A NEW FORMULATION FOR THE VIBRATIONS AND SOUND RADIATION OF FLUID-LOADED PLATES WITH ELASTIC BOUNDARY-CONDITIONS

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.