{"title":"耦合非线性振子:近似有效方程振幅分布的变形- 1:3共振的情况","authors":"J. Kyzioł, A. Okniński","doi":"10.5506/APhysPolB.43.1275","DOIUrl":null,"url":null,"abstract":"We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(\\Omega)$. In the present paper we investigate metamorphoses of the function $A(\\Omega)$ induced by changes of the control parameters in the case of 1:3 resonances.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance\",\"authors\":\"J. Kyzioł, A. Okniński\",\"doi\":\"10.5506/APhysPolB.43.1275\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(\\\\Omega)$. In the present paper we investigate metamorphoses of the function $A(\\\\Omega)$ induced by changes of the control parameters in the case of 1:3 resonances.\",\"PeriodicalId\":166772,\"journal\":{\"name\":\"arXiv: Chaotic Dynamics\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Chaotic Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5506/APhysPolB.43.1275\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Chaotic Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5506/APhysPolB.43.1275","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance
We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(\Omega)$. In the present paper we investigate metamorphoses of the function $A(\Omega)$ induced by changes of the control parameters in the case of 1:3 resonances.
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