Static pull-in instability and free vibration of functionally graded graphene nanoplatelet reinforced micro-sandwich beams under thermo-electrical actuation

This paper investigates the static pull-in instability and free vibration of a multilayer functionally graded graphene nanoplatelet (GPL) reinforced composite (FG-GPLRC) micro-beam sandwiched between two copper layers subjected to a combined action of an electric voltage and a uniform temperature change based on Euler–Bernoulli beam theory. The GPL nanofillers are uniformly dispersed within each individual layer while its weight fraction changes from layer to layer in the multilayer FG-GPLRC micro-beam. The modified Halpin–Tsai model is used to predict the effective Young’s modulus while the rule of mixture is used to determine the effective Poisson’s ratio, mass density and thermal expansion coefficient. The static pull-in voltage and natural frequency of clamped–clamped micro-beams are obtained by employing Galerkin and iterative method. The effects of GPL distribution pattern, weight fraction, geometry and size as well as the geometry of the beam, the temperature change and the total number of layers on the static and dynamic characteristics of the micro-beams are discussed in detail.