Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal (PC) nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory, in which the surface effect and magneto-elastic coupling are considered. By introducing the nonlinear coupling constitutive relation of magnetostrictive materials, Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect, magnetic field, pre-stress, and geometric parameters. The results show that the surface effect has promotive influence on dispersion curves of the band structure, and the band gaps can be improved gradually with the increase in the material intrinsic length. Meanwhile, the band gaps exhibit obvious nonlinear coupling characteristics owing to the competition between the magnetic field and the pre-stress. By considering the surface effect and magneto-elastic coupling, the open and closed points of band gaps are found when the lattice constant to thickness ratio increases. The study may provide a method for flexible tunability of elastic wave propagation in magneto-elastic PC nanoplates and functional design of highperformance nanoplate-based devices.