An orthogonal modes approach to fluid-loaded elastic structures with arbitrary forcing functions

Abstract

A numerical scheme is presented wherein the structural equations for an elastic structure are coupled to the acoustic radiation equations and recast in canonical form. The acoustic impedance matrix, which may be found via boundary element methods or by the superposition method, is expanded in a power series on angular frequency prior to coupling it with the structural matrices. The resulting system of equations is then decomposed to find an orthogonal basis set which uncouples the original equations. Once the basis set has been determined, the structural response and acoustic radiation spectra may be easily reconstructed for any arbitrary forcing function on the structure. Results will be given for two water-loaded examples, a finite plate in an infinite rigid baffle and a spherical shell.