Study of Second-Harmonic Generation of Lamb Waves Propagating in Layered Planar Structures with Weak Interfaces

摘要

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.