  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.
