We theoretically investigate the second-harmonic generation of a plane longitudinal wave normally incident upon a solid plate immersed in liquid. The formulation of the reflected second harmonic is derived within the second-order perturbation. Theoretical analysis and numerical simulation indicate that the reflected second-harmonic amplitude increases sensitively with the increase in the nonlinear acoustic parameter of the plate material at some specific frequencies where the linear reflection coefficient of the normally incident longitudinal wave takes on the minimum value, and that it is independent of the spatial separation between the transmitter/receiver and the solid plate. The results obtained provide a means through which the early state of fatigue-induced damage of the solid plate (characterized by its nonlinear acoustic parameter) can be sensitively assessed by measuring the reflected second harmonic at the specific frequency where the linear reflection coefficient is minimum.

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.

The physical process of second-harmonic generation by the primary Lamb waves, propagating in layered planar structures with weak interfaces, has been studied in this paper. Due to the kinematic nonlinearity and the elastic nonlinearity of materials, there is second-harmonic generation accompanying the primary Lamb wave propagation. The well-known finite interfacial stiffness technique is used to describe the properties of weak interfaces of layered planar structures. It is found that the finite normal and tangential interfacial stiffnesses will effectively influence the effect of second-harmonic generation by Lamb wave propagation at the modal expansion coefficients of the Double Frequency Lamb Waves (abbr. DFLWs, constituting the second-harmonic fields) and at the dispersion relations of Lamb waves (determining the degree of cumulative growth of a DFLW component). Relative to the case where the interface of a layered planar structure is perfect and the phase velocity of the DFLW component is equal to that of the primary Lamb wave propagation at a given frequency where the DFLW component grows with propagation distance, the efficiency of second-harmonic generation of the primary Lamb wave propagation will decrease greatly when the normal and tangential interfacial stiffnesses decrease. The effect of second-harmonic generation by the primary Lamb wave propagation may provide a potential for accurately characterizing the properties of weak interfaces of layered planar structures.

Based on nonlinear measurements of the second harmonics of ultrasonic Lamb waves, this work develops a promising method for NDE of the properties of adhesive joints in layered planar structures. When ultrasonic Lamb waves have a strong nonlinearity, the measurements of amplitude-frequency curves for the second harmonics of Lamb waves at the surfaces of the given layered planar structures (aluminum sheet-epoxy-aluminum sheet) have been carried out. It is verified that there is no overlapping of multi-modes of the double frequency Lamb waves in the received signals. Experimental results show that both the stress wave factors of the nonlinear Lamb waves and the frequency values corresponding to the peaks of the amplitude-frequency curves of the second-harmonic signals can effectively characterize the properties of the adhesive joints.

This is work develops an effective approach for studying second-harmonic generation of Lamb waves in the composite structure consisting of a solid layer on a half space. Using a second-order perturbation approximation and a modal expansion analysis approach for waveguide excitation, an effective theoretical model has been established. The fields of second harmonics of Lamb waves can be regarded as superpositions of a finite series of normal double frequency Lamb waves (DFLW). Despite the strongly dispersive nature of Lamb waves, it is found that a DFLW can grow with propagation distance down the composite structure when the DFLW phase velocity equals that of the primary Lamb wave.