Synchronization of two forced double-well Duffing oscillators with attached pendulums

• Autorzy: Brzeski P. , Karmazyn A. , Perlikowski P.
• Języki publikacji: EN

Abstrakty

EN

We investigate the dynamics of two coupled Duffing oscillators with attached pendulums forced kinematically by a common signal. Our attention is focused on different kinds of synchronization which can appear in the considered system. Different types of coupling (spring, damper and spring and damper simultaneously) are taken into account. We show in a two-parameters space (amplitude and frequency of excitation) existence of complete and phase synchronization and asynchronous ranges.

Słowa kluczowe

EN

Duffing pendulum system; bifurcational analysis; synchronization

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 3
• Strony: 603--613
• Opis fizyczny: Bibliogr. 44 poz., rys., tab.

Twórcy

autor

Brzeski P.

• Lodz University of Technology, Division of Dynamics, Łódź, Poland

autor

Karmazyn A.

• Lodz University of Technology, Division of Dynamics, Łódź, Poland

autor

Perlikowski P.

• Lodz University of Technology, Division of Dynamics, Łódź, Poland

Bibliografia

• 1. Argyris A., Syvridis D., Larger L., Annovazzi-Lodi V., Colet P., Fischer I., Garcia-Ojalvo J., Mirasso C.R., Pesquera L., Shore K.A., 2005, Chaos-based communications aT high bit rates using commercial fibre-optic links,Nature, 438, 343-346
• 2. Bajaj A.K., Chang S.I., Johnson J.M., 1994, Amplitude modulated dynamics of a resonantly excited autoparametric two degree-of-freedom system, Nonlinear Dynamics, 5, 433-457
• 3. Balanov A., Janson N., Postnov D., Sosnovtseva O., 2009, Synchronization: From Simple to Complex, Springer Series in Synergetics, Springer
• 4. Balthazar J., Cheshankov B., Ruschev D., Barbanti L., Weber H., 2001, Remarks on the passage through resonance of a vibrating system with two degrees of freedom, excited by a non-ideal energy source, Journal of Sound and Vibration, 239, 1075-1085
• 5. Blekhman I., 1988, Synchronization in Science and Technology, ASME, New York
• 6. Boccaletti S., Kurths J., Osipov G., Valladares D., Zhou C., 2002, The synchronization of chaotic systems, Physics Reports, 366, 1-101
• 7. Brzeski P., Perlikowski P., Yanchuk S., Kapitaniak T., 2012, The dynamics of the pendulum suspended on the forced Duffing oscillator, Journal of Sound and Vibration, 331, 24, 5347-5357
• 8. Cartmell M., Lawson J., 1994, Performance enhancement of an autoparametric vibration absorber by means of computer control, Journal of Sound and Vibration, 177, 173-195
• 9. Chudzik A., Perlikowski P., Stefanski A., Kapitaniak T., 2011, Multistability and rare attractors in van der Pol-Duffing oscillator, International Journal of Bifurcation and Chaos, 21, 1907-1912
• 10. Clifford M., Bishop S., 1995, Rotating periodic orbits of the parametrically excited pendulum, Physics Letters A, 201), 191-196
• 11. Clifford M., Bishop S., 1996, Locating oscillatory orbits of the parametrically-excited pendulum, Journal of the Australian Mathematical Society Series B-Applied Mathematics, 37, 309-319
• 12. Czolczynski K., Stefanski A., Perlikowski P., Kapitaniak T., 2008, Multistability and chaotic beating of Duffing oscillators suspended on an elastic structure, Journal of Sound and Vibration, 322, 513-523
• 13. Hatwal H., Mallik A.K., Ghosh A., 1983a, Forced nonlinear oscillations of an autoparametric system – part 1: Periodic responses, Journal of Applied Mechanics, 50, 657-662
• 14. Hatwal H., Mallik A.K., Ghosh A., 1983b, Forced nonlinear oscillations of an autoparametric system – part 2: Chaotic responses, Journal of Applied Mechanics, 50, 663-668
• 15. Huygens C., 1665, Letter to de Sluse, [In:] Oeuveres Completes de Christian Huygens (letters; no. 1333 of 24 February 1665, no. 1335 of 26 February 1665, no. 1345 of 6 March 1665), Societe Hollandaise Des Sciences, Martinus Nijhoff, La Haye
• 16. Kapitaniak T., 1985, Stochastic response with bifurcations to non-linear Duffing’s oscillator, Journal of Sound and Vibration, 102, 440-441
• 17. Kapitaniak T., 1988, Combined bifurcations and transition to chaos in a non-linear oscillator with two external periodic forces, Journal of Sound and Vibration, 121, 259-268
• 18. Kecik K., Warminski J., 2011, Dynamics of an autoparametric pendulum-like system with a nonlinear semiactive suspension, Mathematical Problems in Engineering, 2011
• 19. Macias-Cundapi L., Silva-Navarro G., Vazquez-Gonzalez B., 2008, Application of an active pendulum-type vibration absorber for Duffing systems, [In:] Electrical Engineering, Computing Science and Automatic Control, CCE 2008
• 20. Maistrenko Y., Kapitaniak T., Szuminski P., 1997, Locally and globally riddled basins in two coupled piecewise-linear maps, Physical Review E, 56, 6393-6399
• 21. Miles J., 1988, Resonance and symmetry breaking for the pendulum, Physica D, 31, 252-268
• 22. Miles J., 1989, Resonance and symmetry breaking for a Duffing oscillator, SIAM Journal Applied Mathematics, 49, 968-981
• 23. Pecora L.M., Carroll T.L., 1990, Synchronization in chaotic systems, Physical Review Letters, 64, 821-824
• 24. Pecora L.M., Carroll T.L., 1991, Synchronizing chaotic systems, IEEE Transactions Circuits and Systems, 38, 453-456
• 25. Perlikowski P., 2008, Synchronization of mechanical oscillators excited kinematically, Journal of Theoretical and Applied Mechanics, 48, 185-204
• 26. Perlikowski P., Jagiello B., Stefanski A., Kapitaniak T., 2008a, Experimental observation of ragged synchronizability, Physical Review E, 78
• 27. Perlikowski P., Stefanski A., Kapitaniak T., 2008, 1:1 mode locking and generalized synchronization in mechanical oscillators, Journal of Sound and Vibration, 318, 329-340
• 28. Pikovsky A., Rosenblum M., Kurths J., 2001, Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge University Press
• 29. Robinson F.N.H., 1989, Experimental observation of the large-amplitude solutions of Duffing’s and related equations, IMA Journal of Applied Mathematics, 42, 177-201
• 30. Rosenblum M.G., Pikovsky A.S., Kurths J., 1996, Phase synchronization of chaotic oscillators, Physical Review Letters, 76, 1804-1807
• 31. Rulkov N.F., Sushchik M.M., Tsimring L.S., Abarbanel H.D.I., 1995, Generalized synchronization of chaos in directionally coupled chaotic systems, Physical Review E, 51, 980-994
• 32. Sekieta M., Kapitaniak T., 1996, Practical synchronization of chaos via nonlinear feedback scheme, International Journal Bifurcation and Chaos, 6, 1901-1907
• 33. Song Y., Sato H., Iwata Y., Komatsuzaki T., 2003, The response of a dynamic vibration absorber system with a parametrically excited pendulum, Journal of Sound and Vibration, 259, 747-759
• 34. Stefanski A., Kapitaniak T., 2003, Estimation of the dominant Lyapunov exponent of nonsmooth systems on the basis of maps synchronization, Chaos, Solitons and Fractals, 15 233-244
• 35. Stefanski A., Perlikowski P., Kapitaniak T., 2007, Ragged synchronizability of coupled oscillators, Physical Review E, 75
• 36. Strogatz S.H., 2001, Exploring complex networks, Nature, 410, 268-276
• 37. Tass P., 2003, A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations, Biological Cybernetics, 89, 81-88
• 38. Vazquez-Gonzalez B., Silva-Navarro G., 2008, Evaluation of the autoparametric pendulum vibration absorber for a Duffing system, Shock and Vibration, 15, 355-368
• 39. Warminski J., Balthazar J., Brasil R., 2001, Vibrations of a non-ideal parametrically and self-excited model, Journal of Sound and Vibration, 245, 363-374
• 40. Warminski J., Kecik K., 2006, Autoparametric vibration of a nonlinear system with pendulum, Mathematical Problems in Engineering, 2006
• 41. Warminski J., Kecik K., 2009, Instabilities in the main parametric resonance area of a mechanical system with a pendulum, Journal of Sound and Vibration, 322, 612-628
• 42. Watts D.J., Strogatz S.H., 1998, Collective dynamics of small-world networks, Nature, 393, 409-410
• 43. Yamasue K., Hikihara T., 2004, Domain of attraction for stabilized orbits in time delayed feedback controlled Duffing systems, Physical Review E, 69
• 44. Yanchuk S., Schneider K., Lykova O., 2008, Amplitude synchronization in a system of two coupled semiconductor lasers, Ukrainian Mathematics Journal, 60, 495-507