Nonlinear dynamics of a micro-electro-mechanical system with time-varying capacitors

The natural frequency and responses of a micro-electro-mechanical system (MEMS) with time-varying capacitors are determined under an equivalent direct current (DC) voltage. Under alternating current (AC) voltages, the resonant condition and the corresponding resonant motion possessing a wide energy band for such a system are investigated because the motion with the wide energy band is very easily sensed. For a given voltage strength, the AC frequency band is obtained for chaotic resonant motions in the specific resonant layer The numerical and analytical predictions of such a motion are in a acceptable agreement, and the dynamic model provides the range prediction of the alternating current and voltage on the capacitor agreeing with experimental measurements. The lower-order resonant motion has a higher energy than the higher-order resonant motions, which indicates that the lower-order resonant motion can be easily sensed. Although this model is developed from a specified MEMS, the analysis and results can be applied to other dynamic systems.