Non-symmetric transmission of nonlinear elastic waves across a corrugated interface between two half-spaces

In this work, the symmetric transmission is broken in the system with a linear half-space combined by a nonlinear one with a corrugated interface. The interaction between nonlinear materials and elastic waves can generate second harmonics, so the non-symmetric transmission is realized. With the corrugation effects, irregularly reflected and transmitted waves are generated for both fundamental and second harmonics during the incident SH mode across the corrugated interface. Based on the Fourier series expansion method for the interface, the solution with the first order approximation of reflection and transmission coefficients are derived and the effects of the interface corrugation are discussed. The non-symmetric transmission is proved by both theoretical analysis and experiments. It is found that the reflected and transmitted waves are different when the fundamental wave incidents from the opposite direction. Compared with the positive incidence, there is no second harmonic in the linear half-space for the negative case and the generation of second harmonics in the nonlinear half-space is weaker.