Resonant second-harmonic generation accompanying nonlinear Love-wave propagation in an isotropic waveguide

In this article we have studied resonant second-harmonic generation accompanying nonlinear Love-wave propagation in an isotropic waveguide consisting of a solid layer and a semi-infinite solid. Generally, the amplitude of the second harmonic arising from the self-interaction of shear wave is independent of propagation distance, i.e., there is no effect of cumulative growth. However, for Love-wave propagation case, there are two shear partial waves in the solid layer deposited on the semi-infinite solid, and the cross-interaction between two shear waves may cause the "resonance" of the driving second harmonic once the phase velocity of the Love-wave equals the longitudinal velocity of the solid layer. Through second-harmonic boundary conditions and initial conditions of excitation, we formally obtain the analytical expressions for the case of resonant second-harmonic generation. The present analysis yields clearly physical insight into the process of resonant second-harmonic generation accompanying nonlinear Love-wave propagation not previously available.