Modal expansion analyses of second-harmonic generation of Lamb modes in layered planar structures

This work develops an effective approach for studying the generation of second harmonics of the Lamb modes (LMs) in layered planar structures. Within second-order perturbation approximation, there are second-order bulk and surface/interface driving sources in layered planar structures when a primary LM propagates. These driving sources can be thought of as forcing functions of a series of double frequency Lamb modes (DFLMs). The total second-harmonic fields consist of a summation of DFLMs in the corresponding stress-free layered structures. Numerical simulation show that the forcing function associated with the soft adhesive layer of a layered planar structure plays a dominant role in the process of second-harmonic generation.