Resonance reflection of acoustic waves by a perforated bilaminar rubber coating model

We construct the prediction of the resonance scattering theory (RST) for the reflection of sound waves by a bilaminar rubber configuration separating two dissimilar semi-infinite acoustic media. The layers are further assumed to contain distributions of spherical air-filled perforations, of various concentrations in each layer, whose behavior is governed by a simple, static, ‘‘effective parameter’’ model. We compare the direct scattering prediction of the RST to that of the exact solution in order to show the usefulness of the RST to yield clear physical interpretations of complex phenomena. The casting of the direct scattering solution in ‘‘RST-form’’ also provides a systematic method to solve the inverse scattering problem for the composition of the bilaminar rubber configuration. The ‘‘response surface’’ and response curves of the returned echoes are shown to contain certain modulation effects, described in the text, that actually characterize the material composition of each of the layers making up the coating model. The process disentangles which resonance feature present in the reflection coefficient is caused by which one of the interacting layers. In particular, we can separate and identify the impedances and the respective thickness-to-speed ratios (transit times) of each of the layers, and if additionally, either the thicknesses or the speeds are known, then, the process determines the other one and also the layer densities all from the resonances in the remotely sensed acoustic reflections.