Control and chaos for vibro-impact and non-ideal oscillators

de Souza, S. L. T.; Caldas, I. L.; Viana, R. L.; Balthazar, J. M.

Artykuł - szczegóły

Tytuł artykułu

Control and chaos for vibro-impact and non-ideal oscillators

Autorzy

de Souza S. L. T. , Caldas I. L. , Viana R. L. , Balthazar J. M.

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

Warianty tytułu

Sterowanie i chaos w układach drgających z uderzeniami oraz nieidealnych oscylatorów

Języki publikacji

Abstrakty

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implemen- tations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phe- nomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic mo- tion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we inve- stigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

W pracy przedyskutowano zagadnienie dynamiki mechanizmów dwóch rodzajów. Najpierw rozważono układ drgający z uderzeniami, który znajduje liczne aplikacje praktyczne w mechanice stosowanej, począwszy od urządzeń wiertniczych przez procesy cięcia metalu do skrzyń biegów włącznie. Z punktu widzenia dynamiki maszyn układy wibro-uderzeniowe wykazują bogactwo interesujących zjawisk, wliczając w to chaos. W pracy zaprezentowano przegląd ostatnich prac dotyczących dynamiki układów wibro-uderzeniowych, w których zajęto się problemem chaosu i możliwości jego sterowania. Przeanalizowano układy mechaniczne na przykładzie modelu kół zębatych z systemem ”inteligentnego” tłumika do eliminacji ruchu chaotycznego. Zajęto się, po drugie, mechanizmami z nieidealnym źródłem energii odwzorowanym poprzez układ ograniczonego poboru mocy. Jako przykład zbadano dynamikę chaotyczną tłumionego oscylatora Duffinga połączonego z wirnikiem. Pokazano sposób zastosowania płynnego tłumika do sterowania formą atraktorów obserwowanych w nieidealnym oscylatorze.

Słowa kluczowe

vibro-impact chaos control of chaos non-ideal oscillators

chaos kontrola chaosu wibracje z uderzeniem

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2008

Tom

Vol. 46 nr 3

Strony

641--664

Opis fizyczny

Bibliogr. 47 poz., rys.

Twórcy

autor

de Souza S. L. T.

autor

Caldas I. L.

autor

Viana R. L.

autor

Balthazar J. M.

University of Sao Paulo, Institute of Physics, Sao Paulo, SP, Brazil, thomaz@if.usp.br

Bibliografia

1. Alvarez-Ramirez J., Espinosa-Paredes G., Puebla H., 2003, Chaos control using small-amplitude damping signals, Physics Letters A, 316, 196-205
2. Bishop S.R., Wagg D.J., Xu D., 1998, Use of control to maintain period-1 motions during wind-up or wind-down operations of an impacting driven beam, Chaos, Solitons and Fractals, 9, 261-269
3. Blazejczyk-Okolewska B., Czolczynski K., Kapitaniak T., Wojewoda J., 1999, Chaotic Mechanics in Systems with Friction and Impacts, World Scientific, Singapore
4. Blazejczyk-Okolewska B., Czolczynski K., Kapitaniak T., 2004, Classification principles of types of mechanical systems with impacts – fundamental assumptions and rules, European Journal of Mechanics – A/Solids, 23, 3, 517-537
5. Chaterjee S., Mallik A.K., Ghosh A., 1995, On impact dampers for nonlinear vibrating systems, Journal of Sound and Vibration, 187, 403-420
6. Czolczynski K., Blazejczyk-Okolewska B., Kapitaniak T., 2000, Impact force generator: self-synchronization and regularity of motion, Chaos, Solitons and Fractals, 11, 2505-2510
7. de Souza S.L.T., Caldas I.L., 2001, Basins of attraction and transient chaos in a gear-rattling model, Journal of Vibration and Control, 7, 849-862
8. de Souza S.L.T., Caldas I.L., 2004, Calculation of Lyapunov exponents in systems with impacts, Chaos, Solitons and Fractals, 19, 569-579
9. de Souza S.L.T., Caldas I.L., Viana R.L., Balthazar J.M., 2004, Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes, Chaos, Solitons and Fractals, 21, 763-772
10. de Souza S.L.T., Caldas I.L., Viana R.L., Balthazar J.M., Brasil R.M.L.R.F., 2005a, Basins of attraction changes by amplitude constraining of oscillators with limited power supply, Chaos, Solitons and Fractals, 26, 1211-1220
11. de Souza S.L.T., Caldas I.L., Viana R.L., Batista A.M., Kapitaniak T., 2005b, Noise-induced basin hopping in a gearbox model, Chaos, Solitons and Fractals, 26, 1523-1531
12. de Souza S.L.T., Caldas I.L., Viana R.L., Balthazar J.M., Brasil R.M.L.R.F., 2006, Dynamics of vibrating systems with tuned liquid column dampers and limited power supply, Journal of Sound and Vibration, 289, 987-998
13. de Souza S.L.T., Caldas I.L., Viana R.L., 2007a, Damping control law for a chaotic impact oscillator, Chaos, Solitons and Fractals, 32, 745-750
14. de Souza S.L.T., Caldas I.L., Viana R.L., Balthazar J.M., Brasil R.M.L.R.F., 2007b, A simple feedback control for a chaotic oscillator with limited power supply, Journal of Sound and Vibration, 299, 664-671
15. de Souza S.L.T.,Wiercigroch M., Caldas I.L., Balthazar J.M., 2007c, Suppressing grazing chaos in impacting system by structural nonlinearity, Chaos, Solitons and Fractals, in press, doi:10.1016/j.chaos.2007.01.022
16. Dimentberg M.F., McGovern L., Norton R.L., Chapdelaine J., Harrison R., 1997, Dynamics of an unbalanced shaft interacting with a limited power supply, Nonlinear Dynamics, 13, 171-187
17. Felix J.L.P., Balthazar J.M., Brasil R.M.L.R.F., 2005, On tuned liquid column dampers mounted on a structural frame under a non-ideal excitation, Journal of Sound and Vibration, 282, 1285-1292
18. Fradkov A.L., Evans R.J., Andrievksy B.R., 2006, Control of chaos: methods and applications in mechanics, Philosophical Transactions of The Royal Society A, 364, 2279-2307
19. Ing J., Pavlovskaia E., Wiercigroch M., 2006, Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: modelling and experimental verification, Nonlinear Dynamics, 46, 225-238
20. Ivanov A.P., 1996, Bifurcations in impact systems, Chaos, Solitons and Fractals, 7, 1615-1634
21. Jerrelind J., Stensson A., 2000, Nonlinear dynamics of parts in engineering systems, Chaos, Solitons and Fractals, 11, 2413-2428
22. Jin L., Lu Q.S., Twizell E.H., 2006, A method for calculating the spectrum of Laypunov exponents by local maps in non-smooth impact-vibrating systems, Journal of Sound and Vibration, 298, 1019-1033
23. Kapitaniak T., 2000, Chaos for Engineers, Springer Verlag, New York-Berlin-Heidelberg
24. Karagiannis K., Pfeiffer F., 1991, Theoretical and experimental investigations of gear-rattling, Nonlinear Dynamics, 2, 367-387
25. Kononenko V.O., 1969, Vibrating Systems with a Limited Power Supply, Iliffe Books Ltd, London
26. Krasnopolskaya T.S., Shvets A.Y., 1993, Chaos in vibrating systems with a limited power-supply, Chaos, 3, 387-395
27. Lee J.Y., Yan J.J., 2006, Control of impact oscillator, Chaos, Solitons and Fractals, 28, 136-142
28. Luo A.C.J., 2004, Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator, Chaos, Solitons and Fractals, 19, 823-839
29. Luo G.W., Chu Y.D., Zhang Y.L., Zhang J.G., 2006, Double Neimark-Sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops, Journal of Sound and Vibration, 298, 154-179
30. Luo G.W., Zhang Y.L., Chu Y.D., Zhang J.G., 2007, Codimension-two bifurcations of fixed points in a class of vibratory systems with symmetrical rigid stops, Nonlinear Analysis: Real World Applications, 8, 1272-1292
31. McDonald S.W., Grebogi C., Ott E., 1983, Final state sensitivity: an obstruction to predictability, Physics Letters A, 99, 415-418
32. McDonald S.W., Grebogi C., Ott E., 1985, Fractal basin boundaries, Physica D, 17, 125-153
33. Nordmark A.B., 1991, Non-periodic motion caused by grazing incidence in an impact oscillator, Journal of Sound and Vibration, 145, 279-297
34. Ott E., Grebogi C., Yorke J.A., 1990, Controlling chaos, Physical Review Letters, 64, 1196-1199
35. Pavlovskaia E., Wiercigroch M., Grebogi C., 2001, Modeling of an impact system with a drift, Physical Review E, 64, 056224
36. Peterka F., Vacik J., 1992, Transition to chaotic motion in mechanical systems with impacts, Journal of Sound and Vibration, 154, 95-115
37. Pfeiffer F., Kunert A., 1990, Rattling models from deterministic to stochastic processes, Nonlinear Dynamics, 1, 63-74
38. Pyragas K., 1992, Continuous control of chaos by self-controlling feedback, Physics Letters A, 170, 421-428
39. Tereshko V., Chacón R., Preciado V., 2004, Controlling chaotic oscillators by altering their energy, Physics Letters A, 320, 408-416
40. Warminski J., Balthazar J.M., Brasil R.M.L.R.F., 2001, Vibrations of a non-ideal parametrically and self-excited model, Journal of Sound and Vibration, 245, 363-374
41. Wiercigroch M., 2000, Modelling of dynamical systems with motion dependent discontinuities, Chaos, Solitons and Fractals, 11, 2429-2442
42. Wiercigroch M., de Kraker B., 2000, Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities, World Scientific, Singapore
43. Wiercigroch M., Wojewoda J., Krivtson A.M., 2005, Dynamics of ultrasonic percussive drilling of hard rocks, Journal of Sound and Vibration, 280, 739-757
44. Wolf A., Swift J.B., Swinney H.L., Vastano J.A., 1985, Determining Lyapunov exponents from a time series, Physica D, 16, 285-317
45. Xu X., Pavlovskaia E., Wiercigroch M., Romeo F., Lenci S., 2007, Dynamic interactions between parametric pendulum and electro-dynamical shaker, Z. Angew. Math. Mech., 87, 172-186
46. Yalla S.K., Kareem A., 2001, Beat phenomenon in combined structure liquid damper systems, Engineering Structures, 23, 622-630
47. Yalla S.K., Kareem A., Kantor J.C., 2001, Semi-active tuned liquid column dampers for vibration control of structures, Engineering Structures, 23, 1469-1479

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-article-BWM4-0009-0010