Two-way collinear interaction of longitudinal waves in an elastic medium with quadratic nonlinearity

A numerical implementation of two-way collinear interaction of nonlinear ultrasonic longitudinal waves in an elastic medium with quadratic nonlinearity is conducted in this work. A semi-discrete central scheme is used here to solve the numerical problem. The pulse-inversion technique is applied to accentuate the generated resonant waves and remove the fundamental components. The produced resonant waves can be clearly observed in the frequency domain. Variation trends of the resonant waves together with second harmonics along the propagation path are analyzed and results show that apart from the obvious growing of the transverse component with difference frequency, the longitudinal component and the resonant wave of sum frequency have notable responses as well. The spatial distribution of resonant waves will provide necessary information for the related experiments.