Nonstationary Vibrations of a Perforated Cantilever Tube with a Translating Internal Cylinder Under Frictional Moving Contact

Nonstationary Vibrations of a Perforated Cantilever Tube with a Translating Internal Cylinder Under Frictional Moving Contact | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonstationary Vibrations of a Perforated Cantilever Tube with a Translating Internal Cylinder Under Frictional Moving Contact Mete Kalyoncu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9201242/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper develops a theory-first framework for the nonstationary transverse vibration of a slender perforated cantilever tube (fixed–free) excited by a translating internal cylindrical body under continuous frictional moving contact. In contrast to classical moving-load/moving-mass models with prescribed excitation, the proposed formulation treats the interaction as a spatially migrating and state-dependent forcing mechanism, where the contact magnitude is governed by an indentation-based normal law augmented with Coulomb friction and the excitation location follows the internal-body trajectory . Perforation effects are incorporated through effective (equivalent) stiffness and inertia operators, enabling systematic sensitivity studies while preserving analytical transparency. The coupled dynamics are derived from Hamilton’s principle (with non-conservative generalized forces for friction), yielding a non-autonomous PDE–ODE system that couples tube bending to the body’s axial motion and exit-speed prescription. A cantilever-consistent Galerkin modal reduction produces a reduced-order model in which migration enters explicitly through time-varying modal participation factors . A dimensionless formulation is presented to expose the governing control groups (mass ratio, contact stiffness ratio, friction number, and speed/traversal ratios) and to enable regime interpretation. Numerical examples and analysis outputs—including tip displacement/acceleration, fixed-end bending moment, STFT-based time–frequency signatures, Campbell-like speed maps, and contact-induced mode evolution—demonstrate that the translating cylinder acts as a broadband nonstationary source that can reorganize modal dominance, create speed-dependent amplification windows, and yield friction-mediated response growth. The resulting analytical scaffold provides a rigorous basis for prediction and design screening of cantilevered perforated tubular structures with internal translating elements. Perforated tube friction-induced vibration moving internal body nonstationary excitation coupled PDE–ODE dynamics transient resonance modal reduction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9201242","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615470315,"identity":"80ea8386-8e81-4079-bfff-721395054162","order_by":0,"name":"Mete Kalyoncu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYDACHgbGA2AGextU5ABhLVA1PMcYG6BaoAyCWiTSiNSi23P4wWGeijvyBjefpT/m3cEgx3cjgf1xBR4tZmfbDA7znHlmuOF22sFm3jMMxpI3Ehgbz+DTcp7B4DBv2+EEg9vpjc28bQyJG0Ba8LnM7Dz7B4iWm8fBWuoJaznbA7XlBttBkBYgg5CWM2cKDs45c9hw5pm0xJlz2ySAjIeNM/FrSd/44E3FYXm+48cMPrxtswEykg98xKcFBJh4EGwJICYQkyDA+IOgklEwCkbBKBjRAAAE/lqgQZsz4QAAAABJRU5ErkJggg==","orcid":"","institution":"Konya Technical University","correspondingAuthor":true,"prefix":"","firstName":"Mete","middleName":"","lastName":"Kalyoncu","suffix":""}],"badges":[],"createdAt":"2026-03-23 13:38:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9201242/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9201242/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107482651,"identity":"b0095c57-75a8-4ac5-ae44-017a3e4ff86f","added_by":"auto","created_at":"2026-04-22 02:24:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1622346,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptMeteKALYONCU.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9201242/v1_covered_66d38c89-1caa-4895-ae25-fe96512bd33f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonstationary Vibrations of a Perforated Cantilever Tube with a Translating Internal Cylinder Under Frictional Moving Contact","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Perforated tube, friction-induced vibration, moving internal body, nonstationary excitation, coupled PDE–ODE dynamics, transient resonance, modal reduction","lastPublishedDoi":"10.21203/rs.3.rs-9201242/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9201242/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper develops a theory-first framework for the nonstationary transverse vibration of a slender perforated cantilever tube (fixed–free) excited by a translating internal cylindrical body under continuous frictional moving contact. In contrast to classical moving-load/moving-mass models with prescribed excitation, the proposed formulation treats the interaction as a spatially migrating and state-dependent forcing mechanism, where the contact magnitude is governed by an indentation-based normal law augmented with Coulomb friction and the excitation location follows the internal-body trajectory . Perforation effects are incorporated through effective (equivalent) stiffness and inertia operators, enabling systematic sensitivity studies while preserving analytical transparency. The coupled dynamics are derived from Hamilton’s principle (with non-conservative generalized forces for friction), yielding a non-autonomous PDE–ODE system that couples tube bending to the body’s axial motion and exit-speed prescription. A cantilever-consistent Galerkin modal reduction produces a reduced-order model in which migration enters explicitly through time-varying modal participation factors . A dimensionless formulation is presented to expose the governing control groups (mass ratio, contact stiffness ratio, friction number, and speed/traversal ratios) and to enable regime interpretation. Numerical examples and analysis outputs—including tip displacement/acceleration, fixed-end bending moment, STFT-based time–frequency signatures, Campbell-like speed maps, and contact-induced mode evolution—demonstrate that the translating cylinder acts as a broadband nonstationary source that can reorganize modal dominance, create speed-dependent amplification windows, and yield friction-mediated response growth. 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