Second-order perturbation solution and analysis of nonlinear surface waves

Abstract

The properties of ultrasonic nonlinear surface wave in the quasilinear region are investigated. In this work the governing equation of particle displacement potential is employed for surface wave in isotropic elastic solid with quadratic nonlinearity. Then, the quasilinear solution of the nonlinear surface wave is obtained by the perturbation method, and the absolute nonlinear parameter of the surface wave is derived. Subsequently, the main components of the second harmonic surface wave solution are discussed. A finite element model for the propagating nonlinear surface wave is developed, and simulation results of the nonlinear surface wave displacements agree well with the theoretical solutions, which indicates that the proposed theory is effective. Finally, the properties of wave propagation and the characteristic of the nonlinear parameter for the surface wave are analyzed based on the theoretical solutions. It is found that the second harmonic surface wave consists of cumulative and non-cumulative displacement terms. The cumulative displacement term is related to the self-interaction of the longitudinal wave component of the surface wave. However, its amplitude is larger than that of the pure longitudinal wave when the initial excitation conditions and propagation distances are the same. The nonlinear parameters for surface and longitudinal waves are related to each other, and an explicit relationship is found, which can be determined by the second-order elastic coefficients of the material. The propagation properties of nonlinear surface waves and the measurement method of absolute nonlinear parameters are also discussed, which will benefit the practical application of nonlinear surface waves.