A comprehensive study of stability in an electro-statically actuated micro-beam

Abstract

This paper studies the mechanical and bifurcation behavior of a capacitive micro-beam suspended between two conductive stationary plates, which can be used as a micro-switch or as a RF resonator. The equation of dynamic motion of the micro-switch is obtained using Euler–Bernoulli beam theorem. The equilibrium positions or the fixed points of the micro-switch are obtained by solving the equation of the static deflection using the step-by-step linearization method (SSLM) and discretizing by Galerkin weighted residual method. In order to study the global stability of the obtained fixed points a modified non-linear mass–spring model is used. Non-linear motion trajectories in phase portraits are given and regions of bounded and unbounded solutions separated by a homoclinic or heteroclinic orbits and positions of the stationary conductive plates are illustrated. Critical values of the applied voltage leading to qualitative changes in the micro-beam behavior through a saddle node or pitch fork bifurcations for different values of the gap and voltage ratios are obtained. The effects of different gaps and voltage ratios also are investigated.