Analysis of second-harmonic generation of Lamb waves using a combined method in a two-layered solid waveguide

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.