O. O. Agboola, Talib EH. Elaikh, J. G. Oghonyon, Olajide Ibikunle
{"title":"Effect of Mass per Unit Length on freely vibrating Simply Supported Rayleigh Beam","authors":"O. O. Agboola, Talib EH. Elaikh, J. G. Oghonyon, Olajide Ibikunle","doi":"10.37394/232013.2022.17.17","DOIUrl":null,"url":null,"abstract":"In this paper, free vibration characteristics of a uniform Rayleigh beam are studied using the differential transform method. The procedure entails transforming the partial differential equation governing the motion of the beam under consideration and the associated boundary conditions. The transformation yields a set of difference equations. Some simple algebraic operations are performed on the resulting difference equations to determine any ith natural frequency and the closed-form series function for any ith mode shape. Finally, one problem is presented to illustrate the implementation of the present method and analyse the effect of mass per length on the natural frequencies of the beam.","PeriodicalId":39418,"journal":{"name":"WSEAS Transactions on Fluid Mechanics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Fluid Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232013.2022.17.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, free vibration characteristics of a uniform Rayleigh beam are studied using the differential transform method. The procedure entails transforming the partial differential equation governing the motion of the beam under consideration and the associated boundary conditions. The transformation yields a set of difference equations. Some simple algebraic operations are performed on the resulting difference equations to determine any ith natural frequency and the closed-form series function for any ith mode shape. Finally, one problem is presented to illustrate the implementation of the present method and analyse the effect of mass per length on the natural frequencies of the beam.
期刊介绍：
WSEAS Transactions on Fluid Mechanics publishes original research papers relating to the studying of fluids. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of this particular area. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with multiphase flow, boundary layer flow, material properties, wave modelling and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.
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