A theoretical response of the electrostatic parallel plate to constant and low-frequency accelerations

• Published in: Smart materials and structures Vol. 18; no. 11; pp. 115004 - 115004 (9)
• Main Author: Lee, Ki Bang
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.11.2009
• ISSN: 0964-1726; 1361-665X
• DOI: 10.1088/0964-1726/18/11/115004

A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration.