Pull-In Dynamics of Variable-Width Electrostatic Microactuators

Determination of pull-in parameters is vital in the design of electrostatically actuated microdevices. Moreover, it is important to devise some means to gain a control over the pull-in parameters in order to establish the customized microactuator design practice. In this paper, we analyze the influence of the beam geometry on the dynamic pull-in parameters of electrostatically actuated microbeams. Novel width functions are proposed for the microcantilever and the fixed-fixed beam, which smoothly vary the width of the microbeam along its length. We demonstrate the use of these width-functions by comparing six different microbeam geometries, three for cantilevered beam and three for fixed-fixed beam along with their constant width rectangular counterparts. All configurations are analyzed using an energy technique which gives an upper bound on the critical amplitude of the microbeam displacement, which is subsequently used to extract a lower bound on the applied voltage at the point of dynamic pull-in instability. For every case, a comparison is made between the static and the dynamic pull-in parameters. Results indicate a greater pull-in range for concave beam geometries, while the convex geometries exhibit a reduction in the pull-in range. Actuation voltage requirement is found to be proportional to the increase in the travel range. In all cases, the dynamic pull-in displacement is found to be greater than the static pull-in displacement, while the dynamic pull-in voltage is found to be less than the static pull-in voltage.