New approach to beating phenomenon in coupled nonlinear oscillatory chains

Leonid I. Manevitch1
1N.N. Semenor Institute of Chemical Physics, Polymer and Composites Materials, Moscow, Russia

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Akhmeriev N.N., Ankiewicz A. (1992) Solitons: Nonlinear Pulses and Beams. Chapman and Hall, London

Uzunov I.M., Muschall R., Gölles M., Kivshar Yuri S., Malomed B.A., Lederer F. (1995) Pulse switching in nonlinear fiber directional couplers. Phys. Rev. E 51, 2527–2537

Kosevich A.M., Kovalyov A.S. (1989) Introduction to Nonlinear Physical Mechanics. Naukova Dumka, Kiev (in Russian)

Manevich A.I., Manevitch L.I. (2005) The Mechanics of Nonlinear Systems With Internal Resonances, 260p. Imperial College Press, London

Khasnutdinova K.R., Pelinovsky D.E. (2003) On the exchange of energy in coupled Klein–Gordon equations. Wave Motion 38, 1–10

Rosenberg R.M. (1966) On nonlinear vibrations of system with many degrees od freedom. Adv. Appl. Mech. 9, 155–242

Manevitch L.I., Mikhlin Yu.V., Pilipchuk V.N. (1985) The Method of Normal Vibrations for Essentially Nonlinear Systems, 250p. Nauka, Moscow (in Russian)

Vakakis A.F., Manevitch L.I., Mikhlin Yu.V., Pilipchuk V.N., Zevin A.A. (1996) Normal Modes and Localization in Nonlinear Systems, 550p. Wiley, New York

Pilipchuk, V.N.: A transformation for vibrating system based on a non-smooth pair of functions, Doklady AN Ukr, SSR, ser. A, 4, pp. 37–40 (in Russian) (1988)

Manevitch L.I. (2001) The description of localized normal modes in a chain of nonlinear coupled oscillatorsusing complex variables. Nonlin. Dyn. 25, 95–10

Neishtadt A.I. (1975) Passage through a separatrix in a resonance problem with slowly varying parameter. J. Appl. Math. Mech. 39, 594–605

Rand R.H., Quinn D.D. (1995) Resonant capture in a system of two coupled homoclinic oscillators. J. Vibr. Control 1, 41–56

Gendelman O. (2001) Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlin. Dyn. 25, 237–253

Gendelman O., Manevitch L.I., Vakakis A.F., M’Closkey R. (2001) Energy pumping in nonlinear mechanical oscillators. I: dynamics of the underlying hamiltonian systems. ASME J. Appl. Mech. 68, 34–41

Manevitch L.I., Gendelman O., Musienko A.I., Vakakis A.F., Bergman L. (2003) Dynamic interaction of a semi-infinite linear chain of coupled oscillators with a strongly nonlinear end attachment. Physica D 178, 1–18

Gendelman O.V., Gorlov D.V., Manevitch L.I., Musienko A.I. (2005) Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses. J. Sound Vibr. 286, 1–19

Manevitch, L.I., Musienko, A.I., Lamarque, C.H.: Energy pumping in strongly nonhomogeneous 2DoF system with single anchor spring. Meccanica (2005) (in press)