Prediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator

Prediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator | 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 Prediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator Michael McGurk, Jie Yuan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5859544/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 presence of nonlinearities within aerospace systems often triggers self-sustaining oscillations known as Limit Cycle Oscillations (LCO), demanding costly analysis for identification, notably through the resource-intensive generation of bifurcation diagrams. Consequently, the expense incurred tends to sideline nonlinear analysis in initial design phases, constraining design possibilities and impeding data-driven methods for nonlinear aeroelastic analysis reliant on efficient data collection, which has garnered attention in the aerospace sector. This work proposes a computationally efficient numerical framework for calculating LCO amplitudes and determining stability in nonlinear aeroelastic systems. The framework consists of using Harmonic Balance Methods (HBM) combined with the Hill method for the stability analysis. To avoid the sorting problem, the Koopman operator-based data-driven method is implemented. The methodology is applied to numerical test cases, encompassing both smooth and nonsmooth nonlinearities, and validated against outcomes from MATCONT and COCO. Subsequently, an experimental validation of the framework is conducted, comparing its outcomes to existing LCO experimental data acquired through control-based continuation experiments. Mechanical Engineering Nonlinear Aeroelasticity Numerical continutation Stability analysis 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-5859544","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":404104326,"identity":"29a81ab9-50fe-4a90-a221-04636568745c","order_by":0,"name":"Michael McGurk","email":"","orcid":"","institution":"University of Strathclyde","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"McGurk","suffix":""},{"id":404104327,"identity":"4872ae90-7dc1-4f61-8629-cd6e8e7fdbc7","order_by":1,"name":"Jie Yuan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYBACxgYwZYMkxEOcljQGBjZitUDBYRK0MDfwmEn83HHenl+++dgDhho7BoMzBwg5jMdMsvfM7cSZbWzpBgzHkhkMzjYQ1iLB23Y7weAYkMHAdoDB4DwBh4Ft+dt2zh6i5R+RWqR52w4wbgBpYWw7QITDmtmKrWXbkoF+SUuTSOxL5pEk5H3D9uaNN9+22dnzMx8+JvHhm50c35kEAlqaOQwQvARiIlKegf0BQUWjYBSMglEwwgEAbS06uBE4xTUAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-2411-8789","institution":"University of Southampton","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Yuan","suffix":""}],"badges":[],"createdAt":"2025-01-19 12:58:53","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-5859544/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5859544/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":74518788,"identity":"3d5efc3a-97f7-4787-9046-15ca817a3abe","added_by":"auto","created_at":"2025-01-23 05:32:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11560287,"visible":true,"origin":"","legend":"","description":"","filename":"ComputationandValidationofHBMforLCOandstabilitydraft4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5859544/v1_covered_c3566910-4e8d-42cc-b9a8-1de8bc86cf34.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePrediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[{"identity":"fa9b91de-e42b-486c-9d83-9a386e4a9ddb","identifier":"10.13039/501100000266","name":"Engineering and Physical Sciences Research Council","awardNumber":"2581922","order_by":0},{"identity":"8b97e829-a506-444a-a578-35981099ff28","identifier":"10.13039/501100000287","name":"Royal Academy of Engineering","awardNumber":"LTRF2223-19-150","order_by":1}],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Southampton","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":"Nonlinear Aeroelasticity, Numerical continutation, Stability analysis","lastPublishedDoi":"10.21203/rs.3.rs-5859544/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5859544/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe presence of nonlinearities within aerospace systems often triggers self-sustaining oscillations known as Limit Cycle Oscillations (LCO), demanding costly analysis for identification, notably through the resource-intensive generation of bifurcation diagrams. 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