TY - JOUR

T1 - Dynamics of electrostatic microelectromechanical systems actuators

AU - Yang, Yisong

AU - Zhang, Ruifeng

AU - Zhao, Le

PY - 2012/2/2

Y1 - 2012/2/2

N2 - Electrostatic actuators are simple but important switching devices for microelectromechanical systems applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of these actuators. Here we present two sharp theorems concerning the dynamics of an undamped electrostatic actuator with one-degree of freedom, subject to linear and nonlinear elastic forces, respectively. We prove that both situations are characterized by the onset of one-stagnation-point periodic response below a well-defined pull-in voltage and a finite-time touch-down or collapse of the actuator above this pull-in voltage. In the linear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate of the movable electrode may all be determined explicitly, following the recent work of Leus and Elata based on numerics. Furthermore, in the nonlinear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate may be described completely in terms of the electrostatic and mechanical parameters of the model so that they approach those in the linear-force situation monotonically in the zero nonlinear-force limit.

AB - Electrostatic actuators are simple but important switching devices for microelectromechanical systems applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of these actuators. Here we present two sharp theorems concerning the dynamics of an undamped electrostatic actuator with one-degree of freedom, subject to linear and nonlinear elastic forces, respectively. We prove that both situations are characterized by the onset of one-stagnation-point periodic response below a well-defined pull-in voltage and a finite-time touch-down or collapse of the actuator above this pull-in voltage. In the linear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate of the movable electrode may all be determined explicitly, following the recent work of Leus and Elata based on numerics. Furthermore, in the nonlinear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate may be described completely in terms of the electrostatic and mechanical parameters of the model so that they approach those in the linear-force situation monotonically in the zero nonlinear-force limit.

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U2 - 10.1063/1.3684748

DO - 10.1063/1.3684748

M3 - Article

AN - SCOPUS:84863274661

SN - 0022-2488

VL - 53

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 2

M1 - 022703

ER -