Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression

Oscillations of an elastic beam with longitudinal compression are considered. The beam consists of two steel strips connected on free ends and fixed on opposite ones. Compression is achieved by a strained string. Excitation of oscillations is performed by exposure of alternating magnetic field on a...

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Main Authors: Sergey D. Glyzin, Mikhail Vladimirovich Lokhanin, Dmitry Mikhailovich Sirotin
Format: Article
Language:English
Published: Yaroslavl State University 2018-02-01
Series:Моделирование и анализ информационных систем
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Online Access:https://www.mais-journal.ru/jour/article/view/630
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author Sergey D. Glyzin
Mikhail Vladimirovich Lokhanin
Dmitry Mikhailovich Sirotin
author_facet Sergey D. Glyzin
Mikhail Vladimirovich Lokhanin
Dmitry Mikhailovich Sirotin
author_sort Sergey D. Glyzin
collection DOAJ
description Oscillations of an elastic beam with longitudinal compression are considered. The beam consists of two steel strips connected on free ends and fixed on opposite ones. Compression is achieved by a strained string. Excitation of oscillations is performed by exposure of alternating magnetic field on a magnet placed on the loose end. The law of motion with a change in the frequency of the harmonic action is registered. As a result of the full-scale experiment a large set of data is obtained. This set contains ordered periodic oscillations as well as disordered oscillations specific to dynamical systems with chaotic behaviour. To study the invariant numerical characteristics of the attractor of the corresponding dynamical system, a correlation integral and a correlation dimensionality as well as β-statentropy are calculated. A large numerical experiment showed that the calculation of β-statentropy is preferable to the calculation of the correlation index. Based on the developed algorithms the dependence of β- statentropy on the frequency of the external action is constructed. The constructed dependence can serve as an effective tool for measuring the adequacy of the mathematical model of forced oscillations of buckling beam driven oscillations.
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publisher Yaroslavl State University
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series Моделирование и анализ информационных систем
spelling doaj-art-698d5082b1354aeda04b87e78054a4e02025-08-20T03:37:50ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172018-02-01251546210.18255/1818-1015-2018-1-54-62455Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal CompressionSergey D. Glyzin0Mikhail Vladimirovich Lokhanin1Dmitry Mikhailovich Sirotin2P.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State UniversityScientific Center in Chernogolovka RASOscillations of an elastic beam with longitudinal compression are considered. The beam consists of two steel strips connected on free ends and fixed on opposite ones. Compression is achieved by a strained string. Excitation of oscillations is performed by exposure of alternating magnetic field on a magnet placed on the loose end. The law of motion with a change in the frequency of the harmonic action is registered. As a result of the full-scale experiment a large set of data is obtained. This set contains ordered periodic oscillations as well as disordered oscillations specific to dynamical systems with chaotic behaviour. To study the invariant numerical characteristics of the attractor of the corresponding dynamical system, a correlation integral and a correlation dimensionality as well as β-statentropy are calculated. A large numerical experiment showed that the calculation of β-statentropy is preferable to the calculation of the correlation index. Based on the developed algorithms the dependence of β- statentropy on the frequency of the external action is constructed. The constructed dependence can serve as an effective tool for measuring the adequacy of the mathematical model of forced oscillations of buckling beam driven oscillations.https://www.mais-journal.ru/jour/article/view/630buckling beamstabilitybifurcationsduffing’s equationueda attractorchaotic oscillationsentropylyapunov exponents
spellingShingle Sergey D. Glyzin
Mikhail Vladimirovich Lokhanin
Dmitry Mikhailovich Sirotin
Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
Моделирование и анализ информационных систем
buckling beam
stability
bifurcations
duffing’s equation
ueda attractor
chaotic oscillations
entropy
lyapunov exponents
title Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
title_full Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
title_fullStr Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
title_full_unstemmed Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
title_short Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression
title_sort invariant characteristics of forced oscillations of a beam with longitudinal compression
topic buckling beam
stability
bifurcations
duffing’s equation
ueda attractor
chaotic oscillations
entropy
lyapunov exponents
url https://www.mais-journal.ru/jour/article/view/630
work_keys_str_mv AT sergeydglyzin invariantcharacteristicsofforcedoscillationsofabeamwithlongitudinalcompression
AT mikhailvladimirovichlokhanin invariantcharacteristicsofforcedoscillationsofabeamwithlongitudinalcompression
AT dmitrymikhailovichsirotin invariantcharacteristicsofforcedoscillationsofabeamwithlongitudinalcompression