Dynamics of a Canonical Electrostatic MEMS/NEMS System
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The mass-spring model of electrostatically actuated microelectromechanical systems (MEMS) or nanoelectromechanical systems (NEMS) is pervasive in the MEMS and NEMS literature. Nonetheless a rigorous analysis of this model does not exist. Here periodic solutions of the canonical mass-spring model in the viscosity dominated time harmonic regime are studied. Ranges of the dimensionless average applied voltage and dimensionless frequency of voltage variation are delineated such that periodic solutions exist. Parameter ranges where such solutions fail to exist are identified; this provides a dynamic analog to the static “pull-in” instability well known to MEMS/NEMS researchers.
KeywordsMEMS nanotechnology electrostatics periodic solutions saddle-node bifurcation shooting method
Mathematics Subject Classification (1991)34C15 34C60 70K40
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- 5.Camon, H., Larnaudie, F., Rivoirard, F., and B. Jammes, B. (1999). Analytical simulation of a 1D single crystal electrostatic micromirror. Proc. Model. Simul. Microsyst., pp. 628–631.Google Scholar
- 6.Chan E.K., Kan E.C., Dutton R.W., and Pinsky M.P. (1997). Nonlinear dynamic modeling of micromachined microwave switches. IEEE MTT-S Digest 3, 1511–1514Google Scholar
- 7.Chu, P. B., and Pister, K. S. J. (1994). Analysis of closed-loop Control of parallel-plate electrostatic microgrippers. Proc. IEEE Int. Conf. Robotics and Automation, pp. 820–825.Google Scholar
- 11.Hirsch M.W., Smale S., and Devaney R.L. (2004). Diffenential equations, dynamical systems, and an introduction to chaos, 2nd edn. Elsevier/Academic Press, AmsterdamGoogle Scholar
- 13.Muldavin, J. B., and Rebeiz, G. M. (1999). 30 GHz Tuned MEMS Switches. IEEE MTT-S Digest, pp. 1511–1518.Google Scholar
- 17.Seeger, J. I., and Boser, B. E. (1999). Dynamics and Control of Parallel-Plate Actuators Beyond the Electrostatic Instability, Transducers ’99, pp. 474–477.Google Scholar