SH wave generated Lamb wave in a plate with a localized region of material nonlinearity

Abstract

AbstractHigher harmonics are sensitive to micro‐defects, which can be utilized in the development of nonlinear ultrasonic techniques (NLUTs). Thus, the higher harmonic generation by material nonlinearity has attracted considerable attention. However, few works have been done on the elastic wave propagation in a finite structure with a localized region of material nonlinearity. The propagation of the SH wave in a plate with a localized region of quadratic material nonlinearity is investigated in this paper. The nonlinear governing equations are reduced to a set of linear equations at different orders by using the perturbation method. The incident plane SH wave satisfies the zero‐order equations. The elastic waves generated by the nonlinear material region can be obtained by solving the first‐order equations, whose inhomogeneous terms can be regarded as the equivalent body forces and surface tractions. In the first‐order approximation, only the Lamb wave can be generated by the interaction of the SH wave with a region of quadratic material nonlinearity. In this paper, the analytical solution for the generated backward Lamb wave is obtained, whose amplitude varies with a material‐dependent constant linearly and with the length of the nonlinear region in the form of a sine function.