Effect of Microbeam Electrical Resistivity on Dynamic Pull-In Voltage of an Electrostatically Actuated Microbeam

Abstract

The dynamic pull-in voltage as a criterion for the system stability is one of the most important effects considered with the dynamics of microstructures. In this study effect of microbeam electrical resistivity on the pull-in voltage of an electrostatically actuated microbeam is investigated. Assuming Euler-Bernoulli theory for the microbeam, two coupled nonlinear partial differential equations are derived for the beam deflection and voltage. The one parameter Galerkin method is implemented to transform the equations to a set of nonlinear coupled ordinary differential equations. Obtained equations are solved implementing the differential quadrature method (DQM). Variation of dynamic pull-in voltage with changing the microbeam electrical resistivity with different boundary conditions and different configurations of voltage application, is investigated. Considering effect of resistivity on the deflection of the beam, it is observed that at a certain resistivity called critical resistivity there exists a jump in frequency with a peak in damping of the beam. Results indicate that the dynamic pull-in voltage increases when the microbeam electrical resistivity is increased and reaches the static pull-in voltage for resistivities higher than this critical resistivity.