A new formulation for the vibrations and sound radiation of fluid-loaded plates with elastic boundary conditions

Abstract

This paper considers the dynamic response and acoustic radiation of baffled rectangular plates elastically restrained against deflection and rotation along the four edges, and exposed to a half-space of dense fluid. Classical methods using in vacuo plate eigenfunctions to formulate the fluid/structure coupling are limited to the simply supported case and lead to considerable difficulty, both theoretical and numerical. The proposed method employs a variational formulation of the structural motion and a minimization process over a subspace of suitable displacement functions. The selection of simple polynomials to generate this subspace is shown to have many advantages: (i) it permits an analytic solution to be obtained for both the resistive and reactive components of the plate’s radiation impedance, (ii) it furnishes a natural decomposition of the radiator into monopoles, dipoles,..., 2n-upoles, and (iii) it decreases the computation cost and increases the generality of the problem addressed, as compared to available methods.