Cumulative second-harmonic generation of generalized Lamb-wave propagation in a solid waveguide

In this paper we employ second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface to analyse the physical process of cumulative second-harmonic generation of generalized Lamb-wave (GLW) propagation in a solid waveguide consisting of a solid plate and a solid half-space. As in the case of second-harmonic generation of Lamb-wave propagation in a solid plate, in general, cumulative second-harmonic generation of GLW propagation does not occur. However, the present paper shows that, under certain conditions, the GLW second harmonic arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the two boundaries of the solid waveguide does retain a cumulative growth effect. Through a second-order boundary condition, the existence condition of second-harmonic generation of GLW propagation has been determined, and through the initial condition of excitation the analytical solution of the cumulative second harmonic of GLW propagation formally obtained. Numerical results show the cumulative effect of GLW second-harmonic field patterns. The technique of analysis in this paper yields a physical insight into the process of cumulative second-harmonic generation of GLW propagation not previously available.