A numerical study of non-collinear wave mixing and generated resonant components

Abstract

Interaction of two non-collinear nonlinear ultrasonic waves in an elastic half-space with quadratic nonlinearity is investigated in this paper. A hyperbolic system of conservation laws is applied here and a semi-discrete central scheme is used to solve the numerical problem. The numerical results validate that the model can be used as an effective method to generate and evaluate a resonant wave when two primary waves mix together under certain resonant conditions. Features of the resonant wave are analyzed both in the time and frequency domains, and variation trends of the resonant waves together with second harmonics along the propagation path are analyzed. Applied with the pulse-inversion technique, components of resonant waves and second harmonics can be independently extracted and observed without distinguishing times of flight. The results show that under the circumstance of non-collinear wave mixing, both sum and difference resonant components can be clearly obtained especially in the tangential direction of their propagation. For several rays of observation points around the interaction zone, the further it is away from the excitation sources, generally the earlier the maximum of amplitude arises. From the parametric analysis of the phased array, it is found that both the length of array and the density of element have impact on the maximum of amplitude of the resonant waves. The spatial distribution of resonant waves will provide necessary information for the related experiments.

Keywords: Non-collinear mixing waves; Nonlinear ultrasound; Third-order elastic constants.