Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks

Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks | 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 Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks Tobias Weidemann, Lawrence A. Bergman, Alexander F. Vakakis, Malte Krack This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4691661/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Feb, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted 13 You are reading this latest preprint version Abstract We theoretically investigate the strongly nonlinear dynamics, inter-modal targeted energy transfer (IMTET) and energy localization in an elastically coupled cyclic chain of oscillators with vibro-impact nonlinear energy sinks (VI-NESs) under symmetric harmonic standing or traveling wave forcing. Each identical sector of the chain consists of a single linear oscillator hosting a VI-NES, which is a small mass that is freely placed inside a cavity of the oscillator. We show that the VI-NESs are able to synchronize to the global response of the structure in the form of 1:1 resonance captures with the oscillators in each sector. In addition, localized states at higher amplitudes can be found where the VI-NESs synchronize to the motion of their host-oscillators in only a subset of all sectors. We derive an analytical model to predict the frequency-amplitude branches of these synchronized solutions and study their (practical) stability numerically. We show that high and practically stable localized amplitudes only arise for sufficiently low excitation wavenumbers and weak inter-sector coupling strengths. However, even the largest practically stable amplitudes show a significant reduction of the vibration level compared to the corresponding linear resonant responses. Hence, a robust high performance of the VI-NESs is observed for all excitation wavenumbers and inter-sector coupling strengths. Vibration absorber Rotationally periodic structures Vibro-impact nonlinear energy sink Inter-modal targeted energy transfer Nonlinear localization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Feb, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 25 Nov, 2024 Reviews received at journal 22 Nov, 2024 Reviews received at journal 17 Nov, 2024 Reviewers agreed at journal 29 Oct, 2024 Reviewers agreed at journal 29 Oct, 2024 Reviewers agreed at journal 29 Oct, 2024 Reviews received at journal 31 Jul, 2024 Reviewers agreed at journal 12 Jul, 2024 Reviewers agreed at journal 10 Jul, 2024 Reviewers invited by journal 10 Jul, 2024 Editor assigned by journal 06 Jul, 2024 Submission checks completed at journal 06 Jul, 2024 First submitted to journal 05 Jul, 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. 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-4691661","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":333328564,"identity":"671af361-d4f5-4c78-a6f3-5f13c735601f","order_by":0,"name":"Tobias Weidemann","email":"data:image/png;base64,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","orcid":"","institution":"University of Stuttgart","correspondingAuthor":true,"prefix":"","firstName":"Tobias","middleName":"","lastName":"Weidemann","suffix":""},{"id":333328565,"identity":"b311ac07-19c8-4766-89e1-fa475ac64c27","order_by":1,"name":"Lawrence A. Bergman","email":"","orcid":"","institution":"University of Illinois Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Lawrence","middleName":"A.","lastName":"Bergman","suffix":""},{"id":333328566,"identity":"9fd25d93-1031-4833-a990-0f09846aa494","order_by":2,"name":"Alexander F. Vakakis","email":"","orcid":"","institution":"University of Illinois Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Alexander","middleName":"F.","lastName":"Vakakis","suffix":""},{"id":333328567,"identity":"5e85f743-4103-401a-840d-a868a7319178","order_by":3,"name":"Malte Krack","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Malte","middleName":"","lastName":"Krack","suffix":""}],"badges":[],"createdAt":"2024-07-05 10:40:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4691661/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4691661/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-025-10928-4","type":"published","date":"2025-02-04T15:58:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":75930791,"identity":"7edc883b-9b7a-4962-8e30-2ef977c645e1","added_by":"auto","created_at":"2025-02-10 16:13:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4936476,"visible":true,"origin":"","legend":"","description":"","filename":"EnergyTransferandLocalizationinaForcedCyclicChainofOscillatorswithVibroImpactNonlinearEnergySinks.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4691661/v1_covered_d474e854-e8e5-4d6e-b0ca-b018ebe7c9c4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks","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":"Vibration absorber, Rotationally periodic structures, Vibro-impact nonlinear energy sink, Inter-modal targeted energy transfer, Nonlinear localization","lastPublishedDoi":"10.21203/rs.3.rs-4691661/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4691661/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We theoretically investigate the strongly nonlinear dynamics, inter-modal targeted energy transfer (IMTET) and energy localization in an elastically coupled cyclic chain of oscillators with vibro-impact nonlinear energy sinks (VI-NESs) under symmetric harmonic standing or traveling wave forcing. Each identical sector of the chain consists of a single linear oscillator hosting a VI-NES, which is a small mass that is freely placed inside a cavity of the oscillator. We show that the VI-NESs are able to synchronize to the global response of the structure in the form of 1:1 resonance captures with the oscillators in each sector. In addition, localized states at higher amplitudes can be found where the VI-NESs synchronize to the motion of their host-oscillators in only a subset of all sectors. We derive an analytical model to predict the frequency-amplitude branches of these synchronized solutions and study their (practical) stability numerically. We show that high and practically stable localized amplitudes only arise for sufficiently low excitation wavenumbers and weak inter-sector coupling strengths. However, even the largest practically stable amplitudes show a significant reduction of the vibration level compared to the corresponding linear resonant responses. Hence, a robust high performance of the VI-NESs is observed for all excitation wavenumbers and inter-sector coupling strengths.","manuscriptTitle":"Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-30 04:13:56","doi":"10.21203/rs.3.rs-4691661/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-11-25T10:34:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-11-22T15:52:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-11-17T06:54:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"193109775736995253450507404754284846286","date":"2024-10-29T21:11:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"139794480035705918602731198975734289962","date":"2024-10-29T07:41:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"64579070720646222698284670500157934542","date":"2024-10-29T05:36:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-31T06:08:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"206377123458470408371972290045924967077","date":"2024-07-12T14:13:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"55081027853312870261713823987951671355","date":"2024-07-10T16:32:16+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-10T13:16:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-06T14:51:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-06T12:48:36+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2024-07-05T10:39:28+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":"7773b89a-b20c-4d51-94ee-4a3f667180c9","owner":[],"postedDate":"July 30th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-02-10T16:06:32+00:00","versionOfRecord":{"articleIdentity":"rs-4691661","link":"https://doi.org/10.1007/s11071-025-10928-4","journal":{"identity":"nonlinear-dynamics","isVorOnly":false,"title":"Nonlinear Dynamics"},"publishedOn":"2025-02-04 15:58:24","publishedOnDateReadable":"February 4th, 2025"},"versionCreatedAt":"2024-07-30 04:13:56","video":"","vorDoi":"10.1007/s11071-025-10928-4","vorDoiUrl":"https://doi.org/10.1007/s11071-025-10928-4","workflowStages":[]},"version":"v1","identity":"rs-4691661","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4691661","identity":"rs-4691661","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}