A hybrid numerical and analytical solution for the Green’s function of a fluid-loaded elastic plate

Abstract

A fundamental problem in structural acoustics is the scattering or radiation of sound from a fluid-loaded plate with discontinuities. In calculating the response of the plate, as well as the radiated pressure field, the traditional approach has been to evaluate the transform representation of the response or radiated pressure solution using a contour integral. The contour integral evaluation of these representations is numerically inefficient when compared to an approach that utilizes an FFT algorithm to compute the inverse transform by a direct integration along the real wave-number axis. The latter approach however can run into problems because of the presence of singularities along the real wave-number axis. In previous work by other investigators, this problem has been overcome by artificially including structural damping in their formulations, which in some instances may obscure the true effects of the radiation damping. In the present work, a direct integration approach is used after first analytically extracting from the solution the pole-like contributions on or near the real axis, and thus removing the problem of the singularities. The results only represent the influence of the radiation damping. The Green’s functions obtained in this way for the fluid-loaded plate are compared to results obtained by the other techniques. The resulting Green’s functions can be used to solve for the radiation and scattering problems for inhomogeneous fluid-loaded plates.