ANALYTICAL APPROXIMATE SOLUTION FOR NONLINEAR VIBRATION OF MICROELECTROMECHANICAL SYSTEM USING HE'S FREQUENCY AMPLITUDE FORMULATION

Abstract– In this paper, nonlinear free vibration of a micro-beam-based micro electro mechanical
oscillator system is studied using He’s frequency amplitude method. Firstly, by considering midplane
stretching effects and distributed electrostatic forces and implementing Euler-Bernoulli
hypothesis, the governing equations are derived. Then, Galerkin method is used to convert the
resulted partial differential equations into an ordinary differential one. At last this nonlinear
ordinary differential equation is solved by He's frequency Amplitude formulation. The proposed
method offers an analytical closed form solution which is accurate and simple and in order to
study the problem parametrically and in a more general manner the variables are defined in
normalized form. A comparison between the obtained results and the one by an accurate numerical
method shows the good accuracy of this method in solving this kind of problem. In addition, the
relationship between the nonlinear principal frequency and non-dimensional amplitude, electroelastic
and axial loads on the beams has been studied.