Numerical Perspective on Static Component Generation from Primary Lamb waves Propagating in a Plate with Quadratic Nonlinearity

Abstract

Under the discipline of nonlinear ultrasonics, in addition to second harmonic generation, static component generation is another frequently used nonlinear ultrasonic behavior in non-destructive testing (NDT) and structural health monitoring (SHM) communities. However, most previous studies on static component generation are mainly based on using longitudinal waves. It is desirable to extend static component generation from primary longitudinal waves to primary Lamb waves. The static component generated from longitudinal waves is cumulative. When extending the static component generated from the longitudinal waves to Lamb waves, a major concern is that whether the dispersive nature of Lamb will affect the cumulative of the static component or not. In this paper, cumulative effect of static displacement component from different primary Lamb wave modes is investigated. Our study results show that the static components generated from the primary S0, A0 and S1 modes are cumulative regardless of whether the phase velocity of the primary and secondary waves is matched or not. This observation indicates that the static component overcomes the limitations of the traditional nonlinear Lamb waves satisfying phase velocity matching condition to achieve cumulative second harmonic generation. This nature also enables the primary Lamb waves excited at a low center frequency to generate static component used for inspecting large-scale structures with micro-scale damages.