On the Nonlinear Dynamics of Tether Suspensions for MEMS

[+] Author and Article Information
Wyatt O. Davis, Oliver M. O’Reilly

Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740e-mail: oreilly@me.berkeley.edu

Albert P. Pisano

Departments of Mechanical Engineering and Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720-1740e-mail: appisano@me.berkeley.edu

J. Vib. Acoust 126(3), 326-331 (Jul 30, 2004) (6 pages) doi:10.1115/1.1760558 History: Received September 01, 2002; Revised April 01, 2003; Online July 30, 2004
Copyright © 2004 by ASME
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Tang,  W. C., Nguyen,  T. C. H., and Howe,  R. T., 1989, “Laterally Driven Polysilicon Resonant Microstructures,” Sens. Actuators, A, 20A, pp. 25–32.
Clark, W. A., Howe, R. T., and Horowitz, R., 1996, “Surface Micromachined Z-Axis Vibratory Rate Gyroscope,” Proceedings of the Solid-State Sensor and Actuator Workshop, Hilton Head Island, South Carolina, June 2–6, 1996, pp. 283–287.
Juneau, T., and Pisano, A. P., 1997, “Dual-Axis Operation of a Micromachined Rate Gyroscope,” Proceedings of the 9th International Conference on Solid-State Sensors and Actuators (Transducers ’97), Chicago, June 16–19, 1997, pp. 883–886.
Nguyen, C. T.-C., 1995, “Micromechanical Resonators for Oscillators and Filters,” Proceedings of the IEEE International Ultrasonics Symposium, Seattle, November 7–10, 1995, pp. 489–499.
Tilmans,  H. A. C., Elwenspoek,  M., and Fluitman,  J. H. J., 1994, “Micro Resonant Force Gauges,” Sens. Actuators, A, 43A, pp. 35–53.
Wang,  K., Wong,  A.-C., and Nguyen,  C. T.-C., 2000, “VHF Free-Free Beam High-Q Micromechanical Resonators,” J. Microelectromech. Syst., 9(3), 347–360.
Pratt, R. I., Johnson, G. C., Howe, R. T., and Chang, J. C., 1991, “Micromechanical Structures for Thin Film Characterization,” Proceedings of the 6th International Conference on Solid-State Sensors and Actuators (Transducers ’91), San Francisco, June 23–27, 1991, pp. 205–208.
Gui,  C., Legtenberg,  R., Tilmans,  H. A. C., Fluitman,  J. H. J., and Elwenspoek,  M., 1998, “Nonlinearity and Hysteresis of Resonant Strain Gauges,” J. Microelectromech. Syst., 7(1), pp. 122–127.
Fujita, T., Hatano, K., Maenaka, K., Mizuno, T., Matsuoka, T., Kojima, T., Oshima, T., and Maeda, M., 1999 “Vacuum Sealed Bulk-Micromachined Gyroscope,” Proceedings of the 10th International Conference on Solid-State Sensors and Actuators (Transducers ’99), Sendai, Japan, June 7–10, 1999, pp. 914–917.
Turner,  K. L., Miller,  S. A., Hartwell,  P. G., MacDonald,  N. C., Strogatz,  S. H., and Adams,  S. G., 1998, “Five Parametric Resonances in a Microelectromechanical System,” Nature (London), 396(12), pp. 149–152.
Turner, K. L., and MacDonald, N. C., 2000, “Understanding Parametric Resonance Effects in Common MEM Actuators,” Proceedings of the Solid-State Sensor and Actuator Workshop, Hilton Head Island, South Carolina, June 4–8, 2000, pp. 359–362.
Bourouina,  T., Garnier,  A., Fujita,  H., Masuzawa,  T., and Peuzin,  J.-C., 2000, “Mechanical Nonlinearities in a Magnetically Actuated Resonator,” J. Micromech. Microeng., 10, pp. 265–270.
Senturia, S. D., 2001, Microsystem Design, Kluwer Academic Publishers, Dordrecht.
Davis, W. O., 2001, “Mechanical Analysis and Design of Vibratory Micromachined Gyroscopes,” Ph.D. thesis, University of California at Berkeley.
Davis, W. O., and Pisano, A. P., 1998, “On the Vibrations of a MEMS Gyroscope,” Proceedings of the 1st International Conference on the Modelling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM98), Santa Clara, California, April 6–8, 1998, pp. 557–562.
Davis, W. O., Pisano, A. P., and O’Reilly, O. M., 2002, “Designing Tether Suspensions for MEMS in the Presence of Nonlinearities,” Preprint Department of Mechanical Engineering, Uvinversity of California at Berkeley.
Antman, S. S., 1995, Nonlinear Problems of Elasticity, Springer-Verlag, New York.
Naghdi, P. M., 1982, “Finite Deformation of Elastic Rods and Shells,” Proceedings of the IUTAM Symposium on Finite Elasticity, Bethlehem PA 1980, (D. E. Carlson and R. T. Shield, editors), Martinus Nijhoff, The Hague, pp. 47–104.
Rubin, M. B., 2000, Cosserat Theories: Shells, Rods, and Points, Kluwer Academic Publishers, Dordrecht.
Green,  A. E., and Laws,  N., 1973, “Remarks on the Theory of Rods,” J. Elast., 3, pp. 179–184.
O’Reilly, O. M., and Turcotte, J. S., 1996, “Some Remarks on Invariance Requirements for Constrained Rods,” Math. Mech. Solids, 1 (3) pp. 343–348.
Juneau, T., 1998, “Micromachined Dual Input Rate Axis Gyroscope,” Ph.D. thesis, University of California at Berkeley.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley & Sons, New York.
Fedder, G. K., 1994, “Simulation of Microelectromechanical Systems,” Ph.D. thesis, University of California at Berkeley.


Grahic Jump Location
Scanning electron micrograph (SEM) of a surface-micromachined dual-axis gyroscope, after Juneau and Pisano 3. It was fabricated by Sandia National Laboratory for this research. As may be seen from the SEM, the outer ring serves as the proof mass which is attached to the substrate by tethers and actuated by eight comb drives. This gyroscope is designed to measure the two in-plane components of the angular velocity of the substrate.
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Three geometries of tethers suspensions of interest: (a) inside-suspended ring, (b) outside-suspended ring, and (c) translational body.
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The tether geometry and the reference configuration of the Cosserat rod. The axial centerline of the rod coincides with the reference configuration of the material curve C of the Cosserat rod and D3=E3.
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Schematic of a proof mass (rotor) suspended by four identical tethers of length L.
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Predictions of the restoring torque as a function of angular displacement ϕ. The parameter values for the chosen device are given in Table I.
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Sensing method used to measure the frequency response of the gyroscope. The voltages vin and vout were supplied and measured, respectively, using a network analyzer.
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Sample frequency responses for the gyroscope which were measured using the experimental apparatus shown in Fig. 6. The DC bias voltage was 5 V and results are shown for vin=1, 5, and 10 mV. In the interests of clarity, only forward sweeps are shown. The ambient pressure for these results was 22 mTorr.
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Predicted frequency responses of the gyroscope according to (22). In the interests of comparison to Fig. 7, only forward sweeps in frequency are shown.



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