Iterative solution of nonlinear dynamical system of an electrostatically actuated micro-cantilever

This paper presents an iterative method to solve the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. Different from some other iteration methods for nonlinear dynamical systems, no additional procedures have to be carried out to eliminate the so-called secular terms. In addition, an efficient approach is proposed to expand fractional functions into truncated Fourier series. That makes it possible to implement the iterative procedures. Importantly, all the iteration equations are purely linear. Numerical examples show that the solutions provided by the method are in excellent agreement with numerical ones. The effects of applied voltage, cubic nonlinear stiffness and squeeze film damping on vibration responses are discussed in details.