Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors under parametric excitation

IEEE Sensors Journal

Volumn 7, Issue 3, 2007, Pages 370-380

  Zhang, Wen Ming ^a   Meng, Guang ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Electrostatic force; Microelectromechanical systems (MEMS); Parametric excitation; Resonant sensor

Indexed keywords

ELECTROSTATICS; FREQUENCY RESPONSE; MICROSENSORS; NATURAL FREQUENCIES; PARAMETER EXTRACTION; VIBRATIONS (MECHANICAL);

DYNAMIC PARAMETERS; MEMS RESONANT SENSORS; STEADY-STATE DYNAMICS;

MEMS;

EID: 33847759961     PISSN: 1530437X     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSEN.2006.890158     Document Type: Article

References (31)

1. M. I. Younis, E. M. Abdel-Rahman, and A. H. Nayfeh, "Dynamic simulations of a novel RF MEMS switch," in Proc. 7th Int. Conf. Modeling and Simulation of Microsystems: NanoTech, Boston, MA, 2004, pp. 287-290.
2. L. Lin, C. T.-C. Nguyen, R. T. Howe, and A. P. Pisano, "Microelectromechanical filters for signal processing," in Proc. IEEE MEMS, Travemunde, Germany, 1992, pp. 226-231.
3. W. Zhang, R. Baskaran, and K. L. Turner, "Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor," Sens. Actuators A, vol. 102, pp. 139-150, 2002.
4. M. I. Younis and A. H. Nayfeh, "A study of the nonlinear response of a resonant microbeam to electric actuation," Nonlinear Dyn., vol. 31, pp. 91-117, 2003.
5. Z. Jin and Y. Wang, "Electrostatic resonator with second superharmonic resonance," Sens. Actuators A, vol. 64, pp. 273-279, 1998.
6. A. Erbe, H. Krommer, R. H. Blick, G. Corso, and K. Richter, "Mechanical mixing in nonlinear nanomechanical resonators," Appl. Phys. Lett., vol. 77, pp. 3102-3104, 2000.
7. K. L. Turner, S. A. Miller, P. G. Hartwell, N. C. MacDonald, S. H. Strogatz, and S. G. Adams, "Five parametric resonances in a micromechanical system," Nature, vol. 396, pp. 149-152, 1998.
8. J. F. Rhoads, S. W. Shaw, K. L. Turner, and R. Baskaran, "Tunable microelectromechanical filters that exploit parametric resonance," J. Vibr. Acoust., vol. 127, no. 5, pp. 423-430, 2005.
9. S. Krylov, I. Harari, and Y. Cohen, "Stabilization of electrostatically actuated microstructures using parametric excitation," J. Micromech. Microeng., vol. 15, pp. 1188-1204, 2005.
10. W. M. Zhang and G. Meng, "Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS," Sens. Actuators A, vol. 119, pp. 291-299, 2005.
11. D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, "Parametric amplification in a torsional microresonator," Appl. Phys. Lett., vol. 77, pp. 1545-1547, 2000.
12. M. Zalalutdinov, A. Olkhovets, B. Ilic, D. Czaplewski, and H. G. Craighead, "Optically pumped parametric amplification for micromechanical oscillators," Appl. Phys. Lett., vol. 78, pp. 3142-3144, 2001.
13. M. F. Yu and G. J. Wagner, "High order parametric resonance and nonlinear mechanics of nanowires," in Proc. Nanotechnology Conf. Trade Show, San Francisco, CA, 2003, vol. 3, pp. 325-328.
14. E. M. Abdel-Rahman and A. H. Nayfeh, "Secondary resonances of electrically actuated resonant microsensors," J. Micromech. Microeng., vol. 13, pp. 491-501, 2003.
15. B. J. Gallacher, J. S. Burdess, A. J. Harris, and J. Hedley, "The application of parametric excitation to a micro-ring gyroscope," in Proc. Nanotechnology Conf. Trade Show, Boston, MA, 2004, vol. 1, pp. 359-362.
16. R. Lifshitz and M. C. Cross, "Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays," Phys. Rev. B, vol. 67, p. 1343021, 2003.
17. B. J. Gallacher, J. S. Burdess, and K. M. Harish, "A control scheme for a MEMS electrostatic resonant gyroscope excited using combined parametric excitation and harmonic forcing," J. Micromech. Microeng., vol. 16, pp. 320-331, 2006.
18. M. Napoli, R. Baskaran, K. L. Turner, and B. Bamieh, "Understanding mechanical domain parametric resonance in microcantilevers," in Proc. IEEE 16th Int. Annu. Conf. MEMS, pp. 169-172.
19. E. Buks and M. L. Roukes, "Electrically tunable collective response in a coupled micromechanical array," J. Microelectromech. Syst., vol. 11, pp. 802-807, 2002.
20. Y. C. Hu, C. M. Chang, and S. C. Huang, "Some design considerations on the electrostatically actuated microstructures," Sens. Actuators A, vol. 112, pp. 155-161, 2004.
21. R. Baskaran and K. L. Turner, "Mechanical domain coupled mode parametric resonance and amplification in a torsional mode micro electro mechanical oscillator," J. Micromech. Microeng., vol. 13, pp. 701-707, 2003.
22. A. H. Nayfeh and M. I. Younis, "Dynamics of MEMS resonators under superharmonic and subharmonic excitations," J. Micromech. Microeng., vol. 15, pp. 1840-1847, 2005.
23. P. B. Chu, P. R. Nelson, M. L. Tachiki, and K. S. Pister, "Dynamics of polysilicon parallel-plate electrostatic actuator," Sens. Actuators A, vol. 52, pp. 216-220, 1996.
24. S. K. De and N. R. Aluru, "Complex nonlinear oscillations in electrostatically actuated microstructures," J. Microelectromech. Syst., vol. 15, no. 2, pp. 355-369, 2006.
25. K. Wang and C. T.-C. Nguyen, "High-order micromechanical electronic filters," in Proc. IEEE International Micro Electro Mechanical Workshop, Nagoya, Japan, 1997, pp. 25-30.
26. G. N. Jazar, "Mathematical modeling and simulation of thermal effects in flexural microcantilever resonator dynamics," J. Vibr. Control, vol. 12, no. 2, pp. 139-163, 2006.
27. S. G. Adams, F. Bertsch, and N. C. MacDonald, "Independent tuning of linear and nonlinear stiffness coefficients (actuators)," J. Microelectromech. Syst., vol. 7, no. 2, pp. 172-180, 1998.
28. S. K. De and N. R. Aluru, "Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS," J. Microelectromech. Syst., vol. 13, no. 5, pp. 737-758, 2004.
29. S. Liu, A. Davidson, and Q. Lin, "Simulating nonlinear dynamics and chaos in a MEMS cantilever using Poincare mapping," in Proc. 12th Int. Conf. Solid State Sensors, Actuators and Microsystems, Boston, MA, Jun. 8-12, 2003, pp. 1092-1095.
30. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations. New York: Wiley, 1979, pp. 56-59.
31. J. B. Starr, "Squeeze-film damping in solid-state accelerometers," in Proc. IEEE Solid State Sensor and Actuator Workshop, Hilton Head Island, SC, Jun. 4-7, 1990, pp. 44-47.