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Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism

Author(s)
Gendelman, O. V.; Sapsis, Themistoklis P.
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Abstract
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.
Date issued
2016-10
URI
http://hdl.handle.net/1721.1/107958
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Journal of Applied Mechanics
Publisher
American Society of Mechanical Engineers (ASME)
Citation
Gendelman, O. V., and T. P. Sapsis. “Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism.” Journal of Applied Mechanics 84.1 (2016): 011009. © 2017 ASME
Version: Final published version
ISSN
0021-8936
1528-9036

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