Frequency response of an electrostatically actuated micro resonator in contact with incompressible fluid

This paper investigates the nonlinear vibration and frequency response of a micro-resonator operated in an incompressible fluid cavity. The electrical force composed from direct current (DC) and alternative current (AC) is used to excite the micro-beam. Considering nonlinear electrostatic force and inertia effect of operating fluid which formulated using linear Bernoulli’s equation, governing equation of the system are derived. Employing the kinematic and compatibility conditions and making use of Galerkin projection method the nonlinear ordinary differential equations are extracted. Multiple scales method is employed to deal with nonlinear governing equation. A parametric study is conducted to evaluate the effect of fluidic confinement on the frequency response of the system. It is shown that the softening behavior increases with increasing the dielectric constant and density of the operating fluid. However, the softening behavior is shown to decrease due to presence of the viscosity. The obtained results reveal that as the DC voltage increases, the frequency curves bend more to the left, implying that the softening behavior of the system increases. In addition, it is observed that the amplitude of the AC component could change the resonant curves significantly.