The chaotic dynamics of vibrational mechanisms with energy sources of limited power

N. N. Verichev*, S. N. Verichev, V. I. Yerofeyev

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

The dynamics of a vibrational mechanism with an energy source of limited power is considered. A system of two degrees of freedom is reduced to a system of the Lorenz type by the method of averaging. The existence of one of the types of chaotic attractors in a dynamical system which is a vibrational mechanism, that is, a Lorenz attractor, is established by this. The existence of a Feigenbaum attractor and intermittence is also established. Chaotic limit sets determine the chaotic behaviour of the instantaneous frequency of rotation of an asynchronous motor. The qualitative patterns of the rotational characteristic are constructed for different values of the parameters of the system and a physical interpretation of the results is given.

Original languageEnglish
Pages (from-to)396-407
Number of pages12
JournalJournal of Applied Mathematics and Mechanics
Volume71
Issue number3
DOIs
Publication statusPublished - 2007

Bibliographical note

Funding Information:
This research was partially supported by the Russian Foundation for Basic Research (06-08-00520, 06-02-17158, 06-02-17158).

Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

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