{"title":"Analytical solution of couple-mass-spring systems by novel homotopy perturbation method","authors":"Nazmul Sharif, Helal Uddin Molla, M.S. Alam","doi":"10.1016/j.ijnonlinmec.2024.104923","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, a novel homotopy perturbation method is employed to estimate the approximate angular frequencies of highly nonlinear oscillators. This innovative methodology is extended to generate periodic solutions for the nonlinear free vibration observed in a conservative couple-mass-spring system. The system is characterized by both linear and nonlinear stiffness, specifically incorporating cubic nonlinearity. The application of this technique involves a detailed analysis of two practical instances of such systems. The validation process, comparing the results against published findings and exact solutions, reveals a notable alignment in the approximated angular frequencies and the corresponding periodic solutions. Noteworthy for its precision and easy to use application, this approach proves suitable for addressing a diverse range of nonlinear oscillatory problems encountered in both scientific and engineering domains.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104923"},"PeriodicalIF":2.8000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020746224002889","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, a novel homotopy perturbation method is employed to estimate the approximate angular frequencies of highly nonlinear oscillators. This innovative methodology is extended to generate periodic solutions for the nonlinear free vibration observed in a conservative couple-mass-spring system. The system is characterized by both linear and nonlinear stiffness, specifically incorporating cubic nonlinearity. The application of this technique involves a detailed analysis of two practical instances of such systems. The validation process, comparing the results against published findings and exact solutions, reveals a notable alignment in the approximated angular frequencies and the corresponding periodic solutions. Noteworthy for its precision and easy to use application, this approach proves suitable for addressing a diverse range of nonlinear oscillatory problems encountered in both scientific and engineering domains.
期刊介绍：
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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