Analysis of nonlinear vibration and instability of electrostatic functionally graded micro-actuator based on nonlocal strain gradient theory considering thickness effect

In this work, we develop a model of an electrostatic functionally graded (FG) micro-actuator based on the nonlocal strain gradient theory (NSGT) incorporated the thickness effect and the Euler–Bernoulli beam theory (EBT) with the von-Karman’s assumption. The material properties of the micro-beam are assumed to vary continuously through the thickness direction according to a power law distribution of the volume fractions of the constituents. A micro-actuator model consists of a FG micro-beam placed on top of a fixed plate, a DC voltage applied between the FG micro-beam and the fixed plate causes an electrostatic force to be exerted on the FG micro-beam. The intermolecular interaction forces including the Van der Waals and the Casimir forces are also considered in this model. The analytical solution of this problem is solved by applying Galerkin and He’s Laplace methods. Comparing the obtained solution with the numerical and published ones in the literature has shown the accuracy of the obtained results. Effects of the power-law index, the size-dependent parameters, the slenderness ratio, the applied voltage and the intermolecular interaction forces on the vibration and instability behaviors of the FG micro-beam are examined and discussed.