ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Shcherbinin S. A., Goncharov P. P., Chechin G. M. Investigation of stability of nonlinear normal modes in electrical lattices. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 34-51. DOI: 10.18500/0869-6632-2013-21-2-34-51

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-2013-21-2-34-51

Investigation of stability of nonlinear normal modes in electrical lattices

Autors: 
Shcherbinin Stepan Aleksandrovich, Southern Federal University
Goncharov Petr Petrovich, Southern Federal University
Chechin Georgij Mihajlovich, Southern Federal University
Abstract: 

The problems of existence and stability of the symmetry-induced nonlinear normal modes in the electric chain of non-linear capacitors, connected to each other with linear inductors (the model described in Physica D238 (2009) 1228) are investigated. For all modes of this type, the upper limit of the stability region (in amplitude of voltage oscillations on capacitors) as a function of the chain cell number were found. Asymptotic formulas were determined at cell number tends to infinity.

Key words: 
nonlinear dynamics
lattice models
nonlinear normal modes
invariant manifolds
group-theoretical methods
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Received: 
19.07.2012
Accepted: 
19.07.2012
Published: 
31.07.2013
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