Surface effect on band structure of flexural wave propagating in magneto-elastic phononic crystal nanobeam

Abstract

A theoretical model is established to study the size-dependent performance of flexural wave propagation in magneto-elastic phononic crystal (PC) nanobeam with surface effect based on Euler–Bernoulli beam theory and Gurtin–Murdoch theory. Considering the magneto-mechanical coupling constitutive relation of magnetostrictive material, the influence of surface effect on band structure is calculated by the plane wave expansion method for PC nanobeam subjected to pre-stress and magnetic field loadings. Through the example of an epoxy/Terfenol-D PC nanobeam, it can be observed that the characteristics of flexural wave band structures are size-dependent, and remarkably affected by surface effect when the dimension of the PC beam reduces to the nanoscale. The edges and width of the band gap with surface effect are higher than those without surface effect, especially for high frequency region. And surface effect gradually reduces with the increasing of bulk layer-to-surface layer thickness ratio until the band gap descends to a constant for the conventional one in the absence of surface effect. The effects of surface elasticity and piezomagneticity on band gap are more prominent than the residual surface stress. In addition, a distinctly nonlinear variation of band gap appears under the combined effects of pre-stress and magnetic field. Moreover, with the varying of filling fraction, multi-peaks of the width of the band gap are obtained and discussed. These results could be helpful for the intelligent regulation of magneto-elastic PC nanobeam and the design of nanobeam-based devices.