Stability analysis of an electrically actuated microbeam using the Melnikov theorem and Poincaré mapping

Abstract

In this article, the stability of a microbeam under an electric actuation is studied. The electric actuation is induced by applying a voltage between the microbeam and an electrode plate that lies at the opposite side of the microbeam. In microswitches, the electric actuation is applied as a DC voltage, and in microresonators it is applied as a combination of AC—DC voltages. It is assumed that the midplane of the microbeam is stretched when it is deflected. It is also shown that by the altering DC electric actuation as a control parameter in a microswitch system, a stable and an unstable branches of equilibrium solution is observed, which meet each other at a saddle-node bifurcation point. The stability of a microresonator is studied using the phase plane diagram and Poincaré mapping. It is shown that depending on the value of damping factor, AC and DC electric voltages, and other parameters of the microresonator, a periodic solution, a quasi periodic, or a pull-in instability may be realized. The prediction of possible chaotic behaviour for microresonator is studied using the Melnikov theorem. It is shown that although for selected domain of system parameters the Melnikov function is satisfied for occurrence of chaotic behaviour, for theses parameter values the pull-in instability occurs before going into the chaotic behaviour. Briefly, the system does not realize any chaotic behaviour.