An analytical model considering the fringing fields for calculating the pull-in voltage of micro curled cantilever beams

Abstract

This paper derives a high precision analytical solution to determine the pull-in voltages of a micro curled beam subjected to electrostatic loads. The analytical model considers the fringing fields between the micro curled beam and the ground plane as well as the initial curling induced by the stress gradient. Furthermore, the electromechanical coupling effects are also involved in the present analytical model. Then the analytical solution of pull-in voltage is obtained by the energy method. By comparing with the other published analytical models as well as the experimentally measured data, the accuracy of the present analytical solution is verified to be more accurate than the other published works. The present analytical solution can determine the pull-in voltage with a maximum deviation of 1% from the experimentally measured results as the ratio of the beam length to the width is greater than 5.