Exploiting nonlinear spring oscillator chain as acoustic metasurfaces for high harmonic generation

Exploiting nonlinear spring oscillator chain as acoustic metasurfaces for high harmonic generation | 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 Exploiting nonlinear spring oscillator chain as acoustic metasurfaces for high harmonic generation Chenghao Sun, Haoyu Wang, Yuanyuan Li, Zhonghan Fei, Yun Lai, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3916974/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 This paper introduces a novel approach to design acoustic metasurfaces utilizing multiple nonlinear spring oscillator chains, which enables an exceptional ability to generate harmonics in the radiated sound field. The metasurface unit is a chain of masses connected by two nonlinear springs exhibiting two resonance frequencies. The fundamental and second harmonic components of the vibration amplitude are solved by the Multiple Scales Method (MSM). By strategically configuring the higher resonance frequency of the spring oscillator to be n times that of the lower frequency and exciting the system with the lower frequency, the energy transfers from the low-frequency mode to the high-frequency mode induced by nonlinearity, leading to the large vibration amplitude of the high-frequency mode. The robustness and validity of this method are substantiated through the excellent consistency between the theoretical and numerical results. Furthermore, we showcase a nonlinear metasurface with more high-harmonic transmission by judiciously adjusting the structural parameters. Parameter tuning including adjustments to the quadratic nonlinear coefficient, resonance frequency, and excitation frequency further underscores the robustness of this nonlinear system, providing insights for designing general nonlinear metasurfaces. Our work lays a solid foundation for realizing harmonics in nonlinear spring oscillators, extending the research scope of acoustic metasurfaces into nonlinear dynamics. Nonlinear acoustic metasurface Nonlinear spring oscillator chain Multiple Scales Method Internal resonance Harmonic generation 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-3916974","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271642618,"identity":"c4670a3a-781a-4f88-8c86-6a58a63962c3","order_by":0,"name":"Chenghao Sun","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Chenghao","middleName":"","lastName":"Sun","suffix":""},{"id":271642619,"identity":"d404a63d-f4ca-478b-8c74-adb37d0dc248","order_by":1,"name":"Haoyu Wang","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Haoyu","middleName":"","lastName":"Wang","suffix":""},{"id":271642620,"identity":"23ff1490-2de1-4dc2-8bfd-a8f80bdcec12","order_by":2,"name":"Yuanyuan Li","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Yuanyuan","middleName":"","lastName":"Li","suffix":""},{"id":271642621,"identity":"1aa3ad38-90b6-4aad-8296-735d180087a8","order_by":3,"name":"Zhonghan Fei","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Zhonghan","middleName":"","lastName":"Fei","suffix":""},{"id":271642622,"identity":"771f7d08-e056-43f3-800a-114f3c2ea27c","order_by":4,"name":"Yun Lai","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Yun","middleName":"","lastName":"Lai","suffix":""},{"id":271642623,"identity":"ae24ac75-9006-47c9-aa39-8039077cc0c6","order_by":5,"name":"Xiaozhou Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYFAC5oYDDBUMzCCmBJFaGIFazpCqhYGxDcIkTovB+YONh3nn3WE3OMB88DYPg10eQS2SDQcbDvNue8ZscIAt2ZqHIbmYoBZ+xkaQlsNALTxm0jwMBxIbCGlhY2YEapkD0sL/jTgt/GwgLQ1gW9iI0yLZw9hwcM6xw8ySh9mMLecYJBPWYnD+8OEPb2oOJ/Mdb354402FHWEtMJAMiUwDYtUDgR0JakfBKBgFo2CkAQAg9TnVHVs/VQAAAABJRU5ErkJggg==","orcid":"","institution":"Nanjing University","correspondingAuthor":true,"prefix":"","firstName":"Xiaozhou","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-02-01 10:14:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3916974/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3916974/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55664977,"identity":"6f7ace70-2d13-4162-a4da-c1808620f4da","added_by":"auto","created_at":"2024-05-01 11:06:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1019839,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3916974/v1_covered_808d2c3f-c53a-4417-aa7e-e1f75539c63c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exploiting nonlinear spring oscillator chain as acoustic metasurfaces for high harmonic generation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Nonlinear acoustic metasurface, Nonlinear spring oscillator chain, Multiple Scales Method, Internal resonance, Harmonic generation","lastPublishedDoi":"10.21203/rs.3.rs-3916974/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3916974/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a novel approach to design acoustic metasurfaces utilizing multiple nonlinear spring oscillator chains, which enables an exceptional ability to generate harmonics in the radiated sound field. The metasurface unit is a chain of masses connected by two nonlinear springs exhibiting two resonance frequencies. The fundamental and second harmonic components of the vibration amplitude are solved by the Multiple Scales Method (MSM). By strategically configuring the higher resonance frequency of the spring oscillator to be n times that of the lower frequency and exciting the system with the lower frequency, the energy transfers from the low-frequency mode to the high-frequency mode induced by nonlinearity, leading to the large vibration amplitude of the high-frequency mode. The robustness and validity of this method are substantiated through the excellent consistency between the theoretical and numerical results. Furthermore, we showcase a nonlinear metasurface with more high-harmonic transmission by judiciously adjusting the structural parameters. 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