Dynamics and pull-in instability of electrostatically actuated microbeams conveying fluid

The purpose of this paper is to develop a theoretical model for predicting the dynamics and pull-in mechanism of electrostatically actuated microbeams containing internal fluid flow. By considering the effects of nonuniform profile of the flow velocity, material length scale parameter of the microbeam and nonlinear electro-statical force, the equation of motion of the microbeam has been presented. The lateral displacement of the microbeam consists of two parts: a static (steady) displacement and a perturbation displacement about the static. Based on the general differential quadrature rule, the static deflection of the microbeam is calculated numerically. The obtained static deflection is then used to solve the equation governing the perturbed displacement. The natural frequency and flow-induced instability of the microbeam are analyzed for both clamped-clamped and cantilevered boundary conditions. Results show that the internal fluid flow could dramatically affect the static deflection of the microbeam and hence the pull-in voltage. The electric voltage, on the other hand, would significantly influence the dynamics of the microbeam.