Chaotic motion in a micro-electro-mechanical system with non-linearity from capacitors

Communications in Nonlinear Science and Numerical Simulation

Volumn 7, Issue 1-2, 2002, Pages 31-49

  Luo, Albert C J ^a   Wang, F Y ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b Phonic Ear Inc ^*  (United States)

Author keywords

Chaotic motion; Frequency band; MEMS; Resonator

Indexed keywords

INDUSTRIAL APPLICATIONS; MICROELECTROMECHANICAL DEVICES; NATURAL FREQUENCIES; RESONANCE; TRANSDUCERS;

CHAOTIC MOTION; FREQUENCY BANDS; RESONANT LAYERS; RESONANT MOTIONS;

NONLINEAR SYSTEMS;

CHAOS; NON-LINEAR SYSTEM;

EID: 1342337622     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1007-5704(02)00005-9     Document Type: Article

References (28)

1. Nathanson HC, Newell WE, Wickstrom RA, et al. The resonant gate transistor. Trans Electron Dev 1967;ED-14(3):117-33.
2. Syms RRA. Electrothermal frequency turning of folded and coupled vibrating micromechnical resonators. J Microelectromech Syst 1998;7(2): 164-71.
3. Lin L, Howe RT, Pisano AP. Microelectromechanical filters for signal process. J Microelectromech Syst 1998;7(3):194-286.
4. Nguyen CT-C. Frequency-selective MEMS for miniaturized communication devices. In: Proceedings of the 1998 IEEE Aerospace Conference, Snowmass, CO, March 21-28, 1998. p. 445-60.
5. Prak A, Elwenspoek M, Fluitman JHJ. Selective mode excitation and detection of micromachined resonators. J Microelectromech Syst 1992; 1 (4): 179-86.
6. Serry FM, Walliser D, Macklay GJ. The anharmonic Casimir oscillator (ACO) - The Casimir effect in a model microelectromechanical system. J Microelectromech Syst 1995;4(4): 193-205.
7. Hung ES, Senturia SD. Extending the travel range of the analog-turned electrostatic actuators. J Microelectromech Syst 1999;8(4):497-505.
8. Raskin JP, Brown AR, Khuri-Yakub BT, et al. A novel parametric effect MEMS amplifier. J Microelectromech Syst 2000;9(4):528-37.
9. Yeh J-LA, Hui C-Y. Electrostatic model for an asymmetric combdrive. J Microelectromech Syst 2000;9(1): 126-35.
10. Lee KB, Cho YH. Laterally driven electrostatic repulsive-force microactuators using asymmetric field distribution. J Microelectromech Syst 2001;10(1):128-36.
11. Chan EK, Dutton RW. Electrostatic micromechanical actuator with extended range of travel. J Microelectromech Syst 2000;9(3):321-8.
12. Capanu M, Boyd JG, Hesketh PJ. Design, fabrication, and testing of a bistable electromagnetically actuated microvalve. J Microelectromech Syst 2000;9(2):181-9.
13. Johnson RA. Mechanical filters in electronics. New York: John Wiley; 1983.
14. Ziebart V, Paul O, Baits H. Strongly buckled square micromachined membranes. J Microelectromech Syst 1999;8(4):423-32.
15. Mether JE, Gabbay LD, Senturia SD. Computer-aided generation of nonlinear reduced-order dynamic macromodels - II: Stress-stiffened case. J Microelectromech Syst 2000;9(2):270-8.
16. Luo ACJ. An approximate theory for geometrically nonlinear thin plate. Int J Solids Struct 2000;37:7655-70.
17. Luo ACJ, Ran RPS. Analytical prediction of chaos in a nonlinear rod. J Sound Vibr 1999;227(3):524-44.
18. Lichtenberg AJ, Lieberman MA. Regular and chaotic dynamics. 2nd ed. New York: Springer; 1992.
19. Chirikov BV. A universal instability of many-dimensional oscillator system. Phys Rep 1979;52:263-379.
20. Melnikov VK. On the behavior of trajectories of system near to autonomous Hamiltonian systems. Sov Math Dokl 1962;3:109-12.
21. Melnikov VK. On the stability of the center for time periodic perturbations. Trans Moscow Math Soc 1963;12: 1-57.
22. Luo ACJ. Resonant-overlap phenomena in stochastic layers of nonlinear Hamiltonian systems with periodical excitations. J Sound Vibr 2001;240(5):821-36.
23. Greene JM. Two-dimensional measure-preserving mappings. J Math Phys 1968;9:760-8.
24. Greene JM. A method for computing the stochastic transition. J Math Phys 1979;20:1183-201.
25. Han RPS, Luo ACJ. Resonant layers in nonlinear dynamics. ASME J Appl Mech 1998;65:727-36.
26. Luo ACJ. Resonant layers in parametrically excited pendulum. Int J Bifurc Chaos 2002;12(2):409-19.
27. Feng K, Qin MZ. Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study. Comput Phys Commun 1991;65:173-87.
28. McLachlan R, Atela P. The accuracy of symplectic integrators. Nonlinearity 1992;5:541-62.