Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS

In this paper, a simplified model for the dynamics of an electrostatically actuated micro-cantilever in micro-electro-mechanical systems (MEMS) is presented. The harmonic balance (HB) method is applied to simulate the resonant amplitude frequency responses of this system under combined parametric and forcing excitations. The nonlinearities of this system, which is manipulated under different parametrical resonant conditions, applied voltages and various clearances between the two plates, are studied. The possible effects of nonlinear spring stiffness and nonlinear response from the air damping on this system, which can be ignored, are discussed. The nonlinear dynamical behaviors are illustrated using phase portrait and Poincare mapping. In addition, the analytical solutions are agreed well to the numerical resolutions. This investigation is to provide a dependable evidence for design, testing and applications of a micro-cantilever based in MEMS.