Stabilization of Electrostatically Actuated Micro-pipe Conveying Fluid Using Parametric Excitation

Abstract

This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. Mathieu type equation of the system is obtained by applying Taylor series expansion and Galerkin method to the nonlinear partial differential equation of motion. Floquet theory is used to extract the transition curves and stability margins in physical parameters space (Vdc-Vac). In addition, the stability margins are plotted in flow velocity and excitation amplitude space (u-Vac space). The results depict that the micro-pipe remains stable even if the flow velocity is more than the critical value for a certain dc voltage. For instance, in absence of the (ac) component, it is shown that pull-in voltages associated to critical velocities 3 and 6 are 14.06 and 5.4 volt, respectively. However, transition curves show that superimposing an (ac) component with forcing frequency Ω=10 increases the pull-in voltage beyond these values. Furthermore, for the present pull-in voltages the critical velocities 3 and 6 could be increases with imposing some (ac) component. These results are discussed in detail in simulation results section where the transion curves are ploted quantitatively.