Pull-in analysis of non-uniform microcantilever beams under large deflection

Cantilever beams under the influence of electrostatic force form an important subclass of microelectromechanical system(MEMS) and nanoelectromechanical system. Most of the studies concerning these micro-nano resonators are centered around uniform cantilever beams. In this paper, we have investigated another class of micro-resonators consisting of non-uniform cantilever beams. The study is focused around investigating pull-in voltage and resonance frequency of non-uniform cantilever beams when they operate in the linear regime about different static equilibriums. In this paper, we term this frequency as “linear frequency.” Calculation of the linear frequency is done at different static equilibriums corresponding to different DC voltages. We have studied two classes of beams, one with increasing cross sectional area from the clamped edge (diverging beam) and other with decreasing cross sectional area from the clamped edge (converging beam). Within each class, we have investigated beams with linear as well as quartic variation in width. We start by obtaining Euler beam equation for non-uniform cantilever beams considering large deflection and their corresponding exact mode shapes from the linear equation. Subsequently, using the Galerkin method based on single mode approximation, we obtain static and dynamic modal equations for finding pull-in voltage and resonance frequency as a function of DC voltage, respectively. We found that the linear frequency of converging beams increases with increase in non-uniform parameter (α) while those of diverging beams decreases with α. A similar trend is observed for pull-in voltage. Within the converging class, beams with quartic variation in width show significant increase in both frequency and pull-in voltage as compared to corresponding linearly tapered beams. In quantitative terms, converging beams with quartic variation in width and α=−0.6 showed an increase in linear frequency by a factor of 2.5 times and pull-in voltage by 2 times as compared to commonly used uniform beams. Our investigation can prove to be a step forward in designing highly sensitive MEMS sensors and actuators