Dynamic Response of an Electrostatically Actuated Micro-Beam in an Incompressible Viscous Fluid Cavity

This paper studies the dynamic instability of cantilever micro-beam submerged in an incompressible viscous fluid cavity and actuated by electrostatic force. Equivalent squeeze film damping is incorporated in the vibrational equation of the micro-beam to obtain the natural frequencies of the coupled system. Then, imposing various step voltages, dynamic responses, and pull-in conditions of the micro-beam are studied. A parametric study is conducted to evaluate the effect of fluidic confinement on the instability voltage. Dielectric constant of the fluid proves dominantly influential compared with viscosity and density. In addition, values of pull-in voltage are seen to be highly dependent on the vertical position as well as the length of the micro-beam.