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Regul. Chaotic Dyn., 2015, Volume 20, Issue 2, Pages 109–122 (Mi rcd48)  

This article is cited in 3 scientific papers (total in 3 papers)

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

Abstract: 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.

Keywords: energy exchange, energy localization, beam, elastic support, nonlinear normal modes, limiting phase trajectories

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00284 a
The investigation was supported by RFBR (grant 14-01-00284 a).


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Bibliographic databases:

MSC: 34A34, 34C15, 34E05, 70K75, 70K05, 70K30
Received: 20.12.2014

Citation: 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

Citation in format AMSBIB
\by Kseniya G. Silina, Irina P. Kikot, Leonid I. Manevitch
\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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    This publication is cited in the following articles:
    1. I. P. Koroleva (Kikot), L. I. Manevich, “Ostsillyatornaya tsep na uprugoi podlozhke v usloviyakh akusticheskogo vakuuma”, Nelineinaya dinam., 11:3 (2015), 487–502  mathnet
    2. I. P. Koroleva (Kikot), L. I. Manevich, “Ostsillyatornaya tsep c izgibnoi zhestkostyu na uprugoi podlozhke v usloviyakh, blizkikh k akusticheskomu vakuumu”, Nelineinaya dinam., 12:3 (2016), 311–325  mathnet  crossref  mathscinet  elib
    3. A. Kovaleva, L. I. Manevitch, “Internal autoresonance in coupled oscillators with slowly decaying frequency”, Phys. Rev. E, 96:3 (2017), 032213  crossref  isi  scopus
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