{"title":"考虑外部切向载荷的杆侧摆动数学模型","authors":"I. V. Kudinov, A. V. Pashin, Yu. A. Kryukov","doi":"10.1134/s1995080224602431","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load\",\"authors\":\"I. V. Kudinov, A. V. Pashin, Yu. A. Kryukov\",\"doi\":\"10.1134/s1995080224602431\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":\"59 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224602431\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602431","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load
Abstract
A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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