Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement

Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement | 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 Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement Cong Ich Le, Ngoc Duyen Dang, Thu Nga Dinh, Dinh Kien Nguyen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9470035/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 Enriched formulations are efficient in linear analysis, but they are rarely applied to nonlinear vibrations due to the complexity of combining high-order enrichment functions with geometric nonlinearities. This paper bridges this gap by formulating an enriched beam element to study the nonlinear vibration of sandwich beams with a porous core and graphene platelet (GPL) reinforced face layers. The proposed element is based on Euler-Bernoulli theory and von Kármán nonlinearity, using higher-order hierarchical functions to enrich conventional interpolations. Nonlinear frequencies of the sandwich beams with various boundary conditions and sandwich configurations are predicted using a direct iterative method. Extensive parametric studies demonstrate that the proposed element is efficient, providing accurate nonlinear frequencies by using only half the number of elements required by conventional models. Results reveal that the effect of porosity on nonlinear vibration is coupled with the GPL weight fraction, with the impact of porosity diminishing as GPL content increases. Furthermore, the beam with hinged-hinged ends is to be the most sensitive to variations in the GPL fraction and porosity coefficient, whereas the clamped-clamped beam is the least. The influence of GPL distribution patterns and sandwich configurations on the nonlinear vibration behavior is also examined and highlighted. Sandwich beam GPL reinforcement Hierarchical enrichment Beam element Nonlinear vibration 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. 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-9470035","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":639194517,"identity":"20181a79-64af-4082-b2fe-82496ea2643b","order_by":0,"name":"Cong Ich Le","email":"","orcid":"","institution":"Le Quy Don Technical University","correspondingAuthor":false,"prefix":"","firstName":"Cong","middleName":"Ich","lastName":"Le","suffix":""},{"id":639194518,"identity":"9c195d0f-51fb-4245-80c0-a536fde257e3","order_by":1,"name":"Ngoc Duyen Dang","email":"","orcid":"","institution":"Thuyloi University","correspondingAuthor":false,"prefix":"","firstName":"Ngoc","middleName":"Duyen","lastName":"Dang","suffix":""},{"id":639194519,"identity":"14e2cf92-79ce-49e6-a421-20f23036e032","order_by":2,"name":"Thu Nga Dinh","email":"","orcid":"","institution":"Thuyloi University","correspondingAuthor":false,"prefix":"","firstName":"Thu","middleName":"Nga","lastName":"Dinh","suffix":""},{"id":639194520,"identity":"1ea2a122-024d-4428-94e9-df83eb4c81dc","order_by":3,"name":"Dinh Kien Nguyen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYFCCNIYDDAw2DHwgNg8JWtIk2EjSAgSHSdBizp6WeODjjvN1bBIJjA/etjEkbiekxbLn2YGDM8/clgBqYTacC9Sys4GAFoMb6Q2HedvAWtikedsYjA0OEKPlb9s5kBb230RqSTtwmLHtANgWZqAWOcJazjxLONjblizZxvOwWXLOOQkitBxPM/7ws82On589+eCHN2U2PAS1IAHGBiAhQbz6UTAKRsEoGAW4AQAWCD5OBGXvlAAAAABJRU5ErkJggg==","orcid":"","institution":"Thuyloi University","correspondingAuthor":true,"prefix":"","firstName":"Dinh","middleName":"Kien","lastName":"Nguyen","suffix":""}],"badges":[],"createdAt":"2026-04-20 09:38:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9470035/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9470035/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109183960,"identity":"e35724d5-b889-4ed1-a295-be159b1ac287","added_by":"auto","created_at":"2026-05-13 10:44:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":859266,"visible":true,"origin":"","legend":"","description":"","filename":"ActaMechKien.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9470035/v1_covered_f462fa99-37eb-44b6-9e28-cae92a79adfc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement","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":"Sandwich beam, GPL reinforcement, Hierarchical enrichment, Beam element, Nonlinear vibration","lastPublishedDoi":"10.21203/rs.3.rs-9470035/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9470035/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Enriched formulations are efficient in linear analysis, but they are rarely applied to nonlinear vibrations due to the complexity of combining high-order enrichment functions with geometric nonlinearities. This paper bridges this gap by formulating an enriched beam element to study the nonlinear vibration of sandwich beams with a porous core and graphene platelet (GPL) reinforced face layers. The proposed element is based on Euler-Bernoulli theory and von Kármán nonlinearity, using higher-order hierarchical functions to enrich conventional interpolations. Nonlinear frequencies of the sandwich beams with various boundary conditions and sandwich configurations are predicted using a direct iterative method. Extensive parametric studies demonstrate that the proposed element is efficient, providing accurate nonlinear frequencies by using only half the number of elements required by conventional models. Results reveal that the effect of porosity on nonlinear vibration is coupled with the GPL weight fraction, with the impact of porosity diminishing as GPL content increases. Furthermore, the beam with hinged-hinged ends is to be the most sensitive to variations in the GPL fraction and porosity coefficient, whereas the clamped-clamped beam is the least. The influence of GPL distribution patterns and sandwich configurations on the nonlinear vibration behavior is also examined and highlighted.","manuscriptTitle":"Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-13 10:42:32","doi":"10.21203/rs.3.rs-9470035/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"77f10324-61ea-4b21-aa13-22b8554c2085","owner":[],"postedDate":"May 13th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-18T16:42:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-18T00:01:25+00:00","index":43,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-17T06:15:17+00:00","index":42,"fulltext":""},{"type":"reviewerAgreed","content":"155384136214939486677454298658982910421","date":"2026-05-17T03:39:01+00:00","index":41,"fulltext":""},{"type":"reviewerAgreed","content":"302544838160031679732953859070809846858","date":"2026-05-17T01:10:19+00:00","index":40,"fulltext":""},{"type":"reviewerAgreed","content":"60749317656706568399064221737409934252","date":"2026-05-15T08:44:50+00:00","index":39,"fulltext":""},{"type":"reviewerAgreed","content":"297622025286933678062758270868659671005","date":"2026-05-15T02:05:15+00:00","index":38,"fulltext":""},{"type":"reviewerAgreed","content":"258884494935642019403997879397285967874","date":"2026-05-14T09:06:14+00:00","index":37,"fulltext":""},{"type":"reviewerAgreed","content":"279403295801759510356216295140070519433","date":"2026-05-12T16:39:30+00:00","index":36,"fulltext":""},{"type":"reviewerAgreed","content":"255267714786748112246490710419948767509","date":"2026-05-12T15:21:25+00:00","index":35,"fulltext":""},{"type":"reviewerAgreed","content":"251629945147490062255791139347623087303","date":"2026-05-12T10:15:05+00:00","index":33,"fulltext":""},{"type":"reviewerAgreed","content":"185409324986079429511477887524234349832","date":"2026-05-12T06:01:07+00:00","index":32,"fulltext":""},{"type":"reviewerAgreed","content":"298421719713881580337704126266868234677","date":"2026-05-12T05:42:58+00:00","index":31,"fulltext":""},{"type":"reviewerAgreed","content":"12607471276634693840653944779813851244","date":"2026-05-11T23:17:59+00:00","index":30,"fulltext":""},{"type":"reviewerAgreed","content":"157253410850547095923703785959577041103","date":"2026-05-11T23:15:13+00:00","index":29,"fulltext":""},{"type":"reviewersInvited","content":"21","date":"2026-05-11T23:13:06+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T16:54:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-13 10:42:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9470035","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9470035","identity":"rs-9470035","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}