Chaos ; Bifurcation ; MEMS ; Electrostatic actuators
The dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated. The parameter space of the resonator actuation voltage is investigated to determine the optimal operating regions. Bifurcation diagrams of the resonator response are obtained at five different actuation voltage levels. The resonator exhibits bi-stability with two coexisting stable equilibrium points located inside a lower and an upper potential wells. Steady-state chaotic attractors develop inside each of the potential wells and around both wells. The optimal region in the parameter space for mass sensing purposes is determined. In that region, steady-state chaotic attractors develop and spend most of the time in the safe lower well while occasionally visiting the upper well. The robustness of the chaotic attractors in that region is demonstrated by studying their basins of attraction. Further, regions of large dynamic amplification are also identified in the parameter space. In these regions, the resonator can be used as an efficient long-stroke actuator.
Seleim, A., Towfighian, S., Delande, E., Abdel-Rahman, E., & Heppler, G. (2012). Dynamics of a close-loop controlled MEMS resonator. Nonlinear Dynamics, 69(1), doi: 10.1007/s11071-011-0292-z 615-633.
Seleim, Abdulrahman; Towfighian, Shahrzad; Delande, Emmanuel; Abdel-Rahman, Eihab; and Heppler, Glenn, "Dynamics of a Close-Loop Controlled MEMS Resonator" (2012). Mechanical Engineering Faculty Scholarship. 13.