Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle

Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle | 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 harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle Zahra Moeinaddini, Ali Reza Saidi, Mohammad Ali Sabahi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7220108/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract This study analytically investigates the large-amplitude vibrations of a fluid-conveying piezoelectric pipe supported at both ends and resting on a nonlinear viscoelastic foundation. To enable energy harvesting, two piezoelectric layers with varying spanning angles are placed on the upper and lower surfaces of the pipe, which is subjected to external harmonic excitation near primary resonance. The modeling framework is based on Euler-Bernoulli beam theory combined with von Kármán nonlinear strain-displacement relations. Hamilton’s principle is employed to derive the governing equations of motion, which are subsequently reduced to a set of ordinary differential equations using the Galerkin method. The harmonic balance method is then utilized to derive analytical expressions for the amplitude–frequency response, voltage output, harvested power, and force–response behavior. The influence of damping coefficient, excitation force, excitation frequency and load resistance on the system’s response is examined in detail. The findings highlight the existence of optimal values for load resistance and spanning angle that maximize the electrical output. Energy harvesting Large amplitude vibrations Stability analysis Piezoelectric pipe Viscoelastic foundation Harmonic balance method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 24 Aug, 2025 Reviews received at journal 24 Aug, 2025 Reviews received at journal 15 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviews received at journal 05 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers invited by journal 04 Aug, 2025 Editor assigned by journal 28 Jul, 2025 Submission checks completed at journal 28 Jul, 2025 First submitted to journal 26 Jul, 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. 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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-7220108","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":496233923,"identity":"d06eb3f4-8c71-429e-9ab9-3f533a53ff2d","order_by":0,"name":"Zahra Moeinaddini","email":"","orcid":"","institution":"Shahid Bahonar University of Kerman","correspondingAuthor":false,"prefix":"","firstName":"Zahra","middleName":"","lastName":"Moeinaddini","suffix":""},{"id":496233925,"identity":"dd197586-eae4-4023-8a53-6fd1098f9fc3","order_by":1,"name":"Ali Reza Saidi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVRIiWNgGAWjYFACxgaJhAoGAzA7gXgtZ0jTwsAgwdgG1UIUkG8/3Hjj4bzDxgzshx8wPNxDhBaDM4nNFonbDpsx8KQZMCQ8I0YLQ2KbBFCLDQNDDtAvB4hxWP9DoJY5QC38b4jUwnADZEsD0GESxNpicONhs0XCsXRjNolnBgeIdFj6w5s/aqwN+/mTHz78QZTDYIANiEnSMApGwSgYBaMADwAAVtg1hjn4fSsAAAAASUVORK5CYII=","orcid":"","institution":"Shahid Bahonar University of Kerman","correspondingAuthor":true,"prefix":"","firstName":"Ali","middleName":"Reza","lastName":"Saidi","suffix":""},{"id":496233927,"identity":"f19d6513-9bc9-413d-9676-dbb3f9c01395","order_by":2,"name":"Mohammad Ali Sabahi","email":"","orcid":"","institution":"Shahid Bahonar University of Kerman","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Ali","lastName":"Sabahi","suffix":""}],"badges":[],"createdAt":"2025-07-26 09:23:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7220108/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7220108/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88448194,"identity":"b6fdff68-4263-428c-989b-907041aa0b4a","added_by":"auto","created_at":"2025-08-06 13:57:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1864648,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscriptnoname.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7220108/v1_covered_53e2c377-eff4-4af6-93b0-ff62252e9d92.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle","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":"international-journal-of-mechanics-and-materials-in-design","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [International Journal of Mechanics and Materials in Design](https://link.springer.com/journal/10999)","snPcode":"10999","submissionUrl":"https://submission.springernature.com/new-submission/10999/3","title":"International Journal of Mechanics and Materials in Design","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Energy harvesting, Large amplitude vibrations, Stability analysis, Piezoelectric pipe, Viscoelastic foundation, Harmonic balance method","lastPublishedDoi":"10.21203/rs.3.rs-7220108/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7220108/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study analytically investigates the large-amplitude vibrations of a fluid-conveying piezoelectric pipe supported at both ends and resting on a nonlinear viscoelastic foundation. To enable energy harvesting, two piezoelectric layers with varying spanning angles are placed on the upper and lower surfaces of the pipe, which is subjected to external harmonic excitation near primary resonance. The modeling framework is based on Euler-Bernoulli beam theory combined with von K\u0026aacute;rm\u0026aacute;n nonlinear strain-displacement relations. Hamilton\u0026rsquo;s principle is employed to derive the governing equations of motion, which are subsequently reduced to a set of ordinary differential equations using the Galerkin method. The harmonic balance method is then utilized to derive analytical expressions for the amplitude\u0026ndash;frequency response, voltage output, harvested power, and force\u0026ndash;response behavior. The influence of damping coefficient, excitation force, excitation frequency and load resistance on the system\u0026rsquo;s response is examined in detail. 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