Response of an acoustic-elastic system to a transient source in the acoustic medium: Analytical modelling for the air-coupled wave

Abstract

The present work considers an elastic solid half-space contiguous to an acoustic half-space. Since the acoustic half-space does not support shear, gases and liquids are included in the present study. By the analysis, one deduces the stresses in the solid produced by a spherical source of pressure embedded in the acoustic medium. The solution is obtained by using one-sided and two-sided Laplace transforms and by relying quite heavily on the properties of the Green's function for the acoustic medium. These properties make compatible the prescription of the source pressure on a spherical surface and the application of the boundary conditions at the plane acoustic-elastic interface. For an arbitrary pressure history input, the transform inversion is effected by Cagniard's technique to yield the exact solution.