Analysis of second-harmonic generation of Lamb modes using a modal analysis approach

Abstract

An effective technique for analyzing the generation of second harmonics of Lamb modes in elastic plates is presented. The nonlinearity of the wave equation governing the wave propagation ensures that there is second-harmonic generation accompanying primary Lamb mode propagation. This nonlinearity may be treated as a second-order perturbation of the linear elastic response. Using a second-order perturbation approximation and a modal analysis approach, the complicated problems of the generation of second harmonics of Lamb modes have been investigated. The fields of the second harmonics of Lamb modes in elastic plates are considered as superpositions of the fields of a series of double-frequency Lamb modes. The solutions provide physical insight into the generation of second harmonics with a cumulative growth effect, and the corresponding second-harmonic solutions. Although Lamb modes are dispersive, the cumulative growth effect of the second harmonics does exist under some conditions. The influence of Lamb mode dispersion on second-harmonic generation is considered.