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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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2018-02-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/630 |
| _version_ | 1797878016319160320 |
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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. |
| first_indexed | 2024-04-10T02:26:04Z |
| format | Article |
| id | doaj.art-698d5082b1354aeda04b87e78054a4e0 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:26:04Z |
| publishDate | 2018-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-698d5082b1354aeda04b87e78054a4e02023-03-13T08:07:29ZengYaroslavl 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 Sirotin2Ярославский государственный университет им. П.Г. Демидова; НЦЧ РАНЯрославский государственный университет им. П.Г. ДемидоваНЦЧ РАНOscillations 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/630балка с продольным сжатиемустойчивостьбифуркацииуравнение дуффингааттрактор уэдыхаотические колебанияэнтропияляпуновские показатели |
| 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 балка с продольным сжатием устойчивость бифуркации уравнение дуффинга аттрактор уэды хаотические колебания энтропия ляпуновские показатели |
| 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 | балка с продольным сжатием устойчивость бифуркации уравнение дуффинга аттрактор уэды хаотические колебания энтропия ляпуновские показатели |
| url | https://www.mais-journal.ru/jour/article/view/630 |
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