{"title":"Strange Nonchaotic Attractors in a Quasiperiodically Excited Slender Rigid Rocking Block with Two Frequencies","authors":"Jinkai Jiang, Zhengdong Du","doi":"10.1007/s10338-024-00464-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the existence of strange nonchaotic attractors (SNAs) in a slender rigid rocking block under quasi-periodic forcing with two frequencies. We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor, or between two chaotic attractors. In particular, we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors. This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems. The properties of SNAs are verified by the Lyapunov exponent, rational approximation, phase sensitivity, power spectrum, and separation of nearby trajectories.</p></div>","PeriodicalId":50892,"journal":{"name":"Acta Mechanica Solida Sinica","volume":"37 5","pages":"750 - 761"},"PeriodicalIF":2.0000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica Solida Sinica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10338-024-00464-w","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the existence of strange nonchaotic attractors (SNAs) in a slender rigid rocking block under quasi-periodic forcing with two frequencies. We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor, or between two chaotic attractors. In particular, we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors. This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems. The properties of SNAs are verified by the Lyapunov exponent, rational approximation, phase sensitivity, power spectrum, and separation of nearby trajectories.
本文研究了在具有两个频率的准周期强迫下，细长刚性摇摆块中是否存在奇异非混沌吸引子（SNA）。我们发现，奇异非混沌吸引子可能存在于准周期吸引子和混沌吸引子之间，也可能存在于两个混沌吸引子之间。特别是，我们证明了准周期吸引子的环倍增分岔可以在转化为混沌吸引子之前通过分形途径产生 SNA。这种现象在准周期强迫非连续微分方程和振动冲击系统中鲜有报道。通过李亚普诺夫指数、有理近似、相位灵敏度、功率谱和附近轨迹分离验证了 SNA 的特性。
期刊介绍：
Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics.
The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables
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