The effect of large structural perturbations on the response of structural-acoustic systems

Abstract

Due to high sensitivity, first-order perturbation analysis of structural-acoustic systems can be inaccurate for large perturbations. Using high-order derivatives to create a Taylor series approximation for the perturbed solution can result in slow convergence or even divergence. A rational polynomial or Pade approximation may overcome the poor convergence of the Taylor series by canceling out the pole causing the poor convergence. In this study, a finite element framework is used to describe the structural-acoustic system. External radiation and scattering problems are accommodated by truncating the infinite fluid region using exponential decay infinite elements. Changes to a nominal model are introduced through a structural perturbation that modifies the nominal structural stiffness matrix. An efficient method for calculating the solution derivatives with respect to the structural perturbation is presented. A Taylor series expansion is constructed using the derivative information and the convergence criteria for the series is examined. The local solution and derivatives are then used to construct a Pade approximation. The method is illustrated using several numerical examples. The approximation is shown to be quite accurate for large perturbations even when there are one or more nearby poles and the Taylor series fails to converge.