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

• Published in: Applied mathematics and mechanics Vol. 43; no. 2; pp. 203 - 218
• Main Authors: Zhang, Shunzu, Hu, Qianqian, Zhao, Wenjuan
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.02.2022; Springer Nature B.V; School of Civil and Hydraulic Engineering,Ningxia University,Yinchuan 750021,China
• Edition: English ed.
• Subjects: Applications of Mathematics; Band structure of solids; Classical Mechanics; Constitutive relationships; Coupling; Crystal structure; Dispersion curve analysis; Elastic waves; Energy gap; Fluid- and Aerodynamics; Kirchhoff theory; Lattice parameters; Magnetic fields; Magnetostriction; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Plate theory; Terfenol alloys; Thickness ratio; Wave propagation; 78M16; phononic crystal nanoplate; magnetic field; surface effect; band gap; O735; magneto-elastic; phononic crystal (PC) nanoplate
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2806-7

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.