Abstract

This paper derives three analytical models, namely the full-order, the fourth-order and the third-order models, and the corresponding closed form solutions for the pull-in voltages of micro curled beams subjected to electrostatic loads. The analytical models are derived based on the Euler–Bernoulli beam theory and Taylor's series expansion and are then solved by the energy method. The accuracy of the present models is verified through comparing with former analytical models and the experimentally measured data conducted in former works. It is verified that the present closed form solutions are more accurate than past works. This paper also compares three commonly used assumed deflection shape functions and shows that the natural mode of the beam is the best choice in predicting the pull-in voltage. The present closed form solutions for the pull-in voltage are very convenient and accurate enough for implementation in device design.

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