Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations | 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 Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations Xiaohui Liu, Shuguang Yang, Guangyun Min, Ceshi Sun, Haobo Liang, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-430539/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 2 You are reading this latest preprint version Abstract This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and sub-harmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value. Mechanical Engineering Principal resonance Harmonic resonance Approximate analytical solution Quenching phenomenon Iced transmission lines Forced-self-excited system Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Full Text Table Due to technical limitations, table 1 is only available as a download in the Supplemental Files section. Supplementary Files Table.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editor assigned by journal 15 Apr, 2021 First submitted to journal 15 Apr, 2021 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-430539","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":22026221,"identity":"835579af-9e02-494f-b12d-f0826618287c","order_by":0,"name":"Xiaohui Liu","email":"","orcid":"","institution":"State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiaohui","middleName":"","lastName":"Liu","suffix":""},{"id":22026222,"identity":"86e10214-f1fe-40d8-9e2f-449dd6ede774","order_by":1,"name":"Shuguang Yang","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-4554-4795","institution":"Chongqing Jiaotong University, School of Civil Engineering","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Shuguang","middleName":"","lastName":"Yang","suffix":""},{"id":22026223,"identity":"6cd49238-ec13-441c-97e9-701ddbbfba49","order_by":2,"name":"Guangyun 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section.\u003c/p\u003e"}],"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":true,"isPdf":false,"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":"Principal resonance, Harmonic resonance, Approximate analytical solution, Quenching phenomenon, Iced transmission lines, Forced-self-excited system","lastPublishedDoi":"10.21203/rs.3.rs-430539/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-430539/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and sub-harmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.","manuscriptTitle":"Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-04-26 18:45:02","doi":"10.21203/rs.3.rs-430539/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorAssigned","content":"","date":"2021-04-16T00:00:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2021-04-15T13:31:31+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"e32f5bb0-6fb1-425a-944f-b70525c1719b","owner":[],"postedDate":"April 26th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":3904908,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2022-07-15T10:49:06+00:00","versionOfRecord":[],"versionCreatedAt":"2021-04-26 18:45:02","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-430539","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-430539","identity":"rs-430539","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}