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Abstract

This paper presents several analytical solutions for the conventional electrostatic parallel-plate model and explains the effect of the quality factor decrease with the voltage applied. Such a model is of importance in the development of electrostatic (capacitive) sensors and actuators including acoustical transducers and loudspeakers, and micro/nanoelectromechanical systems (MEMS/NEMS). It serves to reveal and interpret the basic phenomena (in particular, the “pull-in” instability and “negative spring” effect) but there is still some room for new effects and analytical results, although the model is nonlinear and provides rather computational than comprehensible close-form relationships as “negative quality factor effect” described in this paper. The new results obtained can be supportive to analyze, test, and design electrostatic sensors and actuators.

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References

Ai, S. and Pelesco, J. A., 2001, “Dynamics of a canonical electrostatic MEMS/NEMS system,” School of Mathematics and CDSNS, Georgia Institute of Technology, Atlanta, Georgia, pp. 1-33 .

Anderson, M. J., Hill, J. A., Fortunko, C. M., Dogan, N. S., and Moore, R. D., 1995, “Broadband electrostatic transducers: modeling and experiments,” Journal of the Acoustical Society of America 97, 262-272 .

Blech, J. J., 1983, “On isothermal squeeze films,” Journal of Lubrication Technology 105, 615-620 .

Den Hartog, J. P., 1985, Mechanical Vibrations, Dover, New York .

Harris, C. M., 1998, Handbook of Acoustical Measurements and Noise Control, Acoustical Society of America, New York .

Hildebrand, F. B., 1974, Introduction to Numerical Analysis, Dover, New York .

Hunt, E. V., 1954, Electroacoustics, Acoustical Society of America, New York .

Kamke, E., 1959, Differentialgleichungen, Teubner, Leipzig .

Kim, P. and Lieber, C. M., 1999, “Nanotube nanotweezers,” Science 286, 2148-2150 .

10.

Korn, G. A., 1961, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York .

11.

Langlois, W. E., 1962, “Isothermal squeeze films,” Quarterly Applied Mathematics 20(2), 131-150 .

12.

Morse, P. M., 1991, Vibration and Sound, Acoustical Society of America, New York .

13.

Muller L., 2000, Gimballed Electrostatic Microactuators with Embedded Interconnects, Ph.D. dissertation, University of California at Berkeley, California.

14.

Nathanson, H. C., Newell, W. E., Wickstrom, R. A., and Davis, J. R., 1967, “The resonant gate transistor,” IEEE Transactions on Electronic Devices 14(3), 117-133 .

15.

Seeger, J. I., and Boser, B. E., 1999, “Dynamics and control of parallel-plate actuators beyond the electrostatic instability,” in Transducers '99, Sendai, Japan, June 7-10, pp. 474-477 .

16.

Shi, E, Ramesh, P., and Murkherjee, S., 1995, “Simulation methods for microelectromechanical structures (MEMS) with application to a microtweezer,” Computers & Structures 56(5), 769-783 .

17.

Srinivasan, P., 1995, Nonlinear Mechanical Vibrations, Wiley, New York .

18.

Wilson, E. B., Jr., 1990, An Introduction to Scientific Research, Dover, New York .

Feasible Analytical Solutions for Electrostatic Parallel-Plate Actuator or Sensor

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