Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint</title> <meta name="description" content="Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint"> <meta name="keywords" content="Non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint"> <meta name="citation_author" content="M. Najafi"> <meta name="citation_author" content="F. Rahimi Dehgolan"> <meta name="citation_publication_date" content="2017/03/01"> <meta name="citation_journal_title" content="International Journal of Mechanical and Mechatronics Engineering"> <meta name="citation_volume" content="11"> <meta name="citation_issue" content="4"> <meta name="citation_firstpage" content="791"> <meta name="citation_lastpage" content="800"> <meta name="citation_pdf_url" content="https://publications.waset.org/10006928/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33093</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Najafi">M. Najafi</a>, <a href="https://publications.waset.org/search?q=F.%20Rahimi%20Dehgolan"> F. Rahimi Dehgolan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.</p> <iframe src="https://publications.waset.org/10006928.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Non-linear%20vibration" title="Non-linear vibration">Non-linear vibration</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=axially%20moving%20beam" title=" axially moving beam"> axially moving beam</a>, <a href="https://publications.waset.org/search?q=bifurcation" title=" bifurcation"> bifurcation</a>, <a href="https://publications.waset.org/search?q=multiple%20scales%20method." title=" multiple scales method."> multiple scales method.</a> </p> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1130105" target="_blank">doi.org/10.5281/zenodo.1130105</a> </p> <a href="https://publications.waset.org/10006928/non-linear-vibration-and-stability-analysis-of-an-axially-moving-beam-with-rotating-prismatic-joint" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006928/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006928/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006928/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006928/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006928/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006928/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006928/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006928/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006928/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006928/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006928.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1340</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] P. 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Botsalı, Lateral and torsional vibration analysis of elastic robot manipulators with prismatic joint, in: Proc. Of ETCE2002, ASME Eng. Technol. Conf. on Energy, Houston, TX, USA, (2002), Paper STRUC-29024. <br>[14] N. G. Chalhoub, L. Chen, A structural flexibility transformation matrix for modelling open-kinematic chains with revolute and prismatic joints, J. Sound Vib. 218 (1) (1998) 45–63. <br>[15] M. Gürgöze, Ş. Yüksel, Transverse vibrations of a flexible beam sliding through a prismatic joint, J. Sound Vib. 223 (3) (1999) 467–482. <br>[16] O. A. Bauchau, On the modeling of prismatic joints in flexible multi-body systems, Comput. Methods Appl. Mech. Eng. 181 (2000) 87–105. <br>[17] M. Kalyoncu, F. M. Botsalı, Vibration analysis of an elastic robot manipulator with prismatic joint and a time varying end mass, Arabian J. Sci. Eng. 29 (1C) (2004) 27–38. <br>[18] A. Ankaralı, M. Kalyoncu, F. M. Botsalı, T. 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Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint