Micro-Electro-Mechanical devices have shown enormous popularity in engineering devices as sensors and actuators. In this paper, the instability, i.e. the dynamic pull-in behavior, of an electrically actuated circular micro-membrane is studied. In order to investigate the periodic solutions, detect bifurcations and follow branches of the solution, the non-linear equation of motion is derived using an energy approach, and, is solved by using a pseudo arc-length continuation and collocation technique. It has been shown that, both hardening and/or softening nonlinear responses could emerge depending on the applied DC voltage. The results indicate that the critical load parameters, namely DC and AC voltages and the excitation frequency, have a major influence on the pull-in characteristics of the micro-membrane. The results reveal different dynamic pull-in mechanisms. In addition, they accurately show the decrease of the pull-in voltage due to dynamic loading.

The proposed approximate solution is very fast and robust for detecting the pull-in instability. It allows observation of both global and local softening behavior even close to dynamic pullin, where the resonance frequency is almost equal to zero.

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