[Paper Review] Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nano-plates

Bin Wu, Chunli Zhang+2 more|arXiv (Cornell University)|Jul 28, 2021

Nonlocal and gradient elasticity in micro/nano structures50 references22 citations

TL;DR

This paper develops a surface magneto-electro-elasticity theory using state-space formalism to investigate anti-plane shear (SH) wave propagation in nano-scale magneto-electro-elastic plates, revealing that surface effects significantly alter dispersion relations and thickness-shear frequencies, enabling wave modulation via 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.

Motivation & Objective

• To analyze the influence of surface effects on anti-plane shear wave propagation in magneto-electro-elastic nano-plates.
• To develop a surface magneto-electro-elasticity theory that captures the mechanical behavior of material surfaces at the nanoscale.
• To derive size-dependent dispersion relations for symmetric and antisymmetric SH waves in transversely isotropic nano-plates.
• To determine thickness-shear frequencies and asymptotic characteristics of the dispersion relations considering surface effects.
• To explore the potential for wave modulation through surface engineering by tuning surface material parameters.

Proposed method

• Formulates a surface magneto-electro-elasticity theory using the state-space formalism to model surface dynamics.
• Applies the theory to a transversely isotropic magneto-electro-elastic plate with nano-thickness.
• Derives analytical expressions for the dispersion relations of both symmetric and antisymmetric SH waves.
• Incorporates surface material parameters (surface elasticity, surface tension, surface mass density) into the boundary conditions.
• Solves the eigenvalue problem to obtain thickness-shear frequencies and analyze asymptotic behavior of the dispersion curves.
• Performs numerical simulations to evaluate the dependence of wave characteristics on surface parameters.

Experimental results

Research questions

• RQ1 How do surface effects influence the dispersion relations of anti-plane shear waves in magneto-electro-elastic nano-plates?
• RQ2 What is the impact of surface material parameters on the thickness-shear frequencies of SH waves?
• RQ3 How do the symmetric and antisymmetric modes of SH waves differ in their size-dependent behavior?
• RQ4 What are the asymptotic characteristics of the dispersion relations when surface effects are included?
• RQ5 Can wave propagation in nano-plates be effectively modulated through surface engineering?

Key findings

• Surface effects significantly alter the dispersion characteristics of anti-plane shear waves in magneto-electro-elastic nano-plates.
• The dispersion relations for both symmetric and antisymmetric SH waves exhibit strong size dependence due to surface effects.
• Thickness-shear frequencies are modified by surface parameters, with notable shifts observed in the numerical results.
• Asymptotic analysis confirms that surface effects dominate at small plate thicknesses, leading to non-monotonic dispersion behavior.
• The wave characteristics are highly sensitive to the choice of surface material parameters, enabling tunable wave propagation.
• Surface engineering offers a viable route to actively control elastic wave behavior in multiferroic nanostructures.