Global Nonlinear Dynamics of MEMS Arches Actuated by Fringing-Field Electrostatic Field

Electrostatically actuated microbeams are a basic structural components mainly used in MEMS and possessing a wide range of applications such as sensors, actuators, resonators, filters, etc.... The pull-in instability and the smaller stroke length, are some of the major challenges in conventional parallel-plates-based electrostatics MEMS actuators, which somehow limit their respective application. Hence, a smart technique relying on the so-called electrical fringing field actuation offers a possibility of overcoming the above limitations and resulting in structural enhancement of MEMS devices. Along this line, the nonlinear dynamic behavior of a resonant MEMS arch microbeam actuated by fringing electric field with the ground electrodes placed at either side of it is presented in this work. The nonlinear equation of motion of the beam is solved using finite difference method to get the dynamic frequency responses of the microbeam. Linear resonant peaks are observed for the cases of low AC dynamic loading and high damping when the actuation frequency coincides with the devices’ various natural frequencies. The peaks of the resonance begin to shift away from the natural frequencies of the device demonstrating nonlinear phenomenon of softening and hardening with the increase in dynamic AC loading and decrease in the damping. Superharmonic frequencies at one-half or one-third of the natural frequencies and subharmonic frequencies at twice or thrice the natural frequencies are also triggered for various cases of nonlinear frequency response.