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

This paper presents a simplified model for the purpose of studying the resonant responses and nonlinear dynamics of idealized electrostatically actuated micro-cantilever based devices in micro-electro-mechanical systems (MEMS). For the common cases of the micro-cantilever excited by periodic voltages, the underlying linearized dynamics are of a periodic or quasi-periodic system described by a modified nonlinear Mathieu equation. The harmonic balance (HB) method is applied to simulate the resonant amplitude frequency responses of the system under the combined parametric and forcing excitations. The resonance responses and nonlinearities of the system are studied under different parametric resonant conditions, applied voltages and various gaps between the capacitor plates. The possible effects of cubic nonlinear spring stiffness and nonlinear response resulting from the gas squeeze film damping on the system can be ignored are discussed in detail. The nonlinear dynamical behaviors are characterized using phase portrait and Poincare mapping in phase space, and the present analytical solutions and numerical simulations show that the nonlinear dynamical system is stable when choosing the rational parameters. This investigation provides an understanding of the nonlinear and chaotic characteristics of micro-cantilever based device in MEMS.