Frequency Analysis of Linearly Coupled Modes of MEMS Arrays

Microelectromechanical system (MEMS) based arrays have been employed to increase the bandwidth and sensitivity of many sensors and actuators. In this paper, we present an approximate model to demonstrate the tuning of in-plane and out-of-plane frequencies of MEMS arrays consisting of fixed-fixed beams. Subsequently, we apply the Galerkin's method with single approximate mode to obtain the reduced-order static and dynamic equations. Corresponding to a given direct current (DC) voltage, we first solve the static equations and then obtain corresponding frequencies from the dynamic equation for single beam and arrays of multibeams. We compare the model with available experimental results. Later, we show the influence of different frequency tuning parameters such as the initial tensions, fringing field coefficients and the variable inter beam gaps between the microbeam and electrodes to control the coupling region and different modal frequencies of the beam. Finally, we obtain a compact model which can be used in optimizing the bandwidth and sensitivity of microbeams array.