An Analytical Investigation on Nonlinear Vibrations of Timoshenko Nanotubes Conveying Flow Based on Stress Driven-Nonlocal Theory Considering Nonlinear Foundation, Magnetic Field and Thermal Effects

An Analytical Investigation on Nonlinear Vibrations of Timoshenko Nanotubes Conveying Flow Based on Stress Driven-Nonlocal Theory Considering Nonlinear Foundation, Magnetic Field and Thermal Effects | 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 An Analytical Investigation on Nonlinear Vibrations of Timoshenko Nanotubes Conveying Flow Based on Stress Driven-Nonlocal Theory Considering Nonlinear Foundation, Magnetic Field and Thermal Effects Nooshin Asadifar, Ali Reza Saidi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8062333/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Mar, 2026 Read the published version in Acta Mechanica → Version 1 posted You are reading this latest preprint version Abstract This study examines the combined effects of magnetic fields, temperature change, and nonlocal elasticity on the nonlinear vibration behavior of nanotubes conveying fluid flow. The analysis is based on Timoshenko beam theory, which accounts for rotational inertia and shear deformation, together with the stress-driven nonlocal theory. The governing equations of the nanotube resting on nonlinear elastic foundations considering the thermomagnetic effects are derived using the Von-Kármán strain relations in conjunction with Hamilton’s principle. These equations are reduced to a set of nonlinear ordinary differential equations via the Galerkin method. The resulting time-dependent system of nonlinear equations are then solved analytically using homotopy analysis method for the first time, yielding closed-form expressions for both the nonlinear frequency and time-domain response. A comprehensive parametric study is conducted to explore the influence of various physical and material parameters on the system’s vibrational characteristics. The findings indicate that increases in magnetic field strength, temperature change, or slenderness ratio lead to a reduction in the nonlinear frequency ratio. Additionally, both the fluid velocity and fluid density decrease the nonlinear frequency but the initial amplitude leads to increase it. Nonlinear vibration Timoshenko beam theory Homotopy analysis method Nonlinear differential equations system Stress-driven nonlocal theory Thermal and magnetic environment Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Mar, 2026 Read the published version in Acta Mechanica → 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-8062333","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":555304289,"identity":"c296b986-0a01-476a-914d-a11efdf04886","order_by":0,"name":"Nooshin Asadifar","email":"","orcid":"","institution":"Shahid Bahonar University of Kerman","correspondingAuthor":false,"prefix":"","firstName":"Nooshin","middleName":"","lastName":"Asadifar","suffix":""},{"id":555304290,"identity":"d07c5162-052c-477e-af87-851deaf26ca7","order_by":1,"name":"Ali Reza 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Effects","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Nonlinear vibration, Timoshenko beam theory, Homotopy analysis method, Nonlinear differential equations system, Stress-driven nonlocal theory, Thermal and magnetic environment","lastPublishedDoi":"10.21203/rs.3.rs-8062333/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8062333/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study examines the combined effects of magnetic fields, temperature change, and nonlocal elasticity on the nonlinear vibration behavior of nanotubes conveying fluid flow. The analysis is based on Timoshenko beam theory, which accounts for rotational inertia and shear deformation, together with the stress-driven nonlocal theory. The governing equations of the nanotube resting on nonlinear elastic foundations considering the thermomagnetic effects are derived using the Von-Kármán strain relations in conjunction with Hamilton’s principle. These equations are reduced to a set of nonlinear ordinary differential equations via the Galerkin method. The resulting time-dependent system of nonlinear equations are then solved analytically using homotopy analysis method for the first time, yielding closed-form expressions for both the nonlinear frequency and time-domain response. A comprehensive parametric study is conducted to explore the influence of various physical and material parameters on the system’s vibrational characteristics. The findings indicate that increases in magnetic field strength, temperature change, or slenderness ratio lead to a reduction in the nonlinear frequency ratio. Additionally, both the fluid velocity and fluid density decrease the nonlinear frequency but the initial amplitude leads to increase it.","manuscriptTitle":"An Analytical Investigation on Nonlinear Vibrations of Timoshenko Nanotubes Conveying Flow Based on Stress Driven-Nonlocal Theory Considering Nonlinear Foundation, Magnetic Field and Thermal Effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-05 06:21:31","doi":"10.21203/rs.3.rs-8062333/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"67c1190a-9509-4a78-9cfd-c46ffdb66e18","owner":[],"postedDate":"December 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-09T16:05:07+00:00","versionOfRecord":{"articleIdentity":"rs-8062333","link":"https://doi.org/10.1007/s00707-026-04642-4","journal":{"identity":"acta-mechanica","isVorOnly":false,"title":"Acta Mechanica"},"publishedOn":"2026-03-02 15:58:44","publishedOnDateReadable":"March 2nd, 2026"},"versionCreatedAt":"2025-12-05 06:21:31","video":"","vorDoi":"10.1007/s00707-026-04642-4","vorDoiUrl":"https://doi.org/10.1007/s00707-026-04642-4","workflowStages":[]},"version":"v1","identity":"rs-8062333","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8062333","identity":"rs-8062333","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}