Nonlinear dynamics of coupled nonlinear oscillators: Using of complex variables

Proceedings of the ASME Design Engineering Technical Conference

Volumn 7B-1999, Issue , 1999, Pages 1845-1854

  Manevitch, L I ^a  

^a SEMENOV INSTITUTE OF CHEMICAL PHYSICS   (Russian Federation)

Author keywords

Complex representation; Coupled oscillators; Localization; Nonlinear dynamics; Nonlinear normal mode

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); OSCILLATORS (MECHANICAL); VIBRATIONS (MECHANICAL);

COMPLEX VARIABLE; COUPLED NONLINEAR OSCILLATORS; DYNAMIC EQUATIONS; NORMAL MODES; STRONG COUPLING; TWO DEGREES OF FREEDOM;

NONLINEAR EQUATIONS;

EID: 33746354409     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC99-VIB-8004     Document Type: Conference Paper

References (23)

1. Bogolyubov N.P, and Mitropolsky Yu.A., 1963, "Asymptotic methods in the theory of nonlinear vibrations", Nauka, Moscow, pp.295-336.
2. Cole J.D, 1968, "Perturbation methods in applied mathematics", Blaisdell Publishing Company, Toronto-London, pp.92-101.
3. Collinns A., 1983, "Solitons in Chemical Physics", Advances in Chemical Physics, Vol.53, 307-320.
4. Gendelman O.V., and Vakakis A.F, Private communication.
5. Kosevich A.M., and Kovalyov A.S., 1989, "Introduction to Nonlinear Physical Mechanics (in Russian), Naukova dumka, Kiev., pp.57-71, 107-119.
6. Kosevich A.M., and Kovalyov A.S., 1974, Self-localization of oscillatios in a one-dimensial anharmonic chain",(in Russian), Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol.67, N5, pp. 1793-1804.
7. Louisell W.H., 1960, "Coupled mode and parametric electronics", Wiley, NY, pp.351.
8. Louisell W.H., 1962, "Correspondence between Pierce's Coupled Mode Amplitudes and Quantum Operators", Journal of Applied Physics, Vol.33, N8, pp.2435-2436.
9. Manevitch L.I., 1997, " Complex representationin Nonlinear Dynamics", Dynamical Systems:Theory and Applications (Ed. J. Awrejcewicz), Poland, Lodz
10. Manevitch L.I., 199, The description of localized normal modes in a chain of nonlinear coupled oscillators:using of complex variables Nonlinear Dynamics, (to be published).
11. Manevitch L.I., Mikhlin Yu.V., and Pilipchuk V.N., 1989, "Normal vibration technique for strongly nonlinear systems", Nauka, Ioscow, pp.
12. Manevitch L.I., and Savin A.V., 1995, "Soliton Mechanism for propagation of endothermal structural transition", Soviet Physical Journal of Experimental and Theoretical Physics, Vol.80, N4,pp 706-712.
13. Manevitch L.I., and Savin A.V., 1997, "Solitons in crystalline polyethylene: Isolated chains in the transconformation", Physical Review E, Vol.55, pp. 4713-4719.
14. Manevitch L.I., Savin A.V, Smirnov VV, and Volkov S.N., 1994, "Solitons in non-degenarated bistable systems", Physics-Uspekhi, Vol.37, N9, pp.859-880.
15. Manevitch L.I., and Smirnov VV, 1992, " Propagation of exothermic reactions in Condensed Matter", Physics Letters A, Vol.165, pp.365-370.
16. Nayfeh A.H., 1981, "Introduction to Perturbation Techniques", Wiley, New York, pp. 182-185.
17. Ovchinnikov A.A, 1970, "Localized long-lived vibrational states in molecular crystals", Soviet Physical Journal of Experimental and Theoretical Physics, Vol.30, pp.147-154.
18. Pierce J.K., 1954, "Coupling of Modes of Propagation", Journal of Applied Physics, Vol.25, N 1, pp.179-183.
19. Rabinovich M.I., and Trubetskov D.I., 1984, "Introduction to the theory of vibrations and waves" (in Russian), Nauka, Moscow, pp.32-34.
20. Sage M.I, and Jornter J., 1981, "Bond modes", Advances in.Chemcal Physics, Vol.47, part 1, pp.293-322.
21. Scott A.C., Lomdahl P.S., and Eilbeek J.C., 1985, "Between the local-mode and normal- mode limits", Chemical Physics Letters, Vol.113, pp.29-36.
22. Vakakis A.F., Manevitch L.I., Mikhlin Yu.V, Pilipchuk V.N., and Zevin A.A., 1996, "Normal Modes and Localzation in Nonlinear Systems", Wiley, NY, pp. 1-22, 285-348.
23. Zaharov V.E., Novicov S.P.,.Shabat B.V, and Pitaevsky L.P., 1980, "Theory of solitons", (in Russian), Nauka, Moscow, pp.85-97.