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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.

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Effect of precipitate-dislocation interactions on generation of nonlinear Lamb waves in creep-damaged metallic alloys

Within the second-order perturbation treatment, the present work analyzed the complex second-harmonic generation of Lamb waves in a two-layered solid waveguide by combining the modal analysis method and the nonlinear reflection of acoustic waves at interfaces. The formal solution of the second-harmonic field is obtained on the basis of the modal analysis approach, from which a phase matching modification factor can be determined. The solution of the cumulative second-harmonic displacement field derived from the nonlinear reflection of acoustic waves at interfaces can be modified by multiplying the phase matching modification factor, and then be more general and applicable for the total second-harmonic field of Lamb wave propagation. Numerical computation results show that amplitude of the second-harmonic displacement increases clearly with propagation distance when the phase velocity of a double frequency Lamb wave (DFLW) component is exactly or approximately equivalent to that of the primary Lamb wave propagation, and reveal that the amplitudes of the second harmonics exhibit a decreasing tendency when the relative deviation of phase velocity between the primary Lamb wave and the DFLW component increases. Primary experimental measurements have been performed to verify the results of the numerical simulations in a FeCrNi alloy steel specimen. The research provides a further understanding for the physical process of the cumulative second-harmonic generation in a two-layered solid waveguide.