INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR Date 25/04/2011 FN Time 3 Hrs Full Marks: 50 No. of Students:23 Spring Semester, 2010-2011 Deptt. Ocean Engineering and Naval Architecture Sub. No. NA60014 Subject Name: Hydroelasticity S'h Year Dual Degree, 3rd/4'h Year B.Tech.

Instruction: Answer any six questions. All questions are of equal marks.

1. (a) Consider the case an elastic beam of length L having both the ends free. Determine the natural frequency and mode shapes for the free beam. Give an example of such a structure in Ocean engmeenng. (b) Find the basic differences among rigid structures, porous structures, flexible structures, membrane structures and the related edge conditions.

2. (a) Discuss the differences between the mathematical formulation of a tlexible horizontal membrane and flexible vertical membrane of finite length 1 submerged in water of finite depth h. Describe physical examples with application of such type of structures in Ocean Engineering. (b) Provide a one dimensional mathematical model for a floating fishing cage assuming that the cage is a partially submerged porous membrane.

3. (a) Outline the major considerations in the design of a very large flexible floating structure. Discuss the basic differences between a ponton type VLFS and a semi-submersible type VLFS. (b) Provide an overview on very large floating structures and discuss various phases of design and installation of such structures.

4. Describe the problem of initial impulse on a floating elastic plate in water of infinite depth. Find the method to determine the structural deflection for large time and space i.e., as x ~ oo and t ~ oo.

5. Using the hydroelastic analysis (from the dispersion relation associated with flexural gravity waves), derive the critical value of the compressive force for which there will not be any flexural gravity wave propagation on a floating elastic plate. Find the criteria beyond which wave energy associated with flexural waves will propagate in the opposite direction. Relate the critical value of the compressive force with the buckling limit assuming the floating plate is on an elastic foundation.

6. Discuss the mathematical formulation and solution procedure to deal with the diffraction of water waves by a finite floating elastic plate under the shallow water approximation.

7. (a) Under the assumption of small amplitude linear shallow water wave theory, discuss one of the procedures for attenuating the deflection of a large floating elastic plate and thus discuss the mathematical formulation for the said problem. (b) Find the basic differences between the hydroelastic analysis of a ship and a VLFS.

8. Discuss the various types of loads that will be acting on a mooring line. Describe a mathematical model assuming that the mooring line can be modeled as a one-dimensional string which is having a fixed end and another spring supported end. To calculate the wave load of a mooring line, whether Hydroelastic analysis will be better compared to the use of Morison equation.