An Arnoldi Based Projection Formulation for Fully Coupled Low Frequency Structural-Acoustic Analysis

A reduced order model is developed for low frequency, fully coupled, undamped and constantly damped structural acoustic analysis of interior cavities, backed by flexible structural systems. The reduced order model is obtained by applying a Galerkin projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving some essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov subspace containing moments of the original higher dimensional system. A simply supported steel plate, backed by a rigid walled cavity is used as a computational test case , and the computational gains and the accuracy obtained via implicit moment matching are compared with the direct method in ANSYS. Further, a reciprocity check is performed on the coupled system by exciting the coupled system using unit structural and acoustic excitations. It is shown that the reduced order modelling technique results in a very significant reduction in simulation time, while maintaining the desired accuracy of the state variables (displacements and pressures) under investigation.