The interaction of source-generated spherical waves with an elastic plate immersed in acoustic fluid

The interaction of acoustic waves generated by a point source with an elastic plate immersed in acoustic fluid is considered. To estimate the range of applicability of various theoretical approaches, a hierarchy of mathematical and computer models has been developed. The models differ in the governing equations for the sounded elastic laminate structure (from a simplified Kirchhoff-Love plate to a multi-layered anisotropic composite plate obeying the full set of 3D Navier-Lamé equations in each sublayer). Explicit integral representations for generated and scattered wave fields have been derived using the Fourier transform technique. In the far-field, the acoustic and guided waves are described by asymptotic representations obtained from those integrals using the stationary phase method and the residual technique. Among others, the derived solutions enable quantitative analysis of time-averaged wave energy fluxes in the considered source-structure system. Analytic representations for the total source energy and its portions carried by reflected, transmitted and guided waves have also been obtained.