Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model

Monostable vibration can eliminate dynamic bifurcation and improve system stability, which is required in many microelectromechanical systems (MEMS) applications, such as microbeam-based and comb-driven resonators. This article aims to theoretically investigate the monostable vibration in size-effected MEMS via a low dimensional model. An improved single degree of freedom model to describe electrically actuated microbeam-based resonators is obtained by using modified couple stress theory and Nonlinear Galerkin method. Static displacement, pull-in voltage, resonant frequency and especially the monostable dynamic behaviors of the resonators are investigated in detail. Through perturbation analysis, an approximate average equation is derived by the application of the method of Multiple Scales. Theoretical expressions about parameter space and maximum amplitude of monostable vibration are then deduced. Results show that this improved model can describe the static behavior more accurately than that of single degree of freedom model via traditional Galerkin Method. This desired monostable large amplitude vibration is significantly affected by the ratio of the gap width to mircobeam thickness. The optimization design results show that reasonable decrease of this ratio can be beneficial to monostable vibration. All these analytical results are verified by numerical results via Differential Quadrature method, which show excellent agreement with each other. This analysis has the potential of improving dynamic performance in MEMS.