Co-dimension-two grazing bifurcations in single-degree-of-freedom impact oscillators

Journal of Computational and Nonlinear Dynamics

Volumn 1, Issue 4, 2006, Pages 328-335

  Thota, Phanikrishna ^a   Zhao, Xiaopeng ^b   Dankowicz, Harry ^c  

^a State University   (United States)

^b Duke University   (United States)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CONFORMAL MAPPING; DEGREES OF FREEDOM (MECHANICS); DYNAMICS; MICROELECTROMECHANICAL DEVICES;

GLOBAL DYNAMICS; GRAZING BIFURCATIONS; IMPACT OSCILLATORS; MICRO-ELECTRO-MECHANICAL SYSTEMS OSCILLATOR;

OSCILLATORS (MECHANICAL);

EID: 33751100890     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2338658     Document Type: Article

References (17)

1. Guckenheimer, J., and Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectorfields, Springer-Verlag, New York.
2. Zeeman, E. C., 1977, Catastrophe Theory: Selected Papers 1972-1977, Addison-Wesley, Reading, MA.
3. Golubitsky, M., and Schaeffer, D. G., 1985, Singularities and Groups in Bifurcation Theory, Springer-Verlag, Berlin.
4. Chin, W., Ott, E., Nusse, H. E., and Grebogi, C., 1994, "Grazing Bifurcations in Impact Oscillators," Phys. Rev. E, 50, pp. 4427-4444.
5. Dankowicz, H., and Nordmark, A. B., 2000, "On the Origin and Bifurcations of Stick-Slip Oscillations," Physica D, 136, pp. 280-302.
6. Di Bernardo, M., Budd, C. J., and Champneys, A. R., 2000, "Normal Form Maps for Grazing Bifurcationsin n-Dimensional Piecewise-Smooth Dynamical Systems," Physica D, 160, pp. 222-254.
7. Nordmark, A. B., and Kowalczyk. P., 2006, "A Codimension-Two Scenario of Sliding Solutions," Nonlinearity, 19, pp. 1-26.
8. Zhao, X., and Dankowicz, H., 2006, "Unfolding Degenerate Grazing Dynamics in Impact Actuators," Nonlinearity, 19, pp. 399-418.
9. Nordmark, A. B., 1991, "Non-periodic Motion Caused by Grazing Incidence in an Impact Oscillator," J. Sound Vib., 145, pp. 279-297.
10. Dankowicz, H., and Zhao, X., 2005, "Local Analysis of Co-dimension-One and Co-dimension-Two Grazing Bifurcations in Impact Microactuators," Physica D, 202, pp, 238-257.
11. Fredriksson, M. H., and Nordmark, A. B., 1997, "Bifurcations Caused by Grazing Incidence in Many Degrees of Freedom Impact Oscillators," Proc. R. Soc. London, Ser. A, 453, pp. 1261-1276.
12. Molenaar, J., de Weger, J. G., and Van de Water, W., 2001, "Mappings of Grazing Impact Oscillators," Nonlinearity, 14(2), pp. 301-321.
13. Foale, S., 1994, "Analytical Determination of Bifurcations in an Impact Oscillator," Proc. R. Soc. London, Ser. A, 347, pp. 373-364.
14. Foale, S., and Bishop, R., 1994, "Bifurcations in Impacting Systems," Nonlinear Dyn., 6, pp. 285-299.
15. Mita, M., Arai, M., Tensaka, S., Kobayashi, D., and Fujita, H., 2003, "A Micromachined Impact Microactuator Driven by Electrostatic Force," J. Microelectromech. Syst., 12(1), pp. 37-41.
16. Zhao, X., Dankowicz, H., Reddy, C. K., and Nayfeh, A. H., 2004, "Modelling and Simulation Methodology for Impact Microactuators," J. Microelectromech. Syst., 14, pp. 775-784.
17. Zhao, X., Reddy, C. K., and Nayfeh, A. H., 2005, "Nonlinear Dynamics of an Electrically Driven Impact Microactuator," Nonlinear Dyn., 40, pp. 227-239.