We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.
On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 30, 2018; final manuscript received January 29, 2019; published online February 15, 2019. Assoc. Editor: Eihab Abdel-Rahman.
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Ilyas, S., Alfosail, F. K., and Younis, M. I. (February 15, 2019). "On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators." ASME. J. Comput. Nonlinear Dynam. April 2019; 14(4): 041006. https://doi.org/10.1115/1.4042694
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