Dynamics of large oscillations in electrostatic MEMS

Abstract

We present a comprehensive experimental study of the dynamics of electrostatic MEMS resonators under large excitations. We identified three frequency ranges where large oscillations occur; a non-resonant region driven by fast–slow dynamic interactions and two resonant regions. In these regions, we found a plethora of dynamic phenomena including cascades of period-doubling bifurcations, a bubble structure, homoclinic and cyclic-fold bifurcations, hysteresis, intermittencies, quasiperiodicity, chaotic attractors, odd-periodic windows within those attractors, Shilnikov orbits, and Shilnikov chaos.

We encountered these complex nonlinear dynamics phenomena under relatively high dissipation levels, the quality factors of the resonators examined in this study were Q $=$ 6.2 and 2.1. In the case of MEMS with higher quality factors $(Q>100)$, it is quite reasonable to expect those phenomena to appear under relatively low excitation levels (compared to the static pull-in voltage). This calls for a new paradigm in the design of electrostatic MEMS that seeks to manage dynamic phenomena rather than attempt to avoid them and, thereby, overly restricting the design space. We believe this is feasible given the repeatable and predictable nature of those phenomena.