Experimentally characterising the dynamical landscape of an active MEMS cantilever

Experimentally characterising the dynamical landscape of an active MEMS cantilever | 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 Article Experimentally characterising the dynamical landscape of an active MEMS cantilever Seigan Hayashi, Chris Cameron, Stefanie Gutschmidt, Rua Murray, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6424847/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 Experimental continuation describes a collection of techniques for constructing bifurcation diagrams by tracking steady-states and/or periodic responses directly in a physical experiment, without the need for a mathematical model. This approach has been used to characterise the nonlinear dynamics of macro-scale systems, which operate at relatively slow timescales. In this work we show that experimental continuation can be adapted to a wide range of engineering applications, namely, the technologically important class of micro-electromechanical systems (MEMS) — which are smaller, highly nonlinear, and operate at much faster timescales. The MEMS device is operated in a parameter range for which the cantilever undergoes self-oscillations at a natural frequency of just under 100 kHz, without external forcing. We investigate nonlinear responses to external, periodic excitation via a sequence of one-parameter response curves. Our experiments are model-free and use control-based continuation to map stable and unstable periodic responses of active MEMS cantilevers. Consequently, we expose the dynamic landscape by rendering a surface that features multi-valued responses across a range of forcing frequencies and amplitudes. An atypical, non-Duffing-like bifurcation structure is revealed. Thus, we showcase experimental continuation as a viable tool for investigating fast-timescale nonlinear oscillators. Our work encourages the integration of control-based testing schemes into standard engineering practice by showing that control-based continuation is an accessible tool for nonlinear analyses of a broader range of engineering applications. Physical sciences/Engineering Physical sciences/Nanoscience and technology Experimental continuation micro-electromechanical systems (MEMS) nonlinear dynamics experimental bifurcation analysis Full Text Additional Declarations There is no conflict of interest 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-6424847","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":442557765,"identity":"ad5999ac-3acf-43d3-947f-a1ef018f1565","order_by":0,"name":"Seigan Hayashi","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-6979-4329","institution":"University of Canterbury","correspondingAuthor":true,"prefix":"","firstName":"Seigan","middleName":"","lastName":"Hayashi","suffix":""},{"id":442557766,"identity":"aad6e9d4-29aa-477d-a227-3fb6410b7645","order_by":1,"name":"Chris Cameron","email":"","orcid":"","institution":"University of Canterbury","correspondingAuthor":false,"prefix":"","firstName":"Chris","middleName":"","lastName":"Cameron","suffix":""},{"id":442557767,"identity":"ff3dba0b-9d0b-4838-9edc-e13425c44def","order_by":2,"name":"Stefanie Gutschmidt","email":"","orcid":"","institution":"University of Canterbury","correspondingAuthor":false,"prefix":"","firstName":"Stefanie","middleName":"","lastName":"Gutschmidt","suffix":""},{"id":442557768,"identity":"8d6af41b-3cd0-404c-9466-0883d9373aed","order_by":3,"name":"Rua Murray","email":"","orcid":"","institution":"University of Canterbury","correspondingAuthor":false,"prefix":"","firstName":"Rua","middleName":"","lastName":"Murray","suffix":""},{"id":442557769,"identity":"ab6ceb82-cf7a-417d-a2e7-418c733f0cae","order_by":4,"name":"Bernd Krauskopf","email":"","orcid":"","institution":"University of Auckland","correspondingAuthor":false,"prefix":"","firstName":"Bernd","middleName":"","lastName":"Krauskopf","suffix":""}],"badges":[],"createdAt":"2025-04-11 05:10:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6424847/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6424847/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81017634,"identity":"7ada7365-c18e-4fa1-96d1-ae07e5232d05","added_by":"auto","created_at":"2025-04-21 09:09:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3206174,"visible":true,"origin":"","legend":"Article File","description":"","filename":"250411HayashietalMEMSCBC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6424847/v1_covered_5dcf5b8f-ab34-4b9c-b639-cc8badce138e.pdf"}],"financialInterests":"There is no conflict of interest","formattedTitle":"Experimentally characterising the dynamical landscape of an active MEMS cantilever","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"Experimental continuation, micro-electromechanical systems (MEMS), nonlinear dynamics, experimental bifurcation analysis","lastPublishedDoi":"10.21203/rs.3.rs-6424847/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6424847/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Experimental continuation describes a collection of techniques for constructing bifurcation diagrams by tracking steady-states and/or periodic responses directly in a physical experiment, without the need for a mathematical model. This approach has been used to characterise the nonlinear dynamics of macro-scale systems, which operate at relatively slow timescales.\r\n\r\nIn this work we show that experimental continuation can be adapted to a wide range of engineering applications, namely, the technologically important class of micro-electromechanical systems (MEMS) — which are smaller, highly nonlinear, and operate at much faster timescales. The MEMS device is operated in a parameter range for which the cantilever undergoes self-oscillations at a natural frequency of just under 100 kHz, without external forcing. We investigate nonlinear responses to external, periodic excitation via a sequence of one-parameter response curves. Our experiments are model-free and use control-based continuation to map stable and unstable periodic responses of active MEMS cantilevers. Consequently, we expose the dynamic landscape by rendering a surface that features multi-valued responses across a range of forcing frequencies and amplitudes. An atypical, non-Duffing-like bifurcation structure is revealed.\r\n\r\nThus, we showcase experimental continuation as a viable tool for investigating fast-timescale nonlinear oscillators. 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