On the dynamics and stability of size-dependent symmetric FGM plates with electro-elastic coupling using meshless local Petrov-Galerkin method

Abstract

In present study, the equations of motion of sandwich symmetric functionally graded size-dependent plates integrated with piezoelectric layers are derived using Hamilton’s variational principle (with modified Lagrangian) based on a higher-order nonlocal strain gradient theory in conjunction with Reddy’s third-order shear deformation plate kinematics. For the first time, a set of sixth-order partial differential equations are derived and solved by meshless local Petrov-Galerkin method to investigate the bifurcation buckling and free vibration of plates under electromechanical in-plane forces with considered nanostructure and various boundary conditions. The shifted and scaled moving least-squares approach is utilized for approximation of unknown variables, and the Gauss weight function is used as test function for deriving local weak form of governing equations. The Gauss-Legendre quadrature is employed for numerical evaluation of weak forms. A power-law distribution and a half cosine variation are applied to model the variation of materials properties and electric potentials, respectively. The obtained results are verified with well-known solutions in the literature. The effect of nonlocal parameter, material length scale parameter, power-law index, predefined electric field, axial compressive and tensile forces, volume ratio of FG core and piezoelectric layers, and stiffness of Pasternak foundation on the critical buckling loads and natural frequencies are presented and discussed comprehensively. The results obtained can be used in the analysis, design and control of composite nanostructures that are widely used in MEMS and NEMS devices.