The Mixed Boundary Conditions Problem of Layered Composites with Meta-Surfaces in Electro Elasticity

  • Ara S. AvetisyanEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)


The influence of taking into account the presence of roughness of both the external mechanically free surfaces, and the internal surfaces connecting various media, on the propagation of a high-frequency wave signal in a multilayer waveguide is investigated. In order to solve the quasistatic problem of the coupled electroelastic (magnetoelastic, thermoelastic) fields, the joints of the rough surfaces at the composites are simulated as meta-surfaces. In different models of the connection of thick piezoelectric layers, in the zone of the connection of their surfaces, the thin geometrically and physically inhomogeneous multilayer zone, which is equivalent to the meta surface with the dynamic loads, virtually arises. Taking into account the known principles of wave formation and propagation of high-frequency (short-wave) wave signals, as well as the magnitude of the surface roughness, hypotheses of magneto (electro, thermo) elastic layered systems are introduced (hypothesis MELS—Magneto Elastic Layered Systems). Proper selection of the surface exponential functions (SEF) in hypotheses, in equations and in thermodynamic relationships of the problem ensures that the surface roughness is taken into account. The introduction of hypothesis MELS allows modeling of the mathematical boundary-value problem of the contact of rough surfaces of continuous media with related physical and mechanical fields. This approach also makes it easy to calculate the equivalent dynamic electro-mechanical loads on the simulated meta-surface at the interface of the media. The following examples have been analyzed: (i) the propagation of the signal of an elastic shear wave in the case of the connection of rough surfaces of two piezoelectric layers with another thin piezoelectric layer, (ii) the propagation of an electroelastic wav(e in a single-shaped piezoelectric layer, the surfaces roughness of which is filled with an isotropic dielectric or ideal conductor, (iii) the propagation of high-frequency shear elastic waves on interface of isotropic elastic half-spaces with canonical surface protrusions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mechanics, National Academy of SciencesYerevanArmenia

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