{"title":"A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force","authors":"Nazmul Sharif, Helal Uddin Molla, Abdul Alim","doi":"10.1177/14613484231198958","DOIUrl":null,"url":null,"abstract":"In this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions of the present method pleasantly agree with the numerical solution obtained by Runge–Kutta fourth order method. Accuracy and simplicity of the present method solution is established when compared with the other method solutions. The present method can be utilized to other nonlinear oscillators.","PeriodicalId":56067,"journal":{"name":"Journal of Low Frequency Noise Vibration and Active Control","volume":"89 1","pages":"0"},"PeriodicalIF":2.4000,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Low Frequency Noise Vibration and Active Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/14613484231198958","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions of the present method pleasantly agree with the numerical solution obtained by Runge–Kutta fourth order method. Accuracy and simplicity of the present method solution is established when compared with the other method solutions. The present method can be utilized to other nonlinear oscillators.
期刊介绍：
Journal of Low Frequency Noise, Vibration & Active Control is a peer-reviewed, open access journal, bringing together material which otherwise would be scattered. The journal is the cornerstone of the creation of a unified corpus of knowledge on the subject.
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