In-plane non-symmetric propagation of nonlinear elastic waves through a corrugated interface

Abstract

The interaction between elastic waves and nonlinear materials can generate second harmonics, which makes inherent properties of linear systems can be broken in nonlinear ones. In this work, two half-spaces composed of nonlinear and linear solids are used to break the symmetric transmission, in which a corrugated interface is considered. Affected by interface corrugations, additional irregularly reflected and transmitted waves of the incident fundamental wave and its second harmonic can be generated. Based on Fourier series and Taylor expansion approximation, the amplitude ratios of irregular waves are derived. Numerical results show that the incident frequency and corrugation length can manipulate the propagation of irregular waves. Due to the asymmetry of material nonlinearity, second harmonics can enter the linear half-space form the nonlinear one, but the reverse transmission is not allowed. Both the theoretical analysis and experimental results can support the in-plane non-symmetric transmission in the two half-spaces, which is an extension of the nonreciprocal phenomena in nonlinear metamaterials.