Classification of the nonlinear dynamics in an initially curved bistable micro/nano-electro-mechanical system resonator

The nonlinear dynamics of a bistable micro/nano-electro-mechanical system resonator composed of an arch-shaped microbeam is investigated. The initially curved microbeam is actuated through a combined DC and AC electrostatic parallel plate field. A single degree of freedom model obtained using the Galerkin´s decomposition method with distributed electrostatic force is implemented in order to investigate the resonator dynamics near its primary resonance. According to the shape of the potential energy function which depends on the system parameters, the nonlinear dynamics of the system are classified into certain categories. The appearance of various nonlinear phenomena including dynamic snap-through, dynamic pull-in, chaotic or large amplitude vibrations, hysteresis and softening-type behaviours are discussed within the introduced categories. A typical case scrutinised on detail, showing consequent snap-through instabilities which are responsible for transitions between the present stable configurations of the arch-shaped microbeam. Details of the resulting hysteresis loop governing these transitions are discussed. Moreover, discussion is provided about the formation of the hysteresis loops which can affect the filtering functionality of the proposed bistable MEMS resonator.