Influences of interfacial properties on second-harmonic generation of Lamb waves propagating in layered planar structures

Abstract

This paper describes influences of interfacial properties on second-harmonic generation of Lamb waves propagating in layered planar structures. The nonlinearity in the elastic wave propagation is treated as a second-order perturbation of the linear elastic response. Due to the kinematic nonlinearity and the elastic nonlinearity of materials, there are second-order bulk and surface/interface driving sources in layered planar structures through which Lamb waves propagate. These driving sources can be thought of as forcing functions of a series of double frequency lamb waves (DFLWs) in terms of the approach of modal expansion analysis for waveguide excitation. The total second-harmonic fields consist of a summation of DFLWs in the corresponding stress-free layered planar structures. The interfacial properties of layered planar structures can be described by the well-known finite interfacial stiffness technique. The normal and tangential interfacial stiffness constants can be coupled with the equation governing the expansion coefficient of each DFLW component. On the other hand, the normal and tangential interfacial stiffness constants are associated with the degree of dispersion between Lamb waves and DFLWs. Theoretical analyses and numerical simulations indicate that the efficiency of second-harmonic generation by Lamb wave propagation is closely dependent on the interfacial properties of layered structures. The potential of using the effect of second-harmonic generation by Lamb wave propagation to characterize the interfacial properties of layered structures are considered. Some experimental results are presented.