Spherical-wave scattering by a finite-thickness solid plate of infinite lateral extent, with some implications for panel measurements

Abstract

The solution to the problem of the interaction of a spherical wave with a homogeneous and isotropic solid plate of infinite lateral extent, but finite thickness, is considered theoretically. Both the source and the plate are immersed in an infinite, inviscid fluid. Appropriate boundary conditions are imposed on the full three-dimensional elasticity equations. The solution is evaluated numerically for a variety of materials for a 1-kHz incident spherical wave and for a 5-kHz incident spherical wave. For the numerical study, the fluid medium is taken to be water. Under certain conditions, ‘‘overpressures’’ are predicted for both the reflected and transmitted fields (i.e., the amplitude of the reflected pressure and/or the transmitted pressure can exceed the maximum value of the amplitude of the incident pressure on the plate surface). These overpressures are consistent with the law of conservation of energy in the sense that, for a plate composed of lossless material, the total incident power is found to be equal to the sum of the total reflected power plus the total transmitted power. An important conclusion of this research is that the practice of attempting to reduce the influence of edge diffraction in panel tests by using samples of increasingly larger lateral extent may result in measurements that are substantially corrupted by wave-front curvature effects, particularly if the sample panel includes a steel backing plate.