Boundary Elements and Perturbation Theory for Vibrating Plates

Abstract

In this work, classical techniques from perturbation theory will be applied to develop a boundary integral formulation for low frequency forced vibrations of elastic plates. The functional form of the applied load and the plate deflection are assumed to be products of a temporal function and corresponding spatial functions. The separation of variables approach removes the difficulties associated with transient analysis. The resulting boundary element formulation requires consecutive solutions to a set of coupled non-homogeneous biharmonic equations. The domain integral normally associated with each non-homogeneous equation is transformed to a set of boundary integrals using the Rayleigh-Green identity. Numerical solutions of the perturbation-based expansion equations of forced vibrations using the boundary element method (BEM) are presented and compared with analytical analysis.