Eigenvalue perturbation in drivetrain analysis and optimization

Eigenvalue perturbation in drivetrain analysis and optimization | 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 Eigenvalue perturbation in drivetrain analysis and optimization Carsten Schulz, Henry Graneß, Stefan Weinzierl, Johannes Nicklas This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6368754/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Multibody System Dynamics → Version 1 posted 11 You are reading this latest preprint version Abstract The optimization of the dynamic behavior of drive systems often involves targeted modifications of the system characteristics. Structural and parametric modifications are used to satisfy the constraints of the dynamic requirements. However, many optimizations are still achieved by intuition or parameter variations, even though more streamlined and easy-to-implement tools such as the eigenvalue perturbation method are available. In this article, the eigenvalue perturbation method in the form of an eigenvalue sensitivity analysis is used to efficiently optimize the dynamic behavior for two different use cases using different optimization measures. This paper demonstrates, how eigenvalue perturbation theory can efficiently optimize drivetrain dynamics by systematically modifying system parameters. Two case studies show how eigenvalue sensitivity analysis achieves targeted frequency shifts to avoid resonances: (1) adapting shaft stiffness and control parameters in a torsional drivetrain, and (2) optimizing structural modifications in a wind turbine bedplate. The study introduces the eigenvector tensor product as a weighting matrix, identifying key parameters for effective redesign. Compared to conventional parameter studies, this method enables precise control over system dynamics with minimal computational effort, making it highly applicable for vibration mitigation and drivetrain optimization. Eigenfrequencies Frequency Tuning Weighting Matrix Structural Mechanics Perturbation Theory Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 09 Aug, 2025 Reviews received at journal 08 Aug, 2025 Reviews received at journal 12 Apr, 2025 Reviews received at journal 08 Apr, 2025 Reviewers agreed at journal 08 Apr, 2025 Reviewers agreed at journal 08 Apr, 2025 Reviewers agreed at journal 08 Apr, 2025 Reviewers invited by journal 08 Apr, 2025 Editor assigned by journal 07 Apr, 2025 Submission checks completed at journal 04 Apr, 2025 First submitted to journal 03 Apr, 2025 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-6368754","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":441943297,"identity":"3c1e2bad-a4f2-44e6-a776-4e8682d3408c","order_by":0,"name":"Carsten Schulz","email":"data:image/png;base64,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","orcid":"","institution":"Regensburg University of Applied Sciences","correspondingAuthor":true,"prefix":"","firstName":"Carsten","middleName":"","lastName":"Schulz","suffix":""},{"id":441943299,"identity":"b9525a87-c96f-469c-b497-fe4fad81b61b","order_by":1,"name":"Henry Graneß","email":"","orcid":"","institution":"Hilti Entwicklungsgesellschaft mbH","correspondingAuthor":false,"prefix":"","firstName":"Henry","middleName":"","lastName":"Graneß","suffix":""},{"id":441943300,"identity":"7cfc813a-56b2-4618-b6b3-1b56cf325a28","order_by":2,"name":"Stefan Weinzierl","email":"","orcid":"","institution":"Regensburg University of Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Stefan","middleName":"","lastName":"Weinzierl","suffix":""},{"id":441943304,"identity":"006e44e7-1d12-4631-9026-f38edc97ac1c","order_by":3,"name":"Johannes Nicklas","email":"","orcid":"","institution":"Regensburg University of Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Johannes","middleName":"","lastName":"Nicklas","suffix":""}],"badges":[],"createdAt":"2025-04-03 11:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6368754/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6368754/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11044-026-10155-8","type":"published","date":"2026-03-13T15:58:03+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":104739962,"identity":"eb3cf68a-19fe-415e-bb91-4e9e8d83043a","added_by":"auto","created_at":"2026-03-16 16:14:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2569357,"visible":true,"origin":"","legend":"","description":"","filename":"20250331PaperECCOMAS2025Latexfinalv5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6368754/v1_covered_f314a90e-dec7-4d6a-ad74-82af4074f53a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Eigenvalue perturbation in drivetrain analysis and optimization","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":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Eigenfrequencies, Frequency Tuning, Weighting Matrix, Structural Mechanics, Perturbation Theory","lastPublishedDoi":"10.21203/rs.3.rs-6368754/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6368754/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The optimization of the dynamic behavior of drive systems often involves targeted modifications of the system characteristics. 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