Acoustic wave propagation and reflection on nonlinear boundaries

Abstract

Unlike optics reflection phenomenon in acoustics has long been considered a linear process. In the present paper a general approach to acoustic reflection problems at nonlinear solid–solid and liquid–solid interfaces will be discussed in terms of perturbation theory. Fresnel formulas for the second-order reflection waves were derived for ideally bonded contacts of isotropic solids. Nonlinear bulk wave reflection was shown to result in efficient second harmonics generation, particularly, for overcritical angles of incidence. Unlike the linear case, nonlinear reflection generally leads to the rotation of the polarization plane for the harmonics of shear waves. Reflected harmonics are to be observed even when acoustic impedance is continuous across the boundary forbidding linear reflection to exist. Based on the nonlinear sound reflection problem, the method for analysis of boundary wave nonlinear propagation has been developed. It uses the idea of partial mode decomposition in wave reflection and takes into account self- and cross-interactions of acoustic waves reflected and transmitted at complex angles. The examples of analytical solutions for the second harmonics, as well as numerical calculations of nonlinear wave profiles, will be demonstrated for the Rayleigh, Stoneley, and Stoneley-Sholte wave propagation along nonlinear boundaries. The results obtained permit general characteristics of boundary acoustic nonlinearity that were shown to be different from those in the bulk of nonlinear medium to be defined.