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Nonlinear normal modes of three degree of freedom mechanical oscillator

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we show the method of calculation of nonlinear normal modes and its application to mechanical coupled systems. We present bifurcation diagram of nonlinear normal modes in three degree of freedom system. We show the appearance of internal resonances and their important role in dynamics of nonlinear coupled oscillators.
Rocznik
Strony
117--124
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
  • Department of Mechanics of Textile Machines, Faculty of Engineering and Marketing of Textiles, Technical University of Lódź, Żeromskiego 116, 90-543 Łódź, Poland
Bibliografia
  • [1] Schuster, H. G.: Deterministic Chaos, Chemie, Weinheim, 1984.
  • [2] Kapitaniak, T.: Chaos for Engineers: Theory, Applications, and Control, Springer-Verlag Berlin and Heidelberg, 1998.
  • [3] Shaw, S.W. and Pierre, C.: Nonlinear normal modes and invariant manifolds, Journal of Sound and Vibration, 150, (1), 1991.
  • [4] Shaw, S.W. and Pierre, C.: Normal modes for nonlinear vibratory systems, Journal of Sound and Vibration, 164, (1), 1993.
  • [5] Vakakis, A.F. and Rand, R.H.: Normal modes and global dynamics of a 2-degree-of-freedom nonlinear-system; part I: low energies, International Journal of Non-Linear Mechanics, 27, 1992.
  • [6] Vakakis, A.F. and Rand, R.H.: Normal modes and global dynamics of a 2-degree-of-freedom nonlinear-system: Part II: high energies, International Journal of Non-Linear Mechanics, 27, 1992.
  • [7] Vakakis, A.F., Manevitch, L.L, Mikhlin, Y.V., Pilipchuk, V.N. and Zevin, A.A.: Normal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.
  • [8] Rosenberg, R.M.: Normal modes of nonlinear dual-mode systems, Journal of Applied Mechanics, 27, 1960.
  • [9] Doedel, E.: A UTO, Software for Continuation and Bifurcation Problems in Ordinary Differential Equations, 2007.
  • [10] Peeters, M., Viguie, R., Serandour, G., Kerschen, G. and Golinval, J.C.: Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques, Mechanical Systems and Signal Processing, 23, 2008.
  • [11] Keller, H. B.: Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems, Applications of Bifurcation Theory, P. Rabinowitz ed., Academic Press, 1977.
  • [12] Kunetsov, Y. A.: Elements of Applied Bifurcation Theory, Springer- Verlag Applied Mathematical Sciences, 112, 1995.
  • [13] Doedel, E.J., Paffenroth, R.C., Keller, H.B., Dickmann, D.J., Galan Vioque, J. and Vanderbauwhede, A.: Computation of periodic solutions of conservative systems with application to the 3-body problem, International Journal of Bifurcations and Chaos, 13, (6), 2003.
  • [14] Perlikowski, P., Stefanski, A. and Kapitaniak, T.: 1:1 Mode locking and generalized synchronization in mechanical oscillators, Journal Sound and Vibration, 2008.
  • [15] Schilder, F: Rauto: running auto more efficiently, Papers from the Department of Mathematics, University of Surrey, no. 131, 2001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0027-0035
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