Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation ofLamb waves propagating in a two-layered solid plate is presented byusing the second-order perturbation and the technique of nonlinearreflection of acoustic waves at an interface. In general, thecumulative second-harmonic generation of a dispersive guided wavepropagation does not occur. However, the present paper shows thatthe second-harmonic of Lamb wave propagation arising from thenonlinear interaction of the partial bulk acoustic waves and therestriction of the three boundaries of the solid plates does have acumulative growth effect if some conditions are satisfied. Throughboundary condition and initial condition of excitation, theanalytical expression of cumulative second-harmonic of Lamb wavespropagation is determined. Numerical results show the cumulativeeffect of Lamb waves on second-harmonic field patterns.