Fractional derivative analysis of axial wave propagation studies in carbon nanorods with elastic medium support using nonlocal strain gradient theory

Fractional derivative analysis of axial wave propagation studies in carbon nanorods with elastic medium support using nonlocal strain gradient theory | 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 Fractional derivative analysis of axial wave propagation studies in carbon nanorods with elastic medium support using nonlocal strain gradient theory VAIYAPURI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5416176/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 The present study provides new insights into the analysis of axial wave propagation in carbon nanorods using fractional derivative analysis and nonlocal strain gradient theory. The conventional classical nonlocal strain theory employs a two-length scale to capture nonlocal phenomena, whereas the proposed fractional derivative approach introduces two additional length scales. This new approach offers a more comprehensive understanding of the axial wave propagation phenomena in carbon nanorods with four-length scales. The study includes investigating the dispersion curve, phase speed, and group speed of wave propagation. For the first time, the effect of the newly proposed two additional length scales shows interesting phenomena in axial wave studies of carbon nanorods besides the two existing length scales in nonlocal strain gradient theory. Furthermore, the present axial wave propagation investigation incorporates the effect of elastic medium support modeled with nonlocal strain gradient theory by including the Caputo fractional derivative approach. Nanoscience Computational Mathematics Nonlocal strain gradient theory Caputo fractional derivative approach Wave propagation studies Full Text Additional Declarations The authors declare no competing interests. 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-5416176","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":375730135,"identity":"3a4ea174-0199-4437-b867-e1507d9e5a83","order_by":0,"name":"VAIYAPURI","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYJACZgYDCzkGBsYGBgkgZCNCB2Mzg4GEMViLBfFaGCQSG0DMCmIcJd/ee/xxQYFEen//4bYPN3dYMPBJN+DXYnDmXGLzDAOJ3Bk3EptnzjwDdJjMAQJaJHIMm3mAWjZIMDYzS7YBtUgkEHDY/DdgLekG/Aebmf8So4XhBg9YS4IBQ2IzA1G2GJzJMZwN1GII8guD5BkJHsIOaz9j8Jnnj408f//xxwySO+rk5GcQchgKAMYmDynqIVpGwSgYBaNgFGAAAKuIOLjYx6iyAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-0231-0443","institution":"SENTHILKUMAR","correspondingAuthor":true,"prefix":"","firstName":"","middleName":"","lastName":"VAIYAPURI","suffix":""}],"badges":[],"createdAt":"2024-11-08 11:33:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-5416176/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5416176/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68678811,"identity":"33045997-a604-4fa1-bed0-ef11cc0bc44d","added_by":"auto","created_at":"2024-11-11 02:59:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1396560,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle14062024copy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5416176/v1_covered_c17a1e31-b5f8-4eb5-8d9e-30252f33da16.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eFractional derivative analysis of axial wave propagation studies in carbon nanorods with elastic medium support using nonlocal strain gradient theory\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Fourth Paradigm Institute","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":"Nonlocal strain gradient theory, Caputo fractional derivative approach, Wave propagation studies","lastPublishedDoi":"10.21203/rs.3.rs-5416176/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5416176/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe present study provides new insights into the analysis of axial wave propagation in carbon nanorods using fractional derivative analysis and nonlocal strain gradient theory. 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