Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nano-plates

TL;DR

This paper develops a surface magneto-electro-elasticity theory to analyze how surface effects influence anti-plane shear wave propagation in nano-plates, revealing significant size-dependent dispersion characteristics and potential for wave modulation via surface engineering.

Contribution

It introduces a novel boundary condition formulation for surface effects in magneto-electro-elastic nano-plates and derives size-dependent dispersion relations for shear waves.

Findings

Surface effects significantly influence wave dispersion in nano-plates.

Dispersion relations depend strongly on surface material parameters.

Wave modulation can be achieved through surface engineering.

Abstract

Material surface may have a remarkable effect on the mechanical behavior of magneto-electro-elastic (or multiferroic) structures at nano-scale. In this paper, a surface magneto-electro-elasticity theory (or effective boundary condition formulation), which governs the motion of the material surface of magneto-electro-elastic nano-plates, is established by employing the state-space formalism. The properties of anti-plane shear (SH) waves propagating in a transversely isotropic magneto-electro-elastic plate with nano-thickness are investigated by taking surface effects into account. The size-dependent dispersion relations of both antisymmetric and symmetric SH waves are presented. The thickness-shear frequencies and the asymptotic characteristics of the dispersion relations considering surface effects are determined analytically as well. Numerical results show that surface effects play a very pronounced role in elastic wave propagation in magneto-electro-elastic nano-plates, and the dispersion properties depend strongly on the chosen surface material parameters of magneto-electro-elastic nano-plates. As a consequence, it is possible to modulate the waves in magneto-electro-elastic nano-plates through surface engineering.