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

Abstract

Abstract– In this paper, nonlinear free vibration of a micro-beam-based micro electro mechanicaloscillator system is studied using He's frequency amplitude method. Firstly, by considering midplanestretching effects and distributed electrostatic forces and implementing Euler-Bernoullihypothesis, the governing equations are derived. Then, Galerkin method is used to convert theresulted partial differential equations into an ordinary differential one. At last this nonlinearordinary differential equation is solved by He's frequency Amplitude formulation. The proposedmethod offers an analytical closed form solution which is accurate and simple and in order tostudy the problem parametrically and in a more general manner the variables are defined innormalized form. A comparison between the obtained results and the one by an accurate numericalmethod shows the good accuracy of this method in solving this kind of problem. In addition, therelationship between the nonlinear principal frequency and non-dimensional amplitude, electroelasticand axial loads on the beams has been studied.