Nonlinear dynamics of rotating functionally graded graphene platelets/titanium alloy trapezoid plates under 1:3 internal resonance

Nonlinear dynamics of rotating functionally graded graphene platelets/titanium alloy trapezoid plates under 1:3 internal resonance | 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 Nonlinear dynamics of rotating functionally graded graphene platelets/titanium alloy trapezoid plates under 1:3 internal resonance Ming-Yang Fan, Jie Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4468070/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Aug, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract Although rotating blades are designed to operate diverging from structural frequencies, internal resonance also occurs under certain rotation speeds that greatly affect the stiffness of the blades. Therefore, a detailed investigation of the resonance mechanisms of rotating blades, especially those introduced by nonlinearities, is of great importance in structural design and optimization. A dynamic model of a functionally graded graphene/titanium alloy composite trapezoid plate is established to investigate the nonlinear dynamics of a rotating blade with varying cross-sections. The ordinary differential equations of the plate are established based on the energy method and Lagrange equations. The occurrence of one to three internal resonance for the trapezoid plate is identified through the analysis of linear and nonlinear free vibrations. Then, the steady-state responses of the rotating plate in the case of 1:3 internal resonance are numerically calculated and verified by the approximation solution of the method of multiple scales. Parametric studies are conducted to investigate the effects of the rotation speed, taper ratio, excitation amplitude and excitation frequency on the amplitude‒frequency and amplitude‒force curves. Rotating blade Nonlinear frequency Internal resonance Nonlinear dynamics Graphene platelet Titanium alloy Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Aug, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 15 Jul, 2024 Reviews received at journal 30 Jun, 2024 Reviews received at journal 09 Jun, 2024 Reviewers agreed at journal 08 Jun, 2024 Reviewers agreed at journal 04 Jun, 2024 Reviewers agreed at journal 04 Jun, 2024 Reviewers invited by journal 04 Jun, 2024 Editor assigned by journal 27 May, 2024 Submission checks completed at journal 27 May, 2024 First submitted to journal 23 May, 2024 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. 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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-4468070","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":312382543,"identity":"552ae465-82f1-4afe-8e5c-fc31f941621e","order_by":0,"name":"Ming-Yang Fan","email":"","orcid":"","institution":"Beijing University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Ming-Yang","middleName":"","lastName":"Fan","suffix":""},{"id":312382544,"identity":"d0f001c8-a755-4706-bf4a-613fc02a4711","order_by":1,"name":"Jie Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYBACxgYeIFlxgBnM4yFeyxmgFjZitYCVMbYdYCBeC3P72YOPC+fdYTe438D44G0bg7w5QYf15CUbz9z2jNngGAOz4dw2BsOdDYS0zOAxk+bddhikhU2at40hweAAYS3mv3nngLWw/yZWixkzbwPEFmbitPTkGEvzHHvGLHkssVlyzjkJww2EtBi2nzH8zFNzJ5nv8OGDH96U2cgTtMWwAUIng2IVSEsQUA8E8lDajrDSUTAKRsEoGLEAAOAWPCe3IbkLAAAAAElFTkSuQmCC","orcid":"","institution":"Beijing University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2024-05-23 16:08:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4468070/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4468070/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-024-10129-5","type":"published","date":"2024-08-23T15:58:02+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":63300487,"identity":"9006e9d1-1b2d-4891-af61-e20763a8ad8b","added_by":"auto","created_at":"2024-08-26 16:14:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1619101,"visible":true,"origin":"","legend":"","description":"","filename":"Fanpaper1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4468070/v1_covered_5ec7613a-1f14-4290-817c-a2aa0097acb6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear dynamics of rotating functionally graded graphene platelets/titanium alloy trapezoid plates under 1:3 internal resonance","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Rotating blade, Nonlinear frequency, Internal resonance, Nonlinear dynamics, Graphene platelet, Titanium alloy","lastPublishedDoi":"10.21203/rs.3.rs-4468070/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4468070/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlthough rotating blades are designed to operate diverging from structural frequencies, internal resonance also occurs under certain rotation speeds that greatly affect the stiffness of the blades. 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