Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

Nonlinear Dynamics

Volumn 54, Issue 1-2, 2008, Pages 31-52

  Vyas, Ashwin ^a   Peroulis, Dimitrios ^a   Bajaj, Anil K ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Autoparametric resonance; Flexural torsional oscillations; Internal resonance; Microelectromechanical resonators; Parametric resonance

Indexed keywords

DYNAMICS; ELECTROSTATIC ACTUATORS; MIXING; RESONANCE; SPECIFICATIONS; VIBRATIONS (MECHANICAL);

AC VOLTAGE; AUTOPARAMETRIC RESONANCE; DEGREES OF FREEDOM; DESIGN SPECIFICATIONS; EXCITATION LEVELS; FLEXURAL MODES; FLEXURAL-TORSIONAL; FLEXURAL-TORSIONAL OSCILLATIONS; HIGHER-ORDER; IN-PLANE; INTERNAL RESONANCE; INTERNAL RESONANCES; LAGRANGIAN FORMULATIONS; LOWER FREQUENCIES; MICRO RESONATORS; MICROELECTROMECHANICAL RESONATORS; NON-LINEARITIES; NONLINEAR MODAL INTERACTIONS; OUT-OF PLANE; PARAMETRIC RESONANCE; PULL-IN; REDUCED ORDER MODELLING; RF MEMS DEVICES; STATIC EQUILIBRIUM; STRUCTURAL PERTURBATIONS; TORSIONAL MODES;

FREQUENCY RESPONSE;

EID: 50249187183     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-007-9326-y     Document Type: Article

References (31)

1. Zhnag, W., Turner, K.L.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sens. Actuators A 122, 23-30 (2005)
2. Gupta, A., Akin, D., Bashir, R.: Single virus particle mass detection using microresonators with nanoscale thickness. Appl. Phys. Lett. 84(11), 1976-1978 (2004)
3. Nguyen, C.T.-C.: Vibrating RF MEMS for next generation wireless applications. In: Proceedings of the Custom Integrated Circuits Conference, Orlando, FL, 3-6 October. IEEE, Piscataway (2004)
4. Rutzel, S., Lee, S.I., Raman, A.: Nonlinear dynamics of atomic-force-microscope probes driven in Lennard-Jones potential. Proc. R. Soc. Lond. 459, 1925-1948 (2003)
5. Younis, M.I., Nayfeh, A.H.: A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dyn. 31, 91-117 (2003)
6. Turner, K.L., Miller, S.A., Hartwell, P.G., MacDonald, N.C., Strogatz, S.H., Adams, S.G.: Five parametric resonances in a microelectromechanical system. Nature 396(6707), 149-152 (1998)
7. Nayfeh, A.H.: Nonlinear Interactions: Analytical, Computational and Experimental Methods. Wiley-Interscience, New York (2000)
8. Balachandran, B., Nayfeh, A.H.: Nonlinear motions of a beam-mass structure. Nonlinear Dyn. 1, 39-61 (1990)
9. Haxton, R.S., Barr, A.D.S.: The autoparametric vibration absorber. ASME J. Eng. Ind. 94, 119-225 (1972)
10. Bajaj, A.K., Chang, S.I., Johnson, J.: Amplitude modulated dynamics of a resonantly excited autoparametric two degree-of-freedom system. Nonlinear Dyn. 5, 433-457 (1994)
11. Vyas, A., Bajaj, A.K.: Microresonators based on 1:2 internal resonance. In: Proceedings of IMECE'05, Orlando, FL, 5-11 November. ASME Paper No. IMECE2005-61955 (2005)
12. Baskaran, R., Turner, K.L.: Mechanical domain coupled mode parametric resonance and amplification in a torsional mode micro electro mechanical oscillator. J. Micromech. Microeng. 13, 701-707 (2003)
13. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-Interscience, New York (1979)
14. Carr, D.W., Evoy, S., Sekaric, L., Craighead, H.G.: Parametric amplification in a torsional microresonator. Appl. Phys. Lett. 77(10), 1545-1547 (2000)
15. Zhang, W., Baskaran, R., Turner, K.: Tuning the dynamic behavior of parametric resonance in a micromechanical oscillator. Appl. Phys. Lett. 82(1), 130-132 (2003)
16. Zalalutdinov, M., Olkhovets, A., Zehnder, A., Ilic, B., Czaplewski, D., Craighead, H.G., Parpia, J.M.: Optically pumped parametric amplification for micromechanical oscillators. Appl. Phys. Lett. 78(20), 3142-3144 (2001)
17. Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics. Wiley-Interscience, New York (2002)
18. Young, W.C.: Roark's Formulas for Stress & Strain. McGraw-Hill, New York (1989)
19. Crespo Da Silva, M.R.M.: Nonlinear flexural-flexural-torsional- extensional dynamics of beams, I: formulation. Int. J. Solids Struct. 24, 1225-1234 (1988)
20. Crespo Da Silva, M.R.M., Zaretzky, C.L.: Nonlinear flexural-flexural- torsional interactions in beams including the effect of torsional dynamics, I: primary resonance. Nonlinear Dyn. 5, 3-23 (1994)
21. Sharpe, W.N. Jr., Yuan, B., Vaidyanathan, R., Edwards, R.L.: Measurements of Young's modulus, Poisson's ratio, and tensile strength of polysilicon. In: Proceedings of the IEEE Micro Electro Mechanical Systems, Nagoya, Japan, pp. 424-429. IEEE, Piscataway (1997)
22. Degani, O., Lipson, A., Leitner, T., Setter, D.J., Kaldor, S., Nemirovsky, Y.: Pull-in study of an electrostatic torsion microactuator. J. Microelectromech. Syst. 7, 373-379 (1998)
23. Pamidighantam, S., Puers, R., Baert, K., Tilmans, H.A.C.: Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions. J. Micromech. Microeng. 12, 458-464 (2002)
24. Daqaq, M.F.: Adaptation of nontraditional control techniques to nonlinear micro and macro mechanical systems. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA (2006)
25. Daqaq, M.F., Abdel-Rahman, E.M., Nayfeh, A.H.: Modal interactions in resonant microscanners. In: Proceedings of IMECE'06, Chicago, 5-10 November. ASME Paper No. IMECE2006-13844 (2006)
26. Murdock, J.A.: Perturbations: Theory and Methods. Wiley, New York (1991)
27. Banerjee, B., Bajaj, A.K., Davies, P.: Resonant dynamics of an autoparametric system: a study using higher-order averaging. Int. J. Non-Linear Mech. 31, 21-39 (1996)
28. Banerjee, B., Bajaj, A.K.: Amplitude modulated chaos in two degree-of-freedom systems with quadratic nonlinearities. Acta Mech. 124, 131-154 (1997)
29. Corman, T., Enoksson, P., Stemme, G.: Gas damping of electrostatically excited resonators. Sens. Actuators A: Phys. 61, 249-255 (1997)
30. Tilmans, H.A.C., Raedt, W.D., Beyne, E.: MEMS for wireless communications: 'from RF-MEMS components to RF-MEMS-SiP'. J. Micromech. Microeng. 13, S139-S163 (2003)
31. Ilic, B., Czaplewski, D., Craighead, H.G.: Mechanical resonant immunospecific biological detector. Appl. Phys. Lett. 77(3), 450-452 (2000)