Spherical-Wave Scattering by a Finite-Thickness Solid Plate of Infinite Lateral Extent, with Some Implications for Panel Measurements

摘要

The solution to the problem of the interaction of spherical wave with a homogenous and isotropic solid state 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 1kHz incident spherical wave an for a 5-kHz incident spherical wave. 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 conversation of energy in the sense that, for a plate composed of lossless material, the total incident power is found to be equal to the sim of the total reflected power plus the total transmitted power. An important conclusion 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. Keywords: Acoustic scattering, Reflection, Panel measurements; Spherical waves; Symbolic computation; Reprints. (jhd)