Modeling and simulation of frequency mixing response of two counter-propagating Lamb waves in a two-layered plate

This work investigates modeling of the frequency mixing response (FMR) induced by two counter-propagating Lamb waves with different frequencies in a two-layered plate, and then numerically simulates and analyzes the influences of interfacial properties on the effect of FMR. Based on a perturbation approach and a normal-mode-expansion technique for waveguide excitation, the second-order bulk driving forces and surface/interface stresses at the mixing frequency, originated from the interaction of two counter-propagating Lamb waves within the wave mixing zone, can be regarded as the excitation sources for generation of a series of combined harmonics. It is found that, under the internal resonance condition including the phase matching and nonzero energy flux, the magnitude of the combined harmonic generated increases with increase in the length of mixing zone of the two counter-propagating Lamb waves, and tends to be stable outside the wave mixing zone. Due to the relatively short mixing zone of the two counter-propagating Lamb waves, the effect of FMR has attracted considerable attention because it can enhance the accuracy of location of the local interfacial degradation in the given layered plate. Both the numerical analyses and finite element (FE) simulations performed show that the local interfacial degradation in the two-layered plate may be assessed and located by spatial scanning of wave mixing zone of the two counter-propagating Lamb waves. Through modeling and FE simulations, this paper provides an insight into the physical process of FMR of the two counter-propagating Lamb waves in a two-layered plate, and meanwhile shows a potential for assessment and location of the local interfacial degradation by using the effect of FMR of the two counter-propagating Lamb waves.