the “one-third” points

along the beam.

– The machines rotate at 300 to 1800 RPM.

• The Beam (3 m x 0.5 m x 25 mm) is made of Steel.

Constrain (Fix)

Both Ends

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new Modal system.

– we will first look at the natural

frequencies and mode shapes of the

system

• Drop a Harmonic Response system

onto the Model cell of the Modal

system to share the material

properties, geometry, and mesh.

– note that this system will not use

the modes from the Modal system


– beam.agdb

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Workshop 3 - Preprocessing


– verify that the material assignment is Structural Steel

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Workshop 3 - Environment

• Constrain both ends of the Beam.

– Click on the Modal Branch and >Insert>Fixed Support.

– Switch to edge selection mode as necessary

– Use LMB to pick the two applicable edges.

– Hold <CTRL> to add to your selections


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Workshop 3 – Modal Results


• Create some Mode Shape Results to review the results.

– note that modes 1 and 2 fall between 0 and 50 Hz

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• Drag and drop the Fixed Support

from the Modal branch to the

Harmonic Response branch.

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• In the Harmonic Response branch, apply one force to one edge.

– There are two edges imprinted on the beam face.

– Switch to Edge selection mode as necessary and >Insert>Force.

– Use LMB and drag over surface to highlight to pick the applicable edge.


– In Details, change the “Defined By” to “Components” (i.e., XYZ).

– Enter 250 for “Y”. Leave Phase Angle = 0

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• Apply another force to the other edge.

– set Y Component to 250 N

– leave Phase Angle = 0

– We will investigate the results as the phase angle between these loads

changes.

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Workshop 3 – Harmonic Response Solution

• Edit the Analysis Settings.

– set the Range Minimum to 0 Hz

– set the Range Maximum to 50 Hz

– set the Solution Intervals to 50

– set the Constant Damping Ratio to 2%

• Solve the Harmonic analysis.

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Workshop 3 – Results

• Insert a Deformation Frequency Response.

– set the scoping to all faces on the beam

– set the Spatial Resolution to Use Maximum

– set the Orientation to Y Axis

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Workshop 3 - Results

• You can also plot contours at specific frequencies.

• Click RMB on the solution object and >Insert>

Stress, Strain, or Deformation

– This will insert the result object(s)

– Step thru the Details for each and specify the

Geometry and other details.

– It is necessary to specify a specific frequency and

phase angle.

Contours at a specific

Frequency

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• Return to the second harmonic force applied.

– set the Phase Angle to 90° (we will try to excite different modes)

– resolve the Harmonic Response

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• Return once more to the second harmonic force applied.

– set the Phase Angle to 180°

– resolve the Harmonic Response



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ANSYS Mechanical

Dynamics

Workshop 4:

Response Spectrum

(Suspension Bridge)

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Workshop 4 - Goals

• Our goal is to determine the response of a prestressed suspension

bridge subjected to a seismic load.

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• From the project schematic, insert a new Static Structural system.

• Drop a Modal system onto the Solution cell of the Static Structural system.

• Drop a Response Spectrum system onto the Solution cell of the Modal

system.


– simple_bridge.agdb

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Workshop 4 - Project Schematic

• Right click on Geometry, choose

Properties, then check Line Bodies

under Basic Geometry Options.

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Workshop 4 - Project Schematic


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• Insert a fixed support on the vertex of all four tower foundations.

– the Modal and Response Spectrum systems will inherit this support

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• Insert a zero-displacement constraint in the Y and Z directions on the

three outer edges at both ends of the bridge deck.

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• Finally, insert Standard Earth Gravity from the Inertial loads toolbar

button.

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Workshop 4 – Modal Solution

• Change the Max Modes to Find to 10, then run the Modal solution.

– verify in Solution Information that a significant portion of the total mass

has been accounted for

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• Insert an RS Acceleration load in the Response Spectrum branch.

Then, change Boundary Condition to All BC Supports and Direction

to Y Axis.

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• Open the supplied seismic data from the Savannah River Earthquake,

copy the spectrum data, and paste it into the Tabular Data.

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Workshop 4 - Results

– Finally, run the solution and insert the result item of your choice.

– Note that the bridge deck may need some mesh refinement. Try changing the mesh settings and re-solving.

• Since the seismic data were supplied in units of G acceleration, insert a

Scale Factor equal to the acceleration due to gravity of the working units.



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ANSYS Mechanical

Dynamics

Workshop 5A:

Random Vibration

(Girder Assembly)

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Workshop 5A - Goals

• Our goal is to investigate the

vibration characteristics of a Girder

Assembly.

• In this workshop, we will examine

the displacements and stresses in a

steel assembly due to an

acceleration spectrum.

• A PSD spectrum can be specified

via Acceleration, Velocity, or

Displacement.

– The spectrum will typically be

measured during physical tests or

documented in a written

specification relating to the system

or component.

– The data points can be entered for

each Freq & Amplitude, or a function

can be entered.

Accele

ration

Frequency

F1 F2 F3 F4

A2 A3

A4

A1

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new Modal system.

• Drop a Random Vibration system

onto the Solution cell of the Modal

system.


– girder.agdb

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Workshop 5A – Preprocessing Thickness

• The first preprocessing task is to

specify the thickness of all the

surfaces.

• Select all the bodies to assign a

uniform thickness

– LMB to select the top Body in the

Part list.

– Hold <shift> and LMB on the last

Surface Body.

• Note: By highlighting “all”, we can

set the thickness on the first one, and

the same thickness gets assigned to

all of them.

– Left click in the thickness field and

set the Thickness = 0.5 in

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Workshop 5A – Preprocessing Mesh Size

• The assembly consists of multiple

slender bodies plus a large flat Roof

plate.

• We want to specify a relatively fine

mesh size on the slender members

but a larger element up top.

– select the roof body

– Mesh >Insert >Sizing

– set Element Size to 2 in

– select all other bodies

– Mesh >Insert >Sizing

– set Element Size to 4 in

• Preview the mesh,

>Mesh>Generate Mesh

– If desired, repeat the steps above to

increase or decrease element sizes

as desired to enhance the model or

reduce CPU time.

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• For the lower edges of the truss,

highlight the “Modal” branch in

the Outline and >Insert >Fixed

Supports.

• Switch to edge selection mode

as necessary

– Reorient model as necessary

throughout.

– Using the “Extend to Limits”

feature is probably the most

convenient.

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• For the PSD Base Excitation loads,

at the Random Vibration Branch,

>Insert>PSD Acceleration

– set Boundary Condition to Fixed

Support

– this is a reference to the Fixed

Support in the modal Branch

Accele

ration

Frequency

F1 F2 F3 F4

A2 A3

A4

A1

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Workshop 5A – PSD Loads

• Enter the following tabular data for the PSD Acceleration load

Frequency [Hz] Acceleration [(in/s^2)^2/Hz]

5 150

20 200

30 200

45 100

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Workshop 5A – Modal Results

• After the solution is completed you can review the (precursor) modal shapes for each frequency.

– In the Outline Tree pertaining to Modal, click on Solution (within the Modal branch)

– Click on the Modal Solution Branch in the Tree. Then LMB on the top of the Frequency Column in the “Tabular Data” region, and >RMB>Create Mode Shape Results

– This will insert “Total Deformation” objects in the Tree for all modes solved.

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Workshop 5A – Random Vibration Results

• Now review Random Vibration

results.

• Due to the applied spectrum, you

can >Insert

– Deformations

– Strains

– Stresses

• >Insert>Deformation>Directional

– Specify the Z “Orientation”

direction in the Details Pane

• >Insert>Strain>Normal

– For instance, specify Y

“Orientation” in the Details Pane

• >Insert>Stress>Equivalent (von

Mises)

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Workshop 5A - Comments

• Review the evaluated results.

• Remember:

– Modal displacements reported

with mode shapes are

“relative” and do not reflect

the actual max magnitudes of

the displacements.

– The PSD simulation generates

statistically “Probable”

resultant magnitudes that

depend on the energy input

magnitude and spectrum

applied to the system.

• The Damping data also plays a

roll in the magnitude of the

response.



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ANSYS Mechanical

Dynamics

Workshop 6A:

Transient

(Caster Wheel Test)

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Workshop 6A - Goals

• Our goal is to determine the

dynamic response of a caster wheel

exposed to a side impact such as

hitting a curb.

• This may be simulated in a physical

test by dropping a heavy Striker

Tool on the side of the wheel.

– The dropped weight represents side

impact on the wheel.

• The Wheel and Striker Tool are

made of Steel.

– Assume the far face of the

Wheel/Axle is constrained.

– Assume the sides of the Striker are

constrained to slide up and down

vertical rails.

– Assume a damping ratio of 0.02 (i.e.

2%)Constrain End

Striker

Tool

Wheel

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new Transient Structural system.


– caster_test2.agdb

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– verify that the material assignment is Structural Steel

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• Suppress the upper Striker.

– Expand the geometry Branch, and

determine which part is the upper

Striker. >RMB>Suppress Body

• We will incorporate the lower Striker

in the simulation only.

• We will apply an initial velocity to the

lower Striker to account for it’s

momentum due to the drop height &

force.

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• Define the contact between the

bottom of the Striker Tool and the

top Edge of the Caster Wheel

– LMB on >Connections in the

Outline Tree.

– >Insert>Manual Contact Region

– Use Face select

– Change “Update Stiffness” to “Each

Equilibrium Iteration”

8

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• Apply constraints on the end

of the bore to oppose loads on

the wheel.

– Within the Flexible Dynamic

Branch >Insert>Fixed

Support

– Use Face Select, LMB and

pick four annular surfaces on

the bottom of the axle hole.

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• The Striker Tool is guided on rails

so it can only travel up and down

when dropped on the wheel.

– >Insert>Frictionless Support

– Use LMB and pick all four sides of

the Striker Tool block.

– Note: The “four sides” of the block

may consist of more than “four”

total faces depending on how the

(CAD) geometry was originally

generated.

a Face

a Face

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• Apply a gravity inertial load

– RMB >Insert>Standard Earth

Gravity to account for weight

(mass) and to accelerate the

Striker downward towards the

Wheel.

– In the Details window, change

the Direction in this case to +X

(look at the XYZ Triad to

understand global orientation)

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• Apply an initial velocity on the Striker.

– Change “At Rest” to “Constant Velocity”

– Use Body Select and pick and >Apply the Striker Part.

– Change the Direction “Defined By” to “Components”

– Enter 10 m/s for “X”

– initial velocity is assigned to the picked Striker but not

the Caster Wheel

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Workshop 6A – Solution Settings

• Check on >Analysis Settings in the

Outline Tree

– define the analysis settings in the

“time domain”

– Verify “1” for Number of Steps

– Verify “1” for Current Step Number

– Verify “0.001” for Step end time

– Enter “0.0001” for Initial Time Step

– Enter “3e-5” for Minimum Time Step

– Enter “2e-4” for Maximum Time Step

• Solve the Transient analysis.

…it may take some hand calculations and/or

trial & error to find values that are appropriate

for the scale and severity of your non-linear

problem.

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• After the Solution is completed review the results.

• Very important in many problems like this…

– Set Result Scale to “ 1.0 (True Scale) “

• >Insert additional solution objects of interest

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• To get an overall view of the

Dynamic (transient) results step

thru the TimeLine for each result

plot of interest.

– Evaluate any objects that have lost

their Green Checkmark (possibly

because the Display time has

changed due to changes in the

Timeline.

– Remember to Animate (Play &

Stop) the mode from the Timeline

window.

• You can typically rotate the model

during animation too. If time permits, make a note of your results, and

>Insert>Sizing (at the mesh object in the outline)

and enter a smaller “Element Size” (refer to the

Graphics Ruler). Then >Solve again and compare

results.

Documents

ANSYS Workbench 12官方中文培训教程--Dynamic动力学模块教程及实例