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-ofplane 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 25 kHz for a 40 microbeam array with a DC bias of 80 V. V

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Microelectromechanical system (MEMS) and Nanoelectromechanical system (NEMS) are mostly actuated by direct forcing due to electrostatic excitation. In general, the electrostatic forcing consists of two main components, the first is the direct forcing which is based on parallel plate capacitance and another is due to the fringing effects. As the size of the beam and its cross section reduces from microscale to nanoscale, the effect of direct forcing diminishes because the overlapping area also reduces. Consequently, the fringing force effect remains the only viable factor to excite the beams electrostatically. In this paper, we present the nonlinear analysis of fixed–fixed and cantilever beams subjected to the direct force excitation, the fringing force excitation, and the combined effect of direct and fringing forces. In the present configuration, while the direct forcing is achieved by applying voltage across the beam and the bottom electrode, the fringing force can be introduced by applying voltage across the beam and the symmetrically placed side electrodes. To do the analysis, we first formulate the equation of motion considering both kinds of forces. Subsequently, we apply the method of multiple scale, MMS, to obtain the approximate solution. After validating MMS with the numerical simulation, we discuss the influence of large excitation amplitude, nonlinear damping, and the nonlinear stiffness under different forcing conditions. We found that fringing force introduces parametric excitation in the system which may be used to significantly increase the response amplitude as well as frequency bandwidth. It is also found that under the influence of the fringing forces from the side electrodes, the pull-in effect can be improved. Furthermore, the present study can be used to increase the sensitivity as well as the operating frequency range of different MEMS and NEMS based sensors under combined forcing conditions.