Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation

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.