Time-domain analysis and experimental examination of cumulative second-harmonic generation by primary Lamb wave propagation

Within the second-order perturbation approximation, the physical process of cumulative second-harmonic generation by the primary Lamb wave propagation has been investigated in the time domain. Based on the preconditions that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero and that the phase velocity matching condition is satisfied, we focus on analyzing the influence of mismatching of the group velocities on the generation of the second harmonic by propagation of a primary Lamb wave tone burst with a finite duration. Our analysis indicates that the time-domain envelope of the second harmonic generated is dependent on the propagation distance when both the duration of the primary Lamb wave tone burst and the group velocity mismatch are given. Furthermore, it can be concluded that the integrated amplitude of the time-domain second harmonic, which quantifies the efficiency of the second-harmonic generation, grows with the propagation distance even when the group velocity matching condition is not satisfied. The experimental examination has been performed, and it verifies our theoretical analysis.