Dynamics of a parallel-plate electrostatic actuator in viscous dielectric media

Abstract

Understanding the dynamics of a parallel-plate electrostatic actuator, that is, the complex temporal interactions between the mechanical and electrostatic nonlinearities will help optimize the actuator performance for micromanipulation applications. In this paper, we analyze the response of the actuator in a clamped–clamped configuration immersed in viscous dielectric media. We model the actuator as a continuous system by deriving a reduced-order model, and solving it by employing the Galerkin method and linear undamped mode shapes for a clamped–clamped beam. Our model incorporates the inertial loading effect and squeeze film damping by the media, nonlinear mid-plane stretching forces in the beam electrode of the actuator, and nonlinear contact force during the physical contact of the beam electrode with the stationary electrode. The model is utilized to study the actuator dynamics over a broad range, three orders of magnitude of viscosity and two orders of magnitude of relative permittivity of the media. We report three main observations: (1) the actuator response near the vicinity of the pull-in instability region is sensitive to the external forces such as electrostatic force and viscous damping force; (2) the actuator at lower actuation voltages and/or higher actuation frequencies can be approximated to be a linear system; and (3) the high relative permittivity of a media amplifies the generated force, resulting in pull-in to occur at lower actuation voltage amplitudes, and the high dynamic viscosity of a media increases the pull-in time.