Bifurcation analysis of electrostatically actuated MEMS micro-beam

Abstract

Abstract The aim of this paper is to investigate the effects of micro-beam stiffness and length change to the dynamic of the system. The nonlinear vibrations model of microbeam is simplified by Galerkin method and then transformed into a dynamical system. Based on the emergence of zero eigen values and the increase in the number of equilibria, the equation is analysed using normalization and the bifurcation diagram is drawn. Hopf and Pitchfork bifurcation showed by the normalized equation. The change of both parameters, stiffness and length, exhibits a codimension 2 bifurcation, Pitchfork–Hopf bifurcation. And, when we make a roundtrip around the Pitchfork–Hopf point, we meet Pitchfork bifurcation twice, a Hopf bifurcation, and a heteroclinic cycle.