State space boundary element–finite element coupling for fluid–structure interaction analysis

Abstract

State space coupling is a new approach for handling computational fluid–structure interaction problems in the low to medium frequency range. The method is based on standard boundary element (BEM) and finite element (FEM) discretizations of the acoustic and structural domains, respectively. The implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion. Once expanded, the acoustic energy of the fluid is directly coupled to that of the structure via Hamilton’s principle. The coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem. Solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid-loaded structure. Biorthogonality properties of the state space eigensystem allow for an uncoupled, modal solution of the forced problem. Results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach.