An accurate design method for the piezoelectric energy harvesters based on the two-dimensional Green’s functions under a tangential line force

An accurate design method for the piezoelectric energy harvesters based on the two-dimensional Green’s functions under a tangential line force | 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 An accurate design method for the piezoelectric energy harvesters based on the two-dimensional Green’s functions under a tangential line force Jie Tong, Yang Zhang, Jiang Su, Peng-Fei Hou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6325667/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 Piezoelectric-coated structures constitute the predominant configuration in contemporary energy harvesting systems, necessitating precise modeling methodologies for their electromechanical coupling behavior under mechanical loading. This study develops an analytical framework for orthotropic piezoelectric-coating substrate systems, deriving two-dimensional Green’s functions in closed-form elementary functions through fundamental solution theory. The formulation specifically addresses tangential line force loading on the coated surface, establishing a mesh-free solution paradigm. The proposed methodology enables reconstruction of full-field electromechanical responses under arbitrary mechanical loading through superposition principles integrated with Gaussian quadrature techniques. Numerical validation demonstrates superior computational attributes, achieving solution accuracy relative to finite element benchmarks while reducing computation time. A critical application lies in coating thickness optimization, where parametric studies reveal a nonlinear correlation between piezoelectric layer geometry and energy conversion efficiency. The framework’s analytical sensitivity coefficients facilitate gradient-based optimization algorithms, yielding efficiency enhancement over conventional empirical designs. These advancements establish a rigorous theoretical foundation for performance prediction in piezoelectric energy harvesters while providing engineers with computationally efficient design tools for thin-film device engineering applications. Mathematics Subject Classification. 74F10. Green’s function Piezoelectric Coated Energy harvesters Full Text Additional Declarations No competing interests reported. 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. 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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-6325667","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":437700879,"identity":"d8fdd59d-e513-47df-9bb4-28a13a248a7d","order_by":0,"name":"Jie Tong","email":"","orcid":"","institution":"School of Robotics, Guangdong Polytechnic of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Tong","suffix":""},{"id":437700884,"identity":"6ecb8b27-6e44-45a4-b790-164376b1a0d4","order_by":1,"name":"Yang Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYDACCTB5gIGBmbHhwAcDGzsStLA3Hzw4oyAtmQQtPMeSD/N8OMTYQEiH/OzmZw+/tt3JM7iRY3DYxuAAMwP74aMb8GlhnHPM3Fi27VkxWEuOwR0+Bp60tBv4tDBLJJhJS7YdTtwA0fKMmUGCxwyvFjaJ9G8ILRYGhxkbCGnhkcgxk/wI0nLmWMJhBmK0SEjklEkznDucOPN484GDPQZpyWyE/CI/I32b5I+yw4l9hxmbP/z4Y2PHz374GF4tIMDMy4bsO0LKQYDxxx9ilI2CUTAKRsGIBQDL6VVHLcE0HwAAAABJRU5ErkJggg==","orcid":"","institution":"Beijing Xinghang Mechanical-Electric Equipment Co., Ltd","correspondingAuthor":true,"prefix":"","firstName":"Yang","middleName":"","lastName":"Zhang","suffix":""},{"id":437700886,"identity":"cc0e896c-3862-4ba3-853f-a5a6bf4a59a1","order_by":2,"name":"Jiang Su","email":"","orcid":"","institution":"School of Robotics, Guangdong Polytechnic of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jiang","middleName":"","lastName":"Su","suffix":""},{"id":437700887,"identity":"c8c7aae7-d4f4-4f96-841a-1f742a886a57","order_by":3,"name":"Peng-Fei Hou","email":"","orcid":"","institution":"Department of Engineering Mechanics, Hunan University","correspondingAuthor":false,"prefix":"","firstName":"Peng-Fei","middleName":"","lastName":"Hou","suffix":""}],"badges":[],"createdAt":"2025-03-28 07:08:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6325667/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6325667/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80306872,"identity":"c66c7a53-935c-41ba-977f-281c9b956efa","added_by":"auto","created_at":"2025-04-10 10:23:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1767110,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscriptreceived0331.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6325667/v1_covered_588f2f9c-b00b-4aa2-96b3-4f19cfe35808.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An accurate design method for the piezoelectric energy harvesters based on the two-dimensional Green’s functions under a tangential line force","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":"Green’s function, Piezoelectric, Coated, Energy harvesters","lastPublishedDoi":"10.21203/rs.3.rs-6325667/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6325667/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePiezoelectric-coated structures constitute the predominant configuration in contemporary energy harvesting systems, necessitating precise modeling methodologies for their electromechanical coupling behavior under mechanical loading. This study develops an analytical framework for orthotropic piezoelectric-coating substrate systems, deriving two-dimensional Green’s functions in closed-form elementary functions through fundamental solution theory. The formulation specifically addresses tangential line force loading on the coated surface, establishing a mesh-free solution paradigm. The proposed methodology enables reconstruction of full-field electromechanical responses under arbitrary mechanical loading through superposition principles integrated with Gaussian quadrature techniques. Numerical validation demonstrates superior computational attributes, achieving solution accuracy relative to finite element benchmarks while reducing computation time. A critical application lies in coating thickness optimization, where parametric studies reveal a nonlinear correlation between piezoelectric layer geometry and energy conversion efficiency. 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