{"title":"Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam","authors":"Abbas Moallemi-Oreh, M. Karkon","doi":"10.1155/2013/841215","DOIUrl":null,"url":null,"abstract":"A two-node element is suggested for analyzing the stability and free vibration of Timoshenko beam. Cubic displacement polynomial and quadratic rotational fields are selected for this element. Moreover, it is assumed that shear strain of the element has the constant value. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy and its stationing to shear strain. By exploiting these interpolation functions, beam elements' stiffness matrix is also examined. Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.","PeriodicalId":44068,"journal":{"name":"Advances in Acoustics and Vibration","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2013-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/841215","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Acoustics and Vibration","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2013/841215","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 9
Abstract
A two-node element is suggested for analyzing the stability and free vibration of Timoshenko beam. Cubic displacement polynomial and quadratic rotational fields are selected for this element. Moreover, it is assumed that shear strain of the element has the constant value. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy and its stationing to shear strain. By exploiting these interpolation functions, beam elements' stiffness matrix is also examined. Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.
期刊介绍：
The aim of Advances in Acoustics and Vibration is to act as a platform for dissemination of innovative and original research and development work in the area of acoustics and vibration. The target audience of the journal comprises both researchers and practitioners. Articles with innovative works of theoretical and/or experimental nature with research and/or application focus can be considered for publication in the journal. Articles submitted for publication in Advances in Acoustics and Vibration must neither have been published previously nor be under consideration elsewhere. Subject areas include (but are not limited to): Active, semi-active, passive and combined active-passive noise and vibration control Acoustic signal processing Aero-acoustics and aviation noise Architectural acoustics Audio acoustics, mechanisms of human hearing, musical acoustics Community and environmental acoustics and vibration Computational acoustics, numerical techniques Condition monitoring, health diagnostics, vibration testing, non-destructive testing Human response to sound and vibration, Occupational noise exposure and control Industrial, machinery, transportation noise and vibration Low, mid, and high frequency noise and vibration Materials for noise and vibration control Measurement and actuation techniques, sensors, actuators Modal analysis, statistical energy analysis, wavelet analysis, inverse methods Non-linear acoustics and vibration Sound and vibration sources, source localisation, sound propagation Underwater and ship acoustics Vibro-acoustics and shock.
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