Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism
Name
Sapsis_Energy exchange.pdf
Size
4.06 MB
Format
Adobe PDF
Checksum (MD5)
0a8a898faceeddb35cda565ee6040d3b
Author(s)
Gendelman, O. V.
Sapsis, Themistoklis P.
Date Issued
October 2016
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1115/1.4034930
