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

In this paper we employ second-order perturbation and the technique of nonl inear 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 sol id half-space. As in the case of second-harmonic generation of Lamb-wave pr opagation in a solid plate, in general, cumulative second-harmonic generati on of GLW propagation does not occur. However, the present paper shows that , under certain conditions, the GLW second harmonic arising from the nonlin ear interaction of the partial bulk acoustic waves and the restriction of t he two boundaries of the solid waveguide does retain a cumulative growth ef fect. Through a second-order boundary condition, the existence condition of second-harmonic generation of GLW propagation has been determined, and thr ough the initial condition of excitation the analytical solution of the cum ulative second harmonic of GLW propagation formally obtained. Numerical res ults show the cumulative effect of GLW second-harmonic field patterns. The technique of analysis in this paper yields a physical insight into the proc ess of cumulative second-harmonic generation of GLW propagation not previou sly available.