Size-dependent free vibration and buckling analysis of magneto-electro-thermo-elastic nanoplates based on the third-order shear deformable nonlocal plate model

Abstract

In this paper, a size-dependent nanoplate model is developed to describe the free vibration and buckling behaviors of magneto-electro-thermo-elastic (METE) rectangular nanoplates. It is assumed that the METE nanoplate is subjected to external electric voltage, external magnetic potential, and uniform temperature rise. The nonlocal elasticity theory along with the third-order shear deformation plate theory is employed for the size-dependent mathematical modeling of nanoplates. The presented model has two advantages over available models: (1) the need for the correction factor is bypassed and (2) it can be successfully applied to thick nanoplates. The governing equations and the corresponding boundary conditions are derived using the Hamilton’s principle which are then discretized on the space domain based on the generalized differential quadrature (GDQ) method. Afterward, an efficient numerical Galerkin procedure is adopted to reduce the discretized equations into Duffing-type ordinary differential equations. Numerical results are presented to examine the influences of nonlocal parameter, length-to-thickness ratio, temperature rise, external electric potential, external magnetic potential and type of boundary condition on the free vibration, and buckling behaviors of METE nanoplates. It is revealed that frequency and critical buckling load of nanoplates are dependent on magneto-electro-mechanical loadings, whereas they are less dependent on thermal loading.