{"title":"Study on chaotic characteristics of horizontal nonlinear roller system with fractional order","authors":"Li Jiang, Tao Wang, Qing-Xue Huang, Wei Shi","doi":"10.1007/s00419-023-02389-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, Duffing oscillator is introduced to study the chaotic characteristics of nonlinear roller system in detail. Firstly, the horizontal nonlinear dynamics equations of the roller system with fractional derivative terms were established . Secondly, amplitude–frequency characteristics of the system by the multi-scale method were solved and the influence relationship of various parameters on the system was discussed. Thirdly, according to the perturbation theory and the Melnikov method, the necessary conditions were studied for generating chaos under the Smale horseshoe meaning of the roller system. Finally, the coincidence of the analytical and numerical solutions was verified . And the chaotic characteristics of the system are studied by numerical simulation.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"93 6","pages":"2435 - 2447"},"PeriodicalIF":2.2000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-023-02389-1","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, Duffing oscillator is introduced to study the chaotic characteristics of nonlinear roller system in detail. Firstly, the horizontal nonlinear dynamics equations of the roller system with fractional derivative terms were established . Secondly, amplitude–frequency characteristics of the system by the multi-scale method were solved and the influence relationship of various parameters on the system was discussed. Thirdly, according to the perturbation theory and the Melnikov method, the necessary conditions were studied for generating chaos under the Smale horseshoe meaning of the roller system. Finally, the coincidence of the analytical and numerical solutions was verified . And the chaotic characteristics of the system are studied by numerical simulation.
期刊介绍：
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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