Size effect on the dynamic analysis of electrostatically actuated micro-actuators

This paper presents a new analytical model for electrostatically actuated micro-actuators to explore the size effect by using the “symmetric stress” gradient elasticity theory. A gradient coefficient (material length scale parameter) is introduced to represent the size-dependent characteristics of micro-beams. The nonlinearities, which associated with the mid-plane stretching force and the electrostatical force, also are considered in this model. By employing Galerkin method, the nonlinear partial differential governing equation is decoupled into a set of nonlinear ordinary differential equations which are then solved using Runge–Kutta method. Numerical results show that, compared with the classical theory, the stiffness of the micro-beam based on the “symmetric stress” gradient elasticity theory is greater. The effects of size effect, geometric nonlinearity, initial gap, beam length and beam height on nonlinear dynamic behavior are studied. It is found that the effects of size effect become more significant when the voltage is higher, the initial gap, the beam length and the beam height are smaller.