ABSTRACT
In this chapter the eigenvalue analysis of acoustic fluid-structure systems encountered in acoustical cavities with flexible structure boundaries, such as a fluid-filled container or an automobile cabin enclosure, is considered. In applications involving acoustic cavities with flexible wall boundaries, the computation of the structural and cavity resonance involves solving the acoustic fluid-structure eigenproblem. Typically, the finite element method (FEM) is used to solve such fluid-structure coupled eigenproblems [178, 186]. However, when the problem size gets larger, as in the case of a structure in contact with a large extent of fluid, the finite element (FE) discretized stiffness and mass matrices of the coupled problem become very large, significantly increasing the eigenvalue computation time. In these situations, the boundary element method (BEM) becomes attractive since the discretization of the acoustic fluid domain leads to placing fluid nodes and elements only on the wetted surface of the structure, thus leading to relatively smaller size matrices for the coupled problem. However, boundary element (BE) matrices are non-symmetric; so also, are the pressure-displacement based finite element matrices even though the system sub-matrices are symmetric. Efficient methods of computing the eigenvalues and eigenvectors of non-symmetric eigenvalue problems will be presented in Chapter 11.
