maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2018-1-54-62mais-630Research ArticleМатериалы конференцииConference PapersИнвариантные характеристики вынужденных колебаний балки с продольным сжатиемInvariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compressionhttps://orcid.org/0000-0002-6403-4061ГлызинСергей ДмитриевичGlyzinSergey D.

д-р физ.-мат. наук, зав. кафедрой компьютерных сетей;

ведущий научный сотрудник

Doctor, Professor

 

glyzin@uniyar.ac.ruЛоханинМихаил ВладимировичLokhaninMikhail Vladimirovich

старший преподаватель

senior lecturer

lokhaninmv@mail.ruСиротинДмитрий МихайловичSirotinDmitry Mikhailovich

старший лаборант-исследователь

senior laboratory assistant researcher

hhiks@yandex.ruЯрославский государственный университет им. П.Г. Демидова; НЦЧ РАНРоссияP.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASRussian FederationЯрославский государственный университет им. П.Г. ДемидоваРоссияP.G. Demidov Yaroslavl State UniversityRussian FederationНЦЧ РАНРоссияScientific Center in Chernogolovka RASRussian Federation2018230220182515462Copyright © Глызин С.Д., Лоханин М.В., Сиротин Д.М., 20182018Глызин С.Д., Лоханин М.В., Сиротин Д.М.Glyzin S.D., Lokhanin M.V., Sirotin D.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/630

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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The authors declare that there are no conflicts of interest present.