Numerical study of the second harmonic generation of Lamb waves at an imperfect joint of plates

Abstract

Lamb waves are attracting significant attention in the nondestructive evaluation for plate structures due to their capability to propagate long distances. In this study, the nonlinear interaction of Lamb waves with an imperfect joint of elastic plates is numerically investigated. In particular, the second harmonic generation behavior from the joint is examined by perturbation analysis. The imperfect joint is modeled as a spring-type interface with quadratic nonlinearity, and the perturbation analysis is carried out using the hybrid finite element method (HFEM). For the incidence of the lowest-order symmetric (S0) Lamb mode below the cut-off frequencies of the higher-order modes, the double-frequency S0 mode is generated from the imperfect joint due to the nonlinear interaction. A nonlinear parameter calculated from the amplitude of the second harmonic S0 mode shows a sharp peak at a certain incident frequency. The peak frequency increases with increasing interfacial stiffness, and the double of the peak frequency corresponds to the resonance frequency of the imperfect joint subjected to the S0 mode incidence. This result shows that the resonance of the imperfect joint leads to the amplification of the second harmonic S0 mode.