Abstract
Electrostatically deflected elastic systems are studied in areas as diverse as optical switching and cloud electrification. All such systems exhibit an instability commonly known as the “pull-in” or “snap-down” instability. In this instability, when applied voltages are increased beyond a certain critical voltage, there is no steady-state configuration of the system where mechanical members remain separate. The widespread use of electrostatic actuation in the design of micro- and nano-electromechanical systems (MEMS and NEMS) has rekindled an interest in this instability. Here, a mathematical model of a disk-shaped electrostatically actuated system is studied. This model represents a configuration typical of many MEMS/NEMS systems. Solutions to the model are examined for the case of a prescribed voltage drop across the system and for the case where the system is embedded in a capacitive control circuit. The curve of solutions, or bifurcation diagram, is shown to bend back upon itself repeatedly implying the existence of multiple steady-state configurations of the system. The effect of the control scheme is studied by examining the effect on the bifurcation diagram.
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