Analysis of generation of cumulative second harmonics of Lamb modes in a layered planar structure

A technique for analyzing the nonlinear generation of the cumulative second har-monics of generalized Lamb modes in a layered planar structure is developed. A theoretical model for nonlinear generalized Lamb mode propagation in a layered planar structure has been established, based on a partial plane wave approach. The nonlinearity is treated as a second-order perturbation of the linear elastic response. This model reveals some interesting features of the physics of the cumulative second harmonic generation. Although Lamb mode propagation is dispersive in a layered structure, the results of this analysis show that the amplitudes of the second harmonics do accumulate with propagation distance under certain special conditions. On the basis of the boundary and initial conditions of excitation, the formal solution of the cumulative second harmonic has been derived. Using the formal solution, we have performed some numerical simulations and obtained the cumulative second harmonic field patterns, illus-trating the distortion effect along the propagation distance, as well as the dependence of the field patterns on the position of the excitation source.