Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

Chaos, Solitons and Fractals

Volumn 21, Issue 3, 2004, Pages 763-772

  De Souza, Silvio L T ^a   Caldas, Iberê L ^a   Viana, Ricardo L ^b   Balthazar, José M ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^c SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BEARINGS (MACHINE PARTS); FRACTALS; GEAR TEETH; SWITCHING; THERMAL EXPANSION; WHEELS;

CHAOTIC ATTRACTORS; GEARBOXES;

CHAOS THEORY;

EID: 1342328187     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2003.12.096     Document Type: Article

References (27)

1. Kapitaniak T. Chaos for engineers. 2000;Springer, New York, Berlin, Heidelberg.
2. Wiercigroch M., DeKraker B. Applied nonlinear dynamics and chaos of mechanical systems with discontinuities. 2000;World Scientific, Singapore.
3. Thompson J.M.T. Global dynamics of oscillations: fractal basins and intermediate bifurcations. Aston P.J. Nonlinear mathematics and its applications. 1996;Cambridge University Press, Cambridge.
4. Nordmark A.B. Non-periodic motion caused by grazing in an impact oscillator. J. Sound Vib. 145:1991;279-297.
5. Dankowicz H., Piiroinen P., Nordmark A.B. Low-velocity impacts of quasi-periodic oscillations. Chaos, Solitons & Fractals. 14:2002;241-255.
6. Jerrelind J., Stensson A. Nonlinear dynamics of parts in engineering systems. Chaos, Solitons & Fractals. 11:2000;2413-2428.
7. Pfeiffer F. Seltsame Attraktoren in Zahnradgetrieben. Ing. Arch. 58:1988;113-125.
8. Karagiannis K., Pfeiffer F. Theoretical and experimental investigations of gear-rattling. Nonlinear Dyn. 2:1991;367-387.
9. Hongler M.-O., Streit L. On the origin of chaos in gearbox models. Physica D. 29:1988;402-408.
10. Blazejczyk-Okolewska B., Czolczynski K., Kapitaniak T., Wojewoda J. Chaotic mechanics in systems with friction and impacts. 1999;World Scientific, Singapore.
11. Blazejczyk-Okolewska B., Kapitaniak T. Coexisting attractors of impact oscillator. Chaos, Solitons & Fractals. 9:1998;1321-1338.
12. Pfeiffer F., Kunert A. Rattling models from deterministic to stochastic processes. Nonlinear Dyn. 1:1990;63-74.
13. de Souza S.L.T., Caldas I.L. Basins of attraction and transient chaos in a gear-rattling model. J. Vib. Control. 7:2001;849-862.
14. de Souza S.L.T., Caldas I.L. Calculation of Lyapunov exponents in systems with impacts. Chaos, Solitons & Fractals. 19:2004;569-579.
15. de Souza S.L.T., Caldas I.L. Controlling chaotic orbits in mechanical systems with impacts. Chaos, Solitons & Fractals. 19:2004;171-178.
16. de Souza S.L.T., Caldas I.L., Balthazar J.M., Brasil R.M.L.R.F. Analysis of regular and irregular dynamics of a non ideal gear rattling problem. J. Brazil. Soc. Mech. Sci. XXIV:2002;111-114.
17. Grebogi C., Ott E., Yorke J.A. Crises, sudden changes in chaotic attractors, and transient chaos. Physica D. 7:1983;181.
18. Moon F.C. Applied dynamics with applications to multibody and mechatronic systems. 1998;John Wiley, New York.
19. Ott E. Chaos in dynamical systems. 1993;Cambridge University Press, Cambridge.
20. Ding M., Grebogi C., Ott E., Yorke J.A. Transition to chaotic scattering. Phys. Rev. A. 42:1990;7025-7040.
21. Bleher S., Grebogi C., Ott E. Bifurcation of chaotic scattering. Physica D. 46:1990;87-121.
22. Poon L., Campos J., Ott E., Grebogi C. Wada basin boundaries in chaotic scattering. Int. J. Bifurcat. Chaos. 6:1996;251-265.
23. da Silva E.C., Caldas I.L., Viana R.L., Sanjuan M. Escape patterns, magnetic footprints, and homoclinic tangles due to ergodic magnetic limiters. Phys. Plasmas. 9:2002;4917.
24. Grebogi C., Ott E., Yorke J.A. Fractal basin boundaries. Physica D. 17:1983;125-153.
25. Blazejczyk-Okolewska B., Brindley J., Kapitaniak T. Practical riddling. Chaos, Solitons & Fractals. 11:2000;2511.
26. Kapitaniak T. Partially nearly riddled basins in systems with chaotic saddle. Chaos, Solitons & Fractals. 12:2001;2363-2367.
27. Woltering M., Markus M. Riddled-like basins of transient chaos. Phys. Rev. Lett. 84:2000;630-634.