Wave scattering by an elastic inclusion with quadratic nonlinearity

Abstract

This paper studies the problem of three-dimensional wave scattering by an elastic inclusion with quadratic nonlinearity in an otherwise linear elastic medium. Due to the nonlinearity of the inclusion, second order wave appears in the scattered field. Under the incidence of a plane longitudinal wave, solution to the scattered second order field is derived explicitly in terms of the Green's function. A far field approximation of the scattered field is also obtained. The results of far field show that the scattered second harmonic field consists of a longitudinal spherical wave and a shear spherical wave. Furthermore, it is found that the amplitude of the forward scattered field is proportional to the acoustic nonlinearity parameter β averaged over the volume of the inclusion, and the amplitude of backscattered field is proportional to a spatially weighted average of β. Finally, a method is described to nondestructively obtain the statistics of the spatial variation of β over the inclusion such as the mean, the variance and autocorrelation length. © 2012 American Institute of Physics.