Anti-plane surface and interfacial waves influenced by layer reinforcement in Piezo-Electro-Magnetic structures with surface energy

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The electro-magnetic coupling parameter which is absent in monolithic piezoelectric materials is a unique property of the composite Piezo-Electro-Magnetic(PEM) materials that enhance the applicability of these composites in magnetic field probes, electric packaging, biotechnological applications, etc. In surgical process of joining bones, the freshly developed bone is softer than the mature bone, and thus the mechanical properties of this soft bone becomes important in the success of the surgery. Hence, these kinds of structures having a soft material reinforced at the surface or interface are the prime motivation of this study. In the present work, the propagation of Anti-plane wave is discussed in two models, namely a PEM half-space with a thin elastic layer reinforced at the free surface - Model $$-1$$ and two imperfectly bonded PEM half-spaces with a thin elastic layer reinforced at the interface - Model $$-2$$ . The presence of imperfectness(mechanical, electrical, and magnetic) at the interface gives rise to the discontinuity of displacement and electric & magnetic potential which result in imperfect signal communications affecting the performance of sensing devices. The Gurtin−Murdoch approach is used to derive the surface strain energy density, surface stress tensor, and surface kinetic energy density accounting for the reinforced elastic layer. Admissible boundary/interface conditions relating to the propagation of Anti-plane wave are defined for Electrically Open-Magnetically Open (EOMO) and Electrically Short-Magnetically Short (ESMS) boundaries/interfaces. Using these conditions, the dispersion relation for the propagating Anti-plane wave in both models and the mechanical-electro-magnetic boundaries/interfaces are derived. The impact of the electro-magnetic coupling parameter, imperfectness parameter, and reinforcement of soft & stiff elastic layer on the dispersion relation of Anti-plane wave is numerically computed and portrayed graphically. The data of two dissimilar PEM composites and surface/interface elastic layer of Iron, Gold, and Aluminum with different crystallographic directions constituting soft and stiff reinforcement are considered for numerical and graphical purposes. The electromechanical efficiency of the models are discussed through electromechanical coupling parameter. Moreover, the Cut-Off frequencies of both the models are portrayed graphically for the three data of soft reinforcement of surface/interface layer.