Vibrations of graphene nanoplatelet reinforced functionally gradient piezoelectric composite microplate based on nonlocal theory

Abstract

This paper investigates the small-scale effect on the linear and nonlinear vibrations of the graphene nanoplatelet (GNPL) reinforced functionally gradient piezoelectric composite microplate based on the nonlocal constitutive relation and von Karman geometric nonlinearity. The GNPL reinforced functionally gradient piezoelectric composite microplate is resting on the Winkler elastic foundation and is subjected to an external electric potential. The parallel model of Halpin Tsai is used to compute the effective Young's modulus of the GNPL reinforced functionally gradient piezoelectric composite microplate. The Poisson's ratio, mass density and piezoelectric properties of the GNPL reinforced functionally gradient piezoelectric composite microplate are calculated by using the rule of mixture. Hamilton's principle is adopted to obtain the higher-order nonlinear partial differential governing equations of motion for the GNPL reinforced functionally gradient piezoelectric composite microplate. The partial differential governing equations of motion are reduced to a system of the nonlinear algebraic eigenvalue equations by using the differential quadrature (DQ) method and are solved by an iteration progress. The efficiency and accuracy of the present approach are verified by comparing with the existed results. Both uniformly and functionally distributing graphene nanoplatelets (GNPLs) are considered to investigate the effects of the GNPL concentration, external voltage, nonlocal parameter, geometrical and piezoelectric characteristics of the GNPLs as well as the elasticity coefficient of the Winkler elastic foundation on the linear and nonlinear dynamic behaviors of the GNPL reinforced functionally gradient piezoelectric composite microplate with various boundary conditions. The numerical results clearly manifest that the GNPLs can significantly enhance the structural stiffness of the micro-electro-mechanical system (MEMS).