This paper investigates the nonlinear response of microelectromechanical system (MEMS) cantilever resonator electrostatically actuated by applying a soft alternating current (AC) voltage and an even softer direct current (DC) voltage between the resonators and a parallel fixed ground plate. The AC frequency is near natural frequency. This drives the resonator into nonlinear parametric resonance. The method of multiple scales (MMS) is used to solve the dimensionless differential equation of motion of the resonator and find the steady-state solutions. The reduced order model (ROM) method is used to validate the results obtained using MMS. The effect of the soft DC voltage (bias) component on the frequency response is reported. It is shown that the DC bias changes the subcritical Hopf bifurcation into a cyclic fold bifurcation and shifts the bifurcation point (where the system loses stability) to lower frequencies and larger amplitudes. 1. Introduction Electrostatically actuated microelectromechanical system cantilever resonators (EA-MEMS-CR) have been explored due to their applications as sensors of small mass objects, such as proteins, viruses, or trace amounts of chemical compounds [1, 2]. Low power, integration into a microchip design, and low cost are a couple of advantages of EA-MEMS-CRs. Resonator sensors are coated for specimen recognition. The sensing principle is based on specimen particles bonding with the coating and increasing the mass of the EA-MEMS-CR. This change in mass causes a change in EA-MEMS-CR’s natural frequency. If the frequency response to input voltage excitation is known accurately, then the increase in mass can be found from the change in natural frequency. One key feature of EA-MEMS-CRs is the nonlinear dynamics they experience [3, 4]. It is crucial to accurately predict the nonlinear dynamics of EA-MEMS-CRs as a precursor to sensing applications. Sources of nonlinearities include micro- and nanoscale surface forces [5], fringe effect [6–8], and damping [1, 9–12]. In order to solve the nonlinear differential equations of motion, methods such as reduced order model (ROM) [1, 5–8], Green’s function [9], multiple scale or perturbation [8, 12], and modal expansion [13], have been used. The steady-state solutions of these systems can be stable and/or unstable. Bifurcation points are points where stability changes. Finding stability change frequencies is necessary to accurately model and take advantage of this phenomenon for sensing purposes. In order to control the behavior of EA-MEMS-CRs, one uses the properties of the applied
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