{"title":"Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire","authors":"M. Mamode","doi":"10.4208/AAMM.11-M1141","DOIUrl":null,"url":null,"abstract":"The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.","PeriodicalId":56331,"journal":{"name":"Advances in Applied Mechanics","volume":"3 1","pages":"689-701"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4208/AAMM.11-M1141","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/AAMM.11-M1141","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 1
Abstract
The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.
期刊介绍：
Advances in Applied Mechanics draws together recent significant advances in all areas of applied mechanics. Published since 1948, it aims to provide the highest quality, authoritative review articles on topics in the mechanical sciences. It is of primary interest to scientists and engineers working in the various branches of mechanics and is also valuable to those who apply the results of investigations in mechanics to areas such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering.
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