Dynamic analysis of an electrostatically actuated circular micro-plate interacting with compressible fluid

This paper investigates the dynamic behavior of a circular micro-plate interacting with compressible fluid and excited by electrostatic force. Utilizing Kirchhoff’s thin plate theory for the actuating micro-plate and assuming inviscidity for the operating fluid, an eigenvalue problem of the coupled system is derived using Fourier-Bessel expansion. Investigating the change in free vibration properties of the system, a parametric study is done accounting for the variation of physical and geometric properties of the bounded domain. Then considering step input voltages, the response of the coupled system, pull-in time, and pull-in voltages are derived. It is shown that besides the electric permittivity the inertial effect of the contained fluid also changes the transient response significantly. The impact of fluid added mass is observed in the decreased response frequencies and increased pull-in times. In addition, by constructing phase plane diagrams, it is found that the attraction zones of stable fixed points vary for different contained fluids. This could affect the response of the micro-plate qualitatively when there exists an uncertainty in the initial conditions.