The nonlinear S₀ Lamb mode in a plate with a linearly-varying thickness

The aim of this paper is to investigate propagation characteristics and the generation mechanism of the nonlinear lowest-order symmetric Lamb mode (S₀) which propagates downslope in free elastic plates with slowly linearly varying-thickness. From theoretical analyses, in a low frequency-thickness product (fd) range, the S₀ mode is slightly dispersive, it is easy to generate, and it approximately satisfies the principle of the phase velocity matching. Therefore, if a S₀ mode is excited at a proper frequency in the low fd range, the amplitude of the second harmonic wave is linearly increasing in a certain propagating-distance, which is valuable for the practical NDE application of the second harmonic wave. Moreover, numerical simulations and experiments have been carried out to validate theoretical results. Our investigation of properties of the second harmonic wave can be applied to characterize and evaluate micro-structural damages in varying-thickness waveguides.