|M.Sc Student||Mar-Or Assaf|
|Subject||Finite Element Solution of Scattering Problems in Structural|
|Department||Department of Applied Mathematics||Supervisor||Professor Dan Givoli|
Fluid-structure interaction is the field that studies the mutual effect that an elastic structure and a fluid volume in contact have on each other. This problem is governed by a coupled system of equations - the elasticity equations and the equation(s) describing the behaviour of the fluid volume. The scope of this is internal structural acoustics, namely the behaviour of a system comprising of an elastic structure enclosing an acoustic fluid volume.
We begin by presenting the strong form of the general linear three-dimensional time harmonic structural acoustic problem, from which the weak formulation is then derived. Application of the finite element discretization to the weak formulation yields a finite set of linear algebraic equations - the finite element formulation for the problem.
Using a simple one dimensional problem, for which a numerical solution is constructed from the general finite element formulation, we exemplify a key issue in the numerical solution of such problems - poor performance in high wave numbers due to numerical dispersion. Harari and Hughes' Galerking/Least Squares (GLS) method, which was originally developed for the purely-acoustic case and which overcomes this difficulty, is then derived and applied to the one dimensional structural-acoustic case, greatly improving the scheme's performance.
Finally, a two dimensional coupled-membrane problem is defined and its finite element formulation is derived. Using the numerical scheme, a series of “numerical experiments” is performed and its results are compared with those of an isolated membrane. The comparison is then used to demonstrate the importance of fluid-structure coupling and its influence on the behaviour of the system's components.