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Nelin. Dinam., 2015, Volume 11, Number 3, Pages 487–502 (Mi nd492)  

This article is cited in 6 scientific papers (total in 6 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

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00284 A


Full text: PDF file (9833 kB)
References: PDF file   HTML file
UDC: 534.015.1, 534-6
MSC: 70K30, 70K50, 70K75
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

Citation in format AMSBIB
\Bibitem{KorMan15}
\by I.~P.~Koroleva~(Kikot), L.~I.~Manevich
\paper Oscillatory chain with grounding support in conditions of acoustic vacuum
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 3
\pages 487--502
\mathnet{http://mi.mathnet.ru/nd492}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Kevorkov, R. K. Khamidullin, I. P. Koroleva, V. V. Smirnov, E. B. Gusarova, L. I. Manevich, “Efficiency of a Three-Particle Energy Sink: Experimental Study and Numerical Simulation”, Nelineinaya dinam., 14:3 (2018), 355–366  mathnet  crossref  elib
    2. V. V. Sminrov, L. I. Manevitch, “Forced oscillations of the string under conditions of ‘sonic vacuum’”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 376:2127 (2018), 20170135  crossref  mathscinet  isi  scopus
    3. L. I. Manevitch, A. Kovaleva, V. Smirnov, Yu. Starosvetsky, “Strongly nonlinear lattices”, Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures, Foundations of Engineering Mechanics, Springer-Verlag Berlin, 2018, 355–390  crossref  mathscinet  isi  scopus
    4. Zh. Zhang, L. I. Manevitch, V. Smirnov, L. A. Bergman, A. F. Vakakis, “Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane”, J. Mech. Phys. Solids, 110 (2018), 1–20  crossref  mathscinet  isi  scopus
    5. C. Liu, Ch. Ma, Zh. Qin, Ch. Zhou, “Lateral vibration analysis of monatomic chains considering atomic longitudinal displacement”, J. Low Freq. Noise Vib. Act. Control, 38:2 (2019), 457–472  crossref  isi  scopus
    6. I. P. Koroleva (Kikot), L. I. Manevitch, “Is energy localization possible in the conditions of non-local acoustic vacuum?”, Problems of Nonlinear Mechanics and Physics of Materials, Advanced Structured Materials, 94, eds. I. Andrianov, A. Manevich, Y. Mikhlin, O. Gendelman, Springer, 2019, 25–38  crossref  mathscinet  isi  scopus
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