Second-harmonic generation accompanying nonlinear reflection of shear waves in an isotropic layered structure

A theory is proposed for solving second-harmonic generation accompanying nonlinear reflection of shear (SH) waves. An analysis is presented for the resonant second-harmonic generation in a layered structure consisting of an isotropic layer and two semi-infinite isotropic solids. The result reveals that the effect of second-harmonic cumulative growth will occur once the component of incident SH-wave vector along the boundary equals the magnitude of the longitudinal wave vector of the elastic medium of the solid layer. Moreover, we have formally obtained the analytical expressions for the resonant second-harmonic generation in each region of the layered structure which yields physical insight into the process of the second-harmonic generation not previously available.