A reduced-order dynamic model is presented for nonlinear devices subjected to in-plane oscillatory motion. Comparisons between numerical and finite element results demonstrate that the nonlinear behavior of a planar resonator can be predicted accurately by the derived dynamic model with significantly less computation. Simulation results illustrate the effects of nonlinear stiffness, damping ratio, electrostatic driving force, and device dimensions on the nonlinear dynamic behavior. The analysis yields two possible stable responses, depending on the initial rotation angle and rotation rate. The present dynamic model can be easily modified to analyze the nonlinear response of various planar resonators.
Issue Section:
Technical Papers
1.
Yao
, J. J.
, and MacDonald
, N. C.
, 1995, “A Micromachined, Single-Crystal Silicon, Tunable Resonator
,” J. Micromech. Microeng.
0960-1317, 5
, pp. 257
–264
.2.
Pratt
, R. I.
, Johnson
, G. C.
, Howe
, R. T.
, and Chang
, J. C.
, 1991, “Micromechanical Structures for Thin Film Characterization
,” Transducers ’91, Int. Conf. Solid-State Sensors and Actuators
, pp. 205
–208
.3.
Bourouina
, T.
, Garnier
, A.
, and Fujita
, H.
, 2002, “Effect of Direct Current Bias Field and Alternating Current Excitation Field on Vibration Amplitudes and Resonance Frequencies of a Magnetostrictively Actuated Bimorph Microresonator
,” J. Appl. Phys.
0021-8979, 91
, pp. 112
–120
.4.
Tilmans
, H. A. C.
, Elwenspoek
, M.
, and Fluitman
, J. H. J.
, 1992, “Micro Resonant Force Gauges
,” Sens. Actuators, A
0924-4247, 30
, pp. 35
–53
.5.
Yazdi
, N.
, Ayazi
, F.
, and Najafi
, K.
, 1998, “Micromachined Inertial Sensors
,” Proc. IEEE
0018-9219, 86
, pp. 1640
–1659
.6.
Ayazi
, F.
, and Najafi
, K.
, 2001, “A HARPSS Polysilicon Vibrating Ring Gyroscope
,” J. Microelectromech. Syst.
1057-7157, 10
, pp. 169
–179
.7.
Gabbay
, L. D.
, Mehner
, J. E.
, and Senturia
, S. D.
, 2000, “Computer-Aided Generation of Nonlinear Reduced-Order Dynamic Macromodels—I: Non-Stress-Stiffened Case
,” J. Microelectromech. Syst.
1057-7157, 9
, pp. 262
–269
.8.
Mehner
, J. E.
, Gabbay
, L. D.
, and Senturia
, S. D.
, 2000, “Computer-Aided Generation of Nonlinear Reduced-Order Dynamic Macromodels—II: Stress-Stiffened Case
,” J. Microelectromech. Syst.
1057-7157, 9
, pp. 270
–278
.9.
Nayfeh
, A. H.
, Younis
, M. I.
, and Abdel-Rahman
, E. M.
, 2005, “Reduced-Order Models for MEMS Applications
,” Nonlinear Dyn.
0924-090X, 41
, pp. 211
–236
.10.
White
, C. D.
, Xu
, R.
, Sun
, X.
, and Komvopoulos
, K.
, 2003, “Dynamic MEMS Devices for Multi-Axial Fatigue and Elastic Modulus Measurement
,” Proc. SPIE
0277-786X, 4980
, pp. 63
–74
.11.
Koskinen
, J.
, Steinwall
, J. E.
, Soave
, R.
, and Johnson
, H. H.
, 1993, “Microtensile Testing of Free-Standing Polysilicon Fibers of Various Grain Sizes
,” J. Micromech. Microeng.
0960-1317, 3
, pp. 13
–17
.12.
Sharpe
, W. N.
, Yuan
, B.
, Vaidyanathan
, R.
, and Edwards
, R. L.
, 1996, “New Test Structures and Techniques for Measurement of Mechanical Properties of MEMS Materials
,” Proc. SPIE
0277-786X, 2880
, pp. 78
–91
.13.
Madou
, M. J.
, 2002, Fundamentals of Microfabrication: The Science of Miniaturization
, 2nd ed., CRC Press
, Boca Raton, FL.14.
ABAQUS/Standard: User’s Manual
, 5.8 ed., 1998, Hibbitt, Karlsson, and Sorensen
, Providence, RI.15.
Tang
, W. C.
, Lim
, M. G.
, and Howe
, R. T.
, 1992, “Electrostatic Comb Drive Levitation and Control Method
,” J. Microelectromech. Syst.
1057-7157, 1
, pp. 170
–178
.16.
Howe
, R. T.
, and Muller
, R. S.
, 1986, “Resonant-Microbridge Vapor Sensor
,” IEEE Trans. Electron Devices
0018-9383, ED-33
, pp. 499
–506
.17.
Krulevitch
, P. A.
, 1994, “Micromechanical Investigations of Silicon and Ni-Ti-Cu Thin Films
,” Ph.D. dissertation, University of California at Berkeley.18.
Tang
, W. C.
, Nguyen
, T.-C. H.
, and Howe
, R. T.
, 1989, “Laterally Driven Polysilicon Resonant Microstructures
,” Sens. Actuators
0250-6874, 20
, pp. 25
–32
.19.
Bert
, C. W.
, and Stricklin
, J. D.
, 1988, “Comparative Evaluation of Six Different Numerical Integration Methods for Non-Linear Dynamic Systems
,” J. Sound Vib.
0022-460X, 127
, pp. 221
–229
.20.
Buser
, R. A.
, and De Rooij
, N. F.
, 1990, “Very High Q-factor Resonators in Monocrystalline Silicon
,” Sens. Actuators, A
0924-4247, 21
, pp. 323
–327
.21.
Rao
, J. S.
, 1992, Advanced Theory of Vibration: Nonlinear Vibration and One Dimensional Structures
, Wiley
, New York.22.
Den Hartog
, J. P.
, 1985, Mechanical Vibrations
, Dover
, New York.23.
Sun
, X.
, Horowitz
, R.
, and Komvopoulos
, K.
, 2002, ”Stability and Resolution Analysis of a Phase-Locked Loop Natural Frequency Tracking System for MEMS Fatigue Testing
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 124
, pp. 599
–605
.Copyright © 2007
by American Society of Mechanical Engineers
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