Regular and Chaotic Dynamics
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Regular and Chaotic Dynamics, 2015, том 20, выпуск 2, страницы 109–122
DOI: https://doi.org/10.1134/S156035471502001X
(Mi rcd48)
 

Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)

Energy Exchange and Localization in the Planar Motion of a Weightless Beam Carrying Two Discrete Masses

Kseniya G. Silina, Irina P. Kikot, Leonid I. Manevitch

Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991 Russia
Список литературы:
Аннотация: We present analytical and numerical studies of nonstationary resonance processes in a system with four degrees of freedom. The system under consideration can be considered as one of the simplest geometrically nonlinear discrete models of an elastic beam supported by nonlinear elastic grounding support. Two symmetrically distributed discrete masses reflect the inertial properties of the beam, two angular springs simulate its bending stiffness. The longitudinal springs, as is usual in systems of oscillators, reflect the tensile stiffness and two transversal springs simulate the reaction of grounding support. Dealing with lowenergy dynamics, we singled out the equations of transversal motion corresponding to the approximation of two coupled oscillators with nonlocal nonlinearity in elastic forces. We have analyzed this model using the concept of limiting phase trajectories (LPT). LPT’s concept was recently developed to study the nonstationary resonance dynamics. An analytical description of intensive interparticle energy exchange was obtained in terms of nonsmooth functions, which is consistent with numerical results. We have identified two dynamic transitions the first of which corresponds to the instability of out-of-phase normal mode and the second one is a transition from the intense energy exchange to the energy localization on the initially excited oscillator. Special attention was paid to the influence of bending stiffness on the conditions that ensure the implementation of each of the dynamic transitions.
Ключевые слова: energy exchange, energy localization, beam, elastic support, nonlinear normal modes, limiting phase trajectories.
Финансовая поддержка Номер гранта
Российский фонд фундаментальных исследований 14-01-00284 a
The investigation was supported by RFBR (grant 14-01-00284 a).
Поступила в редакцию: 20.12.2014
Реферативные базы данных:
Тип публикации: Статья
Язык публикации: английский
Образец цитирования: Kseniya G. Silina, Irina P. Kikot, Leonid I. Manevitch, “Energy Exchange and Localization in the Planar Motion of a Weightless Beam Carrying Two Discrete Masses”, Regul. Chaotic Dyn., 20:2 (2015), 109–122
Цитирование в формате AMSBIB
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\paper Energy Exchange and Localization in the Planar Motion of a Weightless Beam Carrying Two Discrete Masses
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 109--122
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  • https://www.mathnet.ru/rus/rcd48
  • https://www.mathnet.ru/rus/rcd/v20/i2/p109
  • Эта публикация цитируется в следующих 4 статьяx:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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