Modal analysis of second-harmonic generation of generalized Lamb waves in layered planar structures

This research has developed an approach for studying second-harmonic generation of generalized Lamb waves (GLWs) in layered planar structures. On the basis of a modal analysis approach and second-order perturbation treatment, an effective theoretical model has been established. The material non-linearity can result in second-harmonic generation by primary GLWs propagating in layered structures, and the non-linearity is treated as a second-order perturbation of the elastic response of primary GLW propagation. There are second-order bulk and surface/interface driving sources in layered planar structures when primary GLWs propagate. These driving sources can be thought of as the forcing functions of a series of double frequency GLWs (DFGLWs) in terms of the approach of modal expansion analysis of guided waves. The total second-harmonic displacement fields consist of a series of DFGLWs in the stress-free layered structures. Thus, the complicated problem of second-harmonic generation of GLWs can be determined exactly within the second-order perturbation regime. Despite the strongly dispersive nature of primary GLWs in layered planar structures, it is found that the second harmonics of primary GLWs can grow with propagation distance along layered structures when the phase velocities of the DFGLWs are equal to those of the primary GLWs. Also, the formal solution of the second harmonics of the primary GLWs are presented. Numerical simulations were performed to understand the physical process of second-harmonic generation by primary GLW propagation in layered structures. The potential application of the present results to practical inspections of layered structures is discussed.