Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings

摘要

The theories of nonlocal, refined plate, and surface effects are used in this study to investigate the free vibration of magnetoelectroelastic (MEE) nanoplates resting on elastic foundations. For this purpose, the MEE nano-plate is subjected not only to external magnetic and electric potentials but also to thermal and shear in-plane loads. The refined plate theory is used and the Maxwell equations and magnetoelectric boundary conditions employed to determine the variations in the electric and magnetic potentials along the direction of the nanoplate thickness. This is followed by deriving the governing equations based on the Hamilton's principle, which are then solved via the generalized differential quadrature method. In a later stage of the study, the effects of electric and magnetic potentials, nonlocal parameter, thermal and shear in-plane loading, Win-kler and shear moduli, different boundary conditions, and aspect ratio are explored in a parametric study on the surface effects of vibration characteristics of MEE nanoplates. It is found that the effect of surface parameters enhanced with increases in nonlocal parameter, electric potential, in-plane shear load, and temperature change. However, this effect is observed to decrease when the magnetic potential, dimensionless Winkler and shear moduli, and nanoplate thickness are augmented.