On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion

TL;DR

This paper investigates how a nonlinear elastic spherical inclusion scatters incident waves, producing harmonic components whose amplitudes depend on specific nonlinear parameters, with analysis of forward and backward scattering behaviors.

Contribution

It introduces a detailed analysis of harmonic scattering amplitudes from a nonlinear elastic inclusion, linking them to quadratic and cubic nonlinear parameters and comparing with plane wave predictions.

Findings

Second-harmonic amplitude depends on quadratic nonlinearity parameter β.

Forward scattering amplitude is always greater than or equal to backward amplitude.

Harmonic amplitudes are consistent with plane wave model predictions.

Abstract

In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and third-harmonic components. The secondary field is solely a result of the quadratic and cubic elastic nonlinearity present within the region of the inclusion. The second-harmonic scattering amplitude depends on the quadratic nonlinearity parameter $\beta$, while the first- and third-harmonic amplitudes depend on the cubic nonlinearity parameter $\gamma$. The special cases of forward and backward scattering amplitudes were analyzed. For each harmonic, the forward-scattering amplitude is always greater than or equal to the backward scattering amplitude in which the equality is only realized in the Rayleigh scattering limit. Lastly, the amplitudes of the scattered harmonic waves are compared to predicted harmonic amplitudes derived from a plane wave model.