Cumulative second-harmonic generation accompanying nonlinear shear horizontal mode propagation in a solid plate

In this article cumulative second-harmonic generation accompanying nonlinear shear horizontal (SH) mode propagation in a solid plate has been studied. Generally, the amplitude of the driven second harmonic arising from the self-interaction of the shear wave is independent of propagation distance. However, for SH mode propagation consisting of two shear waves, the cross interaction between two shear waves may cause the cumulative effect of the driven second harmonic once the phase velocity of SH mode propagation equals the longitudinal velocity of the plate material. In practical issues, one is especially interested in the case in which the second-harmonic amplitude is dependent of propagation distance. With appropriate boundary and initial conditions of excitation, the process of cumulative second-harmonic generation is clearly shown, and the analytical expression of the cumulative second harmonic is determined. Although the plane second harmonic without the cumulative effect cannot be determined in the present analysis, the cumulative second-harmonic generation accompanying nonlinear SH mode propagation is of substantial significance due to its obvious effect.