Analysis of second-harmonic generation by primary horizontal shear modes in layered planar structures with imperfect interfaces

This paper describes modeling of second-harmonic generation by the primary horizontal shear (SH) mode propagation in layered planar structures with imperfect interfaces. Due to the elastic nonlinearity of the solid, there are second-order bulk driving forces in each solid layer and a second-order stress tensor at each surface/interface, accompanying the primary SH mode propagation. Within second-order perturbation, these bulk driving forces and stress tensors can be thought of as the excitation source of a series of double frequency Lamb modes (DFLMs) in terms of the approach of modal expansion analysis for waveguide excitation. The equation governing the expansion coefficient of each DFLM is developed. It is found that the expansion coefficient of each DFLM is directly coupled with the interfacial properties, characterized by the finite normal and tangential interfacial stiffnesses. Especially, the phase velocity mismatching between the primary SH mode and the DFLM, caused by the degradation of interface (with respect to the case of the perfect interface), can remarkably influence the efficiency of second-harmonic generation by the primary SH mode propagation. The potential is discussed of using the effect of second-harmonic generation by the primary SH mode propagation to evaluate the interfacial properties of layered structures.