Second Harmonic Generation of Lamb Wave in Numerical Perspective**Supported by the National Natural Science Foundation of China under Grant Nos 51325504, 11474093, 11622430 and 11474361, the National Key Research and Development Program of China (2016YFC0801903-02), and the Fundamental Research Funds for the Central Universities.

Abstract

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.