Coupling and tuning of modal frequencies in direct current biased microelectromechanical systems arrays

Understanding the coupling of different modal frequencies and their tuning mechanisms has become essential to design multi-frequency MEMS devices. In this work, we fabricate a MEMS beam with fixed boundaries separated from two side electrodes and a bottom electrode. Subsequently, we perform experiments to obtain the frequency variation of in-plane and out-of-plane mechanical modes of the microbeam with respect to both DC bias and laser heating. We show that the frequencies of the two modes coincide at a certain DC bias, which in turn can also be varied due to temperature. Subsequently, we develop a theoretical model to predict the variation of the two modes and their coupling due to a variable gap between the microbeam and electrodes, initial tension, and fringing field coefficients. Finally, we discuss the influence of frequency tuning parameters in arrays of 3, 33, and 40 microbeams, respectively. It is also found that the frequency bandwidth of a microbeam array can be increased to as high as 25kHz for a 40 microbeam array with a DC bias of 80V.