{"paper_id":"0697a29b-466b-4351-9abb-8487929d7fb5","body_text":"Deep neural network–based mechanical modeling of nonlinear vibration behavior in porous GPL-reinforced plates with cut-outs | 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 Deep neural network–based mechanical modeling of nonlinear vibration behavior in porous GPL-reinforced plates with cut-outs Lida Qiu, Nan Wang, Linyuan Fan, A. Horri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8415753/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Mar, 2026 Read the published version in Acta Mechanica → Version 1 posted You are reading this latest preprint version Abstract This paper introduces a deep learning-based surrogate model based on predicting the nonlinear vibration behaviors of platelets of porous nanocomposites reinforced with graphene platelets (GPLs) with central cut-outs. Conventional numerical approaches can provide precision but are too slow, particularly when dealing with high dimensional parametric analysis, or in real time. To overcome this shortcoming, an artificial neural network (ANN) surrogate model is formulated to effectively learn the complicated nonlinear interactions among design variables, such as plate geometry, GPL distribution patterns, reinforcement volume fractions, and porosity, and modal frequencies. Hamilton principle is used to obtain the motion equations of the reinforced plates of the porous GPL nanocomposite, where von Kármán geometric nonlinearity and Mindlin plate theory are incorporated to include both bending and shear effects. The plate with a central cut-out is divided into sub-domains to find vibration solutions whereby orthogonal polynomials are used to meet the geometric boundary conditions of each sub-domain. Lastly the continuity conditions are imposed and the Rayleigh-Ritz method is used to calculate the natural frequencies, which only gives an efficient and accurate solution strategy to the nonlinear vibration analysis. The model is also verified to agree with the finite element simulation in ABAQUS with the errors of less than 3%. It is shown that parametric analyses that incorporate GPL reinforcement clearly show that the distribution of vibrational frequencies is strongly enhanced by the presence of GPL reinforcement and that porosity decreases the frequencies of vibrations. The proposed surrogate modeling model offers a valuable low cost predictive method of vibration analysis which can easily optimize designs, quantify uncertainties and may be used in real-time structural health monitoring of complex nanocomposite systems. Deep learning Surrogate modeling Nonlinear vibration Graphene platelet (GPL) reinforcement Nanocomposite cut-out plates Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Mar, 2026 Read the published version in Acta Mechanica → 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-8415753\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":578050411,\"identity\":\"887bc886-6ac6-4e3d-95c1-bfae3032b659\",\"order_by\":0,\"name\":\"Lida Qiu\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Minjiang University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Lida\",\"middleName\":\"\",\"lastName\":\"Qiu\",\"suffix\":\"\"},{\"id\":578050412,\"identity\":\"4790d3b3-786d-4ec9-bd98-c387dfe99b6c\",\"order_by\":1,\"name\":\"Nan Wang\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYBADHjZm5gMHEgxsePjZG4jTIsPH3pZ44EFFmoxkzwHitNjI8ZwxPvjgzGEbgxsO+JUaHD97+HVBzR0eNokcgwOJbed5GG4wMH74mINHy5m8NOsZx54BtaQVALXc5mGc3cAsOXMbbi1mB3LMjHnYDgO1JG8Aa2GWOcDGzItPy/k3QC3/QFoSQA47B2IQ0HIjx/gxbxtQC88RgwMJZw7w8BDSYn/jjRkzbx9QC3tbwoGEimQeCZ6DzXj9ItmfY/yZ59the/lm5sMffxjY2dsfbz744SMeLUDAJoEmwNiAVz0QMH8gpGIUjIJRMApGOAAAyUNWJHNiUh0AAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Wuhan Donghu University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Nan\",\"middleName\":\"\",\"lastName\":\"Wang\",\"suffix\":\"\"},{\"id\":578050413,\"identity\":\"cf1055d1-3120-47d6-93a8-f3df08af294f\",\"order_by\":2,\"name\":\"Linyuan Fan\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Minjiang University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Linyuan\",\"middleName\":\"\",\"lastName\":\"Fan\",\"suffix\":\"\"},{\"id\":578050414,\"identity\":\"4d51d64c-8a4e-4462-9c21-77e33231334b\",\"order_by\":3,\"name\":\"A. 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porous GPL-reinforced plates with cut-outs\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"Deep learning, Surrogate modeling, Nonlinear vibration, Graphene platelet (GPL) reinforcement, Nanocomposite cut-out plates\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8415753/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8415753/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThis paper introduces a deep learning-based surrogate model based on predicting the nonlinear vibration behaviors of platelets of porous nanocomposites reinforced with graphene platelets (GPLs) with central cut-outs. Conventional numerical approaches can provide precision but are too slow, particularly when dealing with high dimensional parametric analysis, or in real time. To overcome this shortcoming, an artificial neural network (ANN) surrogate model is formulated to effectively learn the complicated nonlinear interactions among design variables, such as plate geometry, GPL distribution patterns, reinforcement volume fractions, and porosity, and modal frequencies. Hamilton principle is used to obtain the motion equations of the reinforced plates of the porous GPL nanocomposite, where von K\\u0026aacute;rm\\u0026aacute;n geometric nonlinearity and Mindlin plate theory are incorporated to include both bending and shear effects. The plate with a central cut-out is divided into sub-domains to find vibration solutions whereby orthogonal polynomials are used to meet the geometric boundary conditions of each sub-domain. Lastly the continuity conditions are imposed and the Rayleigh-Ritz method is used to calculate the natural frequencies, which only gives an efficient and accurate solution strategy to the nonlinear vibration analysis. The model is also verified to agree with the finite element simulation in ABAQUS with the errors of less than 3%. It is shown that parametric analyses that incorporate GPL reinforcement clearly show that the distribution of vibrational frequencies is strongly enhanced by the presence of GPL reinforcement and that porosity decreases the frequencies of vibrations. The proposed surrogate modeling model offers a valuable low cost predictive method of vibration analysis which can easily optimize designs, quantify uncertainties and may be used in real-time structural health monitoring of complex nanocomposite systems.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Deep neural network–based mechanical modeling of nonlinear vibration behavior in porous GPL-reinforced plates with cut-outs\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-01-22 04:32:33\",\"doi\":\"10.21203/rs.3.rs-8415753/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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}}],\"origin\":\"\",\"ownerIdentity\":\"f1b4a889-9c3c-4452-be3b-78ac1f4e30d5\",\"owner\":[],\"postedDate\":\"January 22nd, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-03-23T16:01:30+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-8415753\",\"link\":\"https://doi.org/10.1007/s00707-026-04677-7\",\"journal\":{\"identity\":\"acta-mechanica\",\"isVorOnly\":false,\"title\":\"Acta Mechanica\"},\"publishedOn\":\"2026-03-20 15:58:44\",\"publishedOnDateReadable\":\"March 20th, 2026\"},\"versionCreatedAt\":\"2026-01-22 04:32:33\",\"video\":\"\",\"vorDoi\":\"10.1007/s00707-026-04677-7\",\"vorDoiUrl\":\"https://doi.org/10.1007/s00707-026-04677-7\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-8415753\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-8415753\",\"identity\":\"rs-8415753\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}