Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures

International Journal of Non-Linear Mechanics

Volumn 42, Issue 4, 2007, Pages 626-642

  Krylov, Slava ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Dynamic pull in; Electrostatic actuator; Lyapunov exponents; Reduced order model

Indexed keywords

ELECTRODES; ELECTROSTATIC ACTUATORS; GALERKIN METHODS; LYAPUNOV FUNCTIONS; PARAMETER ESTIMATION;

BASE FUNCTIONS; DYNAMIC PULL-IN INSTABILITY; REDUCED ORDER MODEL;

MICROSTRUCTURE;

EID: 34249878462     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2007.01.004     Document Type: Article

References (44)

1. Nathanson H.C., Newell W.E., Wickstrom R.A., and Davis J.R. The resonant gate transistor. IEEE Trans. Electron Devices 14 (1967) 11733
2. Senturia S.D. Microsystems Design (2001), Kluwer Academic Publishers, Boston, Dortrecht, London
3. Rebeiz G.M. RF MEMS: Theory, Design, and Technology (2003), Wiley-Interscience, Hoboken, NJ
4. Gupta K.G., and Senturia S.D. Pull-in dynamics as a measure of the ambient pressure. Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems. Piscataway, NJ (1997) 290-294
5. Hung E.S., and Senturia S.D. Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs. IEEE J. MEMS 8 (1999) 280-289
6. Castaner L.M., and Senturia S.D. Speed-energy optimization of electrostatic actuators based on pull-in. IEEE J. MEMS 8 (1999) 290-298
7. Luo A.C.J., and Wang F.Y. Chaotic motion in a Micro-Electro-Mechanical System with non-linearity from capacitors. Commun. Nonlinear Sci. Numer. Simulation 7 (2002) 31-49
8. McCarthy B., Adams G.G., McGruer N.E., and Potter D. A dynamic model, including contact bounce, of an electrostatically actuated microswitch. IEEE J. MEMS 11 (2002) 276-283
9. G. Flores, G.A., Mercado, J.A. Pelesko, Dynamics and touchdown in electrostatic MEMS, in: Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference and 19th Biennial Conference on Mechanical Vibration and Noise, Sep 206, 2003, Chicago, IL, vol. 5, 2003, pp. 1807-1814.
10. Younis M.I., Abdel-Rahman E.M., and Nayfeh A.H. A reduced-order model for electrically actuated microbeam-based MEMS. IEEE J. MEMS 12 (2003) 672-680
11. Krylov S., and Maimon R. Pull-in dynamics of an elastic beam actuated by continuously distributed electrostatic force. J. Vib. Acoust. 126 (2004) 332-342
12. Rocha L.A., Cretu E., and Wolffenbuttel R.F. Behavioural analysis of the pull-in dynamic transition. J. Micromech. Microeng. 14 (2004) S37-S42
13. Gabbay L.D., Mehner J.E., and Senturia S.D. Computer-aided generation of nonlinear reduced-order dynamic macromodels-II: stress-stiffened case. IEEE J. MEMS 9 (2000) 270-278
14. Nayfeh A.H., Younis M.I., and Abdel-Rahman E.M. Reduced-order models for MEMS applications. Nonlinear Dyn. 41 (2005) 211-236
15. Li G., and Aluru N.R. Efficient mixed-domain analysis of electrostatic MEMS. IEEE Trans. Comput.-Aided Des. Integrated Cirquits Syst. 22 (2003) 1228-1242
16. Simitses G.J. Dynamic stability of suddenly loaded structures (1990), Springer, Berlin
17. Budiansky B. Dynamic buckling of elastic structures: criteria and estimates. In: Herrmann G. (Ed). Dynamic Stability of Structures (1967), Pergamon Press, Oxford
18. Gilat R., and Aboudi J. The Lyapunov exponents as a quantitative criterion for the dynamic buckling of composite plates. Int. J. Solids Struct. 39 (2002) 467-481
19. Younis M.I., Miles R., and Jordy D. Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces. J. Micromech. Microeng. 16 (2006) 2463-2474
20. A.H. Nayfeh, M.I. Younis, E.M. Abdel-Rahman, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dyn. 48 (2007) 153-163.
21. A.H. Nayfeh, M.I. Younis, E.M. Abdel-Rahman, Dynamic analysis of MEMS resonators under primary resonance excitation, in: Proceedings of the 20th Biennial Conference on Mechanical Vibration and Noise (VIB), Long Beach, CA, DETC2005-84146, 2005.
22. Nayfeh A.H., and Younis M.I. Dynamics of MEMS resonators under superharmonic and subharmonic excitations. J. Micromech. Microeng. 15 (2005) 1840-1847
23. Goldhirsch I., Sulem P.L., and Orszag S.A. Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method. Physica D 27 (1987) 311-337
24. Pamidighantam S., Puers R., Baert K., and 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 (2002) 458-464
25. Villagio P. Mathematical Models for Elastic Structures (1997), Cambridge University Press, Cambridge
26. Osterberg P.M., and Senturia S.D. M-Test: a test chip for MEMS material property measurement using electrostatically actuated test structures. IEEE J. MEMS 6 (1997) 107-117
27. Pelesko J.A., and Bernstein D.H. Modeling of MEMS and NEMS (2002), Chapman & Hall, A CRC Press Company, London, New York, Washington, DC
28. Hamrock B.J. Fundamentals of Fluid Film Lubrication (1994), McGraw-Hill, New York
29. Blech J.J. On isothermal squeeze films. J. Lubrication Technology 105 (1983) 615-620
30. Burgdorfer A. The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. J. Basic Eng. Trans. ASME 81 (1959) 94-99
31. Kierzenka J., and Shampine L.F. A BVP solver based on residual control and the MATLAB PSE. ACM Trans. Math. Software 27 (2001) 299-316
32. Parnes R. Bending of an axially constrained beam. Int. J. Mech. Sci. 13 (1970) 285-290
33. Ijntema D.J., and Tilmans H.A.C. Static and dynamic aspects of an air-gap capacitor. Sensors and Actuators A 35 (1992) 121-128
34. Bochobza-Degani O., Elata D., and Nemirovsky Y. An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices. IEEE J. MEMS 11 (2002) 612-620
35. S. Krylov, S. Seretensky, Higher order correction of electrostatic pressure and its influence on pull-in behavior of microstructures, J. Micromech. Microeng. 2006.
36. Krylov S., Harari I., and Cohen Y. Stabilisation of electrostatically actuated microstructures using parametric excitation. J. Micromech. Microeng. 15 (2005) 1188-1204
37. Nayfeh A.H., and Younis M.I. A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. J. Micromech. Microeng. 14 (2004) 170-181
38. Veijola T., Kuisma H., Lahdenperä J., and Ryhänen T. Equivalent-cirquit model of the squeezed gas film in a silicon accelerometer. Sensors and Actuators A 48 (1995) 239-248
39. Shampine L., and Reichelt M. The Matlab ODE Suite. SIAM J. Sci. Comput. 18 (1997) 1-22
40. Hung E.S., and Senturia S.D. Extending the travel range of analog-tuned electrostatic actuators. J. MEMS 8 (1999) 497-505
41. W.A. Bonin, Capacitive transducer with electrostatic actuation, US Patent 5,576,483, 1996.
42. Abu-Salih S., and Elata D. Experimental validation of electromechanical buckling. J. MEMS 15 (2006) 1656-1662
43. Rhoads J.F., Shaw S.W., and Turner K.L. The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation. J. Micromech. Microeng. 16 (2006) 890-899
44. R.H. Rand, Lecture Notes on Nonlinear Vibrations, Version 34a, 2000, available at 〈http://www.tam.cornell.edu/randdocs〉.