RecentDevelopmentsinExternalAcous5cModelsforFlexibleUnderwaterVehicleDynamics**

K.C.Park,Professor WCUVisi5ngProfessor DepartmentofAerospaceEngineering DivisionofOceanSystemsEngineeringSciences, SchoolofMechanicalEngineeringUniversityofColorado KAISTBoulder,CO,USA,and Daejeon,Korea

**Joint Collaborations with Moonseok Lee, Youn-Sik Park and Youngjin Park Center for Noise and Vibration Control Department of Mechanical Engineering KAIST Daejeon, Korea 305-701.

JointKAIST‐UniversityofTokyoWorkshoponOceanSystemsEngineering,Kashiwa,Japan.16October2009

Essentials in Developing New Technologies or Advancing Existing Technologies

1.  Articulate Technology Needs (e.g., Floating City);

2.  Identify Present and Future Expected Customers;

3.  Survey Pillar Technology Base and Match with Existing Ones;

4.  Identify New Technology Needs, and Existing Technologies that need to be significantly improved;

5.  Prioritize Research Needs and Match with Manpower Needs.

University Roles for New Technology Development They say students do not learn much in university; yet it is where a student

experiences profound transformation in terms of maturity and career readiness.

1.  Base Research (or Basic Research) and Professional Manpower;

2.  However, university is a self-surviving entity; it wishes that industry would depend on university for technology innovation, expert professional production, even patents to utilize…

3.  Within university community, each campus must compete for talents (faculty and students recruits) and resources (funds).

My Personal Preference/Goals as a Professor

1. Educate both undergraduate and graduate students;

1.  Conduct Basic Research, in particular: 1.  Analysis methods developments – FEM, transient algorithms, etc; 2.  New modeling theory – acoustic-structure interaction models (Today’s talk); 3.  Multiphysics simulation, system identification, etc.

2.  Conduct Engineering Analysis such as: 1.  Space rendezvous dynamics and control; 2.  Underwater vehicle dynamics; 3.  Shell structures and membranous reflectors 4.  Containment vessels health monitoring 5.  MEMS resonators and Gyroscope performance 6.  Health monitoring of structures 7.  Contact-impact problems .. ..

My Past Activities

Past Activities: Transient analysis methods (direct time integration) Helicopter and general aviation crashworthiness Shell finite elements Computational methods for fluid-structure interactions Large space structures and control Space construction and space rendezvous dynamics Partitioned analysis methods for coupled-field problems Multi-body dynamics and space assembly Structural system identification and damage detection Contact-impact mechanics

My Current Activities

Current Activities: Multi-physics dynamics and computational methods Health monitoring of structural systems MEMS Gyroscopes for space applications Membranous structures for solar sails and reflectors Hilbert-Huang transform for nonlinear dynamics Loose coupling of tightly coupled multi-physics problems via partitioned analysis procedures.

BackgroundinToday’sTalk

1.  Today’stalkisconsideredasanewtheoryasopposedtoimprovingexis5ngtheories;

2.  ItwasatestcaseinthatIhaveconsistentlyadvocatedthatmoreKAISTengineeringthesesshouldtakeondevelopingnewmethodologies,newtheoriesandnewmodelinginsteadofimprovingexis5ngengineeringtools;

3.  IthasbeencarriedoutatKAISTduringthepastfouryearsbyDr.MoonseokLeeashisPhDthesis;

4.  Iamhopingthatyouwouldgetaglimpseofwhatittakestotakeonresearchthatrequiresriskandopen‐ended5mecommitment...

MyObjec5vesasWCU‐OSEFacultyMember

• First,workwithstudents!

• AssistOSEfacultytopromote‘basicresearch’emphasis;

• Byengagingintheabovetwoac5vi5es,helpthemwritefundamentalpapersthatwillbecitedbyothersinyearstocome(outofmanypapers,Iamsure).

• Inotherwords,Iamintenselyacademicallyoriented.Butthenbewareof‘맑은 물엔 고기가 크게 자라지 않습니다.’

• IamanAmericanandweAmericansbelieveinpursuitofhappiness!Hence,Iwillenjoydoingtheaboveac5vi5es.

BackgroundinToday’sTalk–Cont’d

Classifica5onofFluid‐StructureInterac5ons

• Waves(e.g.,hurricanes)bombardingthestructures

• LiquidSloshinginContainerCompartment

• IntensePressureOrigina5ngfromTsunamiandExplosions–Today’sTopics

Waves(e.g.,hurricanes&NorthSea)bombardingthestructures(Height:10‐25mandPeriod:10‐15seconds,speedofwave∼ 1-5 /s)

LiquidSloshinginContainerCompartment

Today’sTopics:IntensePressureOrigina5ngfromTsunamiand/orExplosions(wavespeed~1450m/s)

AlsoapplicabletoSurfaceShipsandFloa5ngLargeStructures

Whysimula5onandwhynotrealexperiments?

• Abicyclecanbetestednotonlyforpartsbutthewholebicycle;

• Acarcanbecrash‐tested,althoughexpensive.Evenforcars,simula5onusingcomponenttestdatasavescostandexpeditefromdesigntomarketturnaround.

• Totestanairplaneforitscrashlandingsafety?Noway!Tooexpensiveand5meconsuming.

• Howaboutsatellites?Howaboutasubmarine?Howaboutalargefloa5ngstructuressuchasoil/gasdrillingplajorms?

Acous5c‐StructureInterac5onProblemsinOceanEngineering

SonarDetec5onProblem:Sendpressurewavesandmeasurethescakered(return)pressure.Byanalyzingthescakeredpressure,onecaniden5fytheloca5on,theshapeandthespeedbywhichtheshiporsubmarineismoving.

DynamicResponseofSurfaceandUnderwaterShips:Vibra5onandvulnerabilityofvehiclessubjectedtointensepressurewaves(ProfessorYoungShinisanexpertinthisfield).Allfutureoceaninfrasystemsmustwithstandhos5leakacksaswellastsunamishockwaves.

Aren’tThereTheoriesAvailabletoModelDynamicsofAcous5c‐StructureInterac5ons?

Atpresent,weusetwoseparatemodelingtechniques:

a. Variousacous5c‐rigidscakeringmodelforunderwaterdetec5on

b.  Acous5c‐flexibleinterac5onmodelforstructuralresponse

Objec5veofPresentResearch:

Developonemodelthatisapplicablebothtoacous5cscakeringandflexiblestructuraldynamicsresponse.

ShockAnalysis

RelatedLiterature:

Baker and Copson(1949): My favorite theoretical text

G. Carrier(1951): Cylindrical shells excited by incident waves

JungerandFeit(1950s):soundscakeringbythinelas5cshells

MindlinandBleich(1953):Perhapsthefirstplanewaveapproxima5on

Huang(1969):Asuccessfulsolu5onofretardedpoten5alforasphere

Geers (1978): The seminal paper on doubly asymptotic approximation (DAA)

Felippa (1980): A systematic derivation for early-time response

Geers and Felippa (1983): Application of DAA to vibration problems

Astley et al (1998): Wave envelope elements that treats the scattering in addition to radiation in applying retarded potential.

TwoViewsonExternalAcous5c‐StructureInterac5ons

• Solvethewaveequa5onwithapproximateinfiniteradia5onboundarycondi5ons;

• ApproximateKirchhoff’sretardedpoten5althatproperlyincorporatestheinfiniteradia5onboundarycondi5ons.

• Thereare,ofcourse,ahostofapproachesthattrytoexploitthedesirablefeaturesofthetwoviews.

Mo5va5onsforPresentStudy

Whentheprimaryinterestistoobtainstructuralresponsearisingfromexternalacous5c‐structuralinterac5ons,exis5ngDAA(DoublyAsympto5cApproxima5on;Geers,1978)modelsseemadequate;

However,whenoneisinterestedintheacous5cfield,e.g.,foriden5fica5onofsoundsources,exis5ngDAAsareconsideredinadequate,primarilyduetoitsinconsistentimpulseresponsecharacteris5cs.

Inaddi5on,DAAsareobtainedviaanimpedancematchingprocedurebetweenearly‐5meandlate‐5meapproxima5ons.Newapproxima5onswithoutresor5ngtoimpedancematchingshouldbeatleastintellectuallypleasing!

Mo5va5onsforPresentStudy‐con5nued

Formodeldetermina5onthroughsystemiden5fica5on,oneassumesthesystemmodelintermsofdiscreteeventequa5onasInternaldynamics:x(n+1)=Axn+BunMeasureoutput:yn=Cxn+Dun

Systemiden5fica5onistoobtain(A,B,C,D)withgiveninput(un)andmeasuredoutput(yn)

Kirchhoff’sretardedpoten5al(aswillbeshownshortly)doesnotrendtothisstandardsystemiden5fica5onmodel!

Hence,ahigh‐fidelityordinarydifferen5alacous5cmodelisneeded.

(Whysphericalwaves?)‐Thatishowwavespropagatesinhomogeneousmedium.

(adoptedinexis5ngmodels)

(viafilteringconcept)

Theore5calFounda5onforPresentApproxima5ons

Seriesexpansionoftheretardedoperator,

where

in

hasbeenresponsibleforunstableformunlessamodifica5onisincorporated.

Possiblestabiliza5on:Employadvancedpoten5al!

TheRoleofAdvancedPoten5alinComputa5onalContext

Physically,whiletheretardedoperator(RO)istoforeseethewavefront,theadvancedoperator(AO)looksbackthewavefront.

Hence,computa5onallyROisapredictorwhileAOisabackwardinterpolator,henceastableoperator.

WaveFront,Time=t

AdvancedWaveFront,=me=t+r/c

RetardedWaveFront,=me=t–r/c

Time(t)

GeometricalInterpreta5onofRetardedandAdvancedWaves

(Itisabackwardinterpola5on.Hence,generallystabletocompute)

(Itisaforwardextrapola5on.Hence,generallyunstabletocompute!)

KeyIdeaforPresentApproxima5ons

Observa5onsonthePresentBasicApproxima5on

ThefactthatsR/c<1impliesthattheapproxima5onisaccurateforlate‐5meresponseduetotheinherentpropertyoftheFinalValueTheoremoftheLaplaceTransform.

Observethatandaretransientterms,hencedomina5ngearly‐5meresponses.

Hence,thesetermswouldnotbeaccuratewiththeexpansionrestric5onofsR/c<1.

Modifica5onsforTransientorEarly‐TimeResponse

(a)ConsistencyforImpulseResponsecomparedwithanaly5calsolu5ons;

(b)Incorpora5onofclassicalresultswhereinearly‐5meresponseisdominatedbyplanewaves;

Theprecedingrequirementsaremetfortuitouslyifoneapproximatesinthefollowingterms

byreplacingwith

ImpulseResponseConsistency

Presentmodelsa5sfiestheearly‐5meconsistencyindependentofthechoiceoftheweigh5ngparameter,χ

Determina5onofWeigh5ngParameter,χ

1.  Plotthecharacteris5crootsoftheexactanaly5calsolu5onforasphere

2.Assumeχ inthefollowingform:

Anddeterminethebestfiungconstants,

Analy5calPressureCharacteris5cRootLociforaSphere

Determina5onofWeigh5ngParametricMatrix,χ

• Itspecializestothemodalformofχnwhenappliedtosphericalgeometries

• Itshouldberobustwithrespecttocomputa5onalerrorsforgeneralgeometries

Ageneralmatrixformofχthatsa5sfiestheaboverequirementsisfoundtobe

ThecaseofS=0issymbolicallyequivalenttoDAA2withcurvatureCorrec5onwhichisfoundtobepronetoinstabilityforn=0mode.

•  Proposedmodalequa=onsandDAA2withcurvature

correc=on

0n =

Modelparameterselec5on

0n >

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1=C. 1=@. 1=4. 1=:. 1=6.1=<.

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Proposed model curvature DAA2 2

0 0[ 1] [ 1]s p s s u+ = +

2[ (1 ) ( 1)] [ ]n ns n s n n p s s n u+ + + + = +

20 0[ 1]s s p s u+ =

ComparisonofAnaly5calandPresentPrincipal

Rootswithχ-1 n=n,χ-1 0=1

ComputerImplementa5onofInterac5onProblems

Problemsthatcanbetreatedbythepresentmodels

GoverningInterac5onEqua5ons

Applica5on

BenchmarkTest:elas5cspheresubjectedtoIncidentacous5cexcita5ons

•  Transientresponsesofasubmergedsphericalshellexcitedbycosine‐typeimpulsepressure–  Asphericalshellsurroundedwithfluidmedium.–  Inwatermedium–  h/a=0.01,ρs/ρ=7.7,cs/c=3.7

O

h , ,sE vρ

cos ( )Ip tθδ= −

r v w

a

θP

Q

PQR

NumericalSimula5on

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

3.5

4

Tc/a

I

n

c

i

d

e

n

t

P

r

e

s

s

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PI =7! -1/2Exp[72(t-0.5)]

simula5on

simula5on

Conclusions

 Astableapproximatemodelforexternalacous5candstructuralinterac5onproblemshasbeenderivedbyemployingacombina5onofretardedandadvancedpoten5als.

 Themaximumorderof“regular”approxima5onisfoundtobetwo.

 Thepresentapproximatemodelisconsistentwithrespecttoimpulseresponse,importantforinverseiden5fica5onastheFrequencyResponseFunc5onsareinfactthe5me‐domaincounterpartofimpulseresponsefunc5ons.

 Itremainstoassessthepresentapproxima5onsasappliedtomorerealis5cproblems.