Pulse response of a nonlinear layer

A simple analytical theory is developed for the description of the non-steady-state response of a thin nonlinear layer, which differs markedly in its linear properties from the surrounding medium. Such a layer can model the behavior of real inhomogeneities like a cloud of gas bubbles in a liquid, a crack or split plane in a solid, or the contact between two slightly tightened rough surfaces. Both weakly nonlinear pulse and harmonic responses are calculated and the general properties of the spectral and temporal structures of the scattered field are discussed. Exact strongly nonlinear solutions are derived for a special type of stress-strain relationship corresponding to the behavior of real condensed media under strong loads. Profiles and spectra shown conform with experimental results. The pulse response on the short delta-pulse shaped incident wave is calculated for arbitrary nonlinear properties of the layer. The possibilities to apply the sets of data on measured characteristics of pulse response in the solution of inverse problems are briefly discussed.