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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 3, Pages 487–502
(Mi nd492)
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This article is cited in 8 scientific papers (total in 8 papers)
Original papers
Oscillatory chain with grounding support in conditions of acoustic vacuum
I. P. Koroleva (Kikot), L. I. Manevich N.N.Semenov Institute of Chemical Physics, Russian Academy of Sciences,
Kosygina st. 4, Moscow, 117977, Russia
Abstract:
In this work we investigate dynamics of a string with uniformly distributed discrete masses without tension both analytically and numerically. Each mass is also coupled to the ground through lateral spring which provides effect of cubic grounding support. The most important limiting case of low-energy transversal oscillations is considered accounting for geometric nonlinearity. Since such oscillations are governed by motion equations with purely cubic stiffness nonlinearities, the chain behaves as a nonlinear acoustic vacuum.We obtained adequate analytical description of resonance non-stationary processes in the system which correspond to intensive energy exchange between parts (clusters) of the chain in low-frequency domain. Conditions of energy localization are given. Obtained analytical results agree well with results of computer simulations. The considered system is shown to be able to be used as very effective energy sink.
Keywords:
nonlinear dynamics, nonlinear normal mode, limiting phase trajectory, energy exchange, localization.
Received: 26.06.2015 Revised: 25.08.2015
Citation:
I. P. Koroleva (Kikot), L. I. Manevich, “Oscillatory chain with grounding support in conditions of acoustic vacuum”, Nelin. Dinam., 11:3 (2015), 487–502
Linking options:
https://www.mathnet.ru/eng/nd492 https://www.mathnet.ru/eng/nd/v11/i3/p487
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Statistics & downloads: |
Abstract page: | 249 | Full-text PDF : | 71 | References: | 81 |
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