Abstract

During the past decades, phononic crystals and elastic wave metamaterials as the artificial periodic structures have received considerable attention. Due to their distinguishing properties, these structures can be used for the wave energy manipulation, e.g., band gaps, elastic wave cloaking and topological state, etc. A well-known characteristic is the band gap which means that the elastic wave cannot propagate in some certain frequency regions. Based on this property, many engineering applications can be achieved, e.g., filtering and wave isolation, etc. The investigations mentioned above are mainly focused on the linear elastic problems which cannot present the nonlinear wave properties. However, the nonlinearity appearing in the materials and structures can bring new and interesting wave phenomena. One of the nonlinear characteristics is the generation of the higher order harmonics. It can be applied to the nonlinear nondestructive testing. Recently, increasing attention has been focused on the nonlinear wave motion, which can result in the nonlinear band gap and acoustic diode. The new concept named as the acoustic diode has been presented by the combination of the band gap and material nonlinearity, which permits the wave propagation in only one direction. It can be achieved when the fundamental wave sits in the stop band but the second harmonic belongs to the pass band. However, the acoustic wave has one direction displacement component and usually propagates in the air or liquid. Thus we wonder whether the nonreciprocal phenomenon of the elastic wave can be achieved in the solid materials. The problem will become more interesting and necessary because of the coupling displacements with the vector characteristic in solids. In our previous work, we have discussed the nonreciprocal transmission for the incident SH and in-plane elastic waves in a nonlinear elastic wave metamaterial. The interface in the consecutive layers is always assumed as perfect, which means that the displacement and stress components are continuous across the interface. But perfect interfaces may become imperfect in practice during the manufacture, which indicates that the interfacial property on the band gaps is obvious. Then the imperfect interface can offer a new opportunity to tune the nonreciprocal transmission of the elastic wave which depends on the band gap property. In this work, the nonreciprocal transmission for the SH wave in a layered nonlinear elastic wave metamaterial with the imperfect interfaces is investigated. The combination of the structural asymmetry and material nonlinearity breaks the inherent reciprocity of the classic wave system. The second harmonic can be generated by the interaction between the incident SH wave and material nonlinearity. Based on the Bloch’s law and stiffness matrix method, the band gaps and transmission coefficients of both the fundamental and second harmonic waves are obtained. The effects of the interfacial properties on the nonlinear phononic crystal and elastic wave metamaterial are discussed. We find that comparing with the perfect interface system, the central frequency of the nonreciprocal regions shifts towards the low frequency region by the effects of imperfect interfaces. This present work is expected to be helpful to design the practical devices with the tuning nonreciprocal transmission of the elastic wave.

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