Many MEM devices feature tether suspensions and it is known that the tethers induce a stiffening behavior. In this paper, we develop a model for a tether and, from it, establish several useful expressions for the nonlinear restoring forces and torques it provides. For a specific gyroscope, the expressions we find are compared to experimental results.

1.
Tang
,
W. C.
,
Nguyen
,
T. C. H.
, and
Howe
,
R. T.
,
1989
, “
Laterally Driven Polysilicon Resonant Microstructures
,”
Sens. Actuators, A
,
20A
, pp.
25
32
.
2.
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.
3.
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.
4.
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.
5.
Tilmans
,
H. A. C.
,
Elwenspoek
,
M.
, and
Fluitman
,
J. H. J.
,
1994
, “
Micro Resonant Force Gauges
,”
Sens. Actuators, A
,
43A
, pp.
35
53
.
6.
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
.
7.
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.
8.
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
.
9.
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.
10.
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
.
11.
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.
12.
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
.
13.
Senturia, S. D., 2001, Microsystem Design, Kluwer Academic Publishers, Dordrecht.
14.
Davis, W. O., 2001, “Mechanical Analysis and Design of Vibratory Micromachined Gyroscopes,” Ph.D. thesis, University of California at Berkeley.
15.
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.
16.
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.
17.
Antman, S. S., 1995, Nonlinear Problems of Elasticity, Springer-Verlag, New York.
18.
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.
19.
Rubin, M. B., 2000, Cosserat Theories: Shells, Rods, and Points, Kluwer Academic Publishers, Dordrecht.
20.
Green
,
A. E.
, and
Laws
,
N.
,
1973
, “
Remarks on the Theory of Rods
,”
J. Elast.
,
3
, pp.
179
184
.
21.
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.
22.
Juneau, T., 1998, “Micromachined Dual Input Rate Axis Gyroscope,” Ph.D. thesis, University of California at Berkeley.
23.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley & Sons, New York.
24.
Fedder, G. K., 1994, “Simulation of Microelectromechanical Systems,” Ph.D. thesis, University of California at Berkeley.
You do not currently have access to this content.