Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper, we are going to demonstrate that the structure of the resonance manifold can be conveniently described in terms of canonical action–angle (AA) variables. Such formalism has important theoretical advantages: all resonance manifolds may be described at the same level of complexity, appearance of additional conservation laws on these manifolds is easily proven both in autonomous and nonautonomous settings. The harmonic balance-based complexification approach, used in many previous studies on the subject, is shown to be a particular case of the canonical formalism. Moreover, application of the canonic averaging allows treatment of much broader variety of dynamical models. As an example, energy exchanges in systems of coupled trigonometrical and vibro-impact oscillators are considered.
Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism
Massachusetts Institute of Technology,
Cambridge, MA 02139
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 17, 2016; final manuscript received October 5, 2016; published online October 26, 2016. Assoc. Editor: Alexander F. Vakakis.
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Gendelman, O. V., and Sapsis, T. P. (October 26, 2016). "Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism." ASME. J. Appl. Mech. January 2017; 84(1): 011009. https://doi.org/10.1115/1.4034930
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