Gradient-Based Optimization of Wave Propagation in Dual Directional Porous Functionally Graded Beams

Gradient-Based Optimization of Wave Propagation in Dual Directional Porous Functionally Graded Beams | 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 Gradient-Based Optimization of Wave Propagation in Dual Directional Porous Functionally Graded Beams Slimane Debbaghi, Mouloud Dahmane, Abderrahim Boussaid This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7411138/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 study presents a gradient-driven optimization framework to enhance the dynamic performance of bi-directional porous functionally graded (FG) beams. Material properties are tailored along both the thickness (z) and width (y) directions using power-law distributions, with porosity modeled via uniform and non-uniform approaches.Using Touratier’s higher-order shear deformation theory (HSDT), the formulation captures nonlinear shear stresses and dynamic behaviors more accurately than classical beam theories. A gradient-based optimization strategy is applied to optimize power-law indices, porosity factors, and geometric parameters to maximize natural frequencies and minimize structural weight.The analytic solution results from the literature used to computes bending stiffness and mass matrices. The optimization employs the Quasi-Newton BFGS algorithm , avoiding explicit Hessian computation while ensuring fast convergence.The optimized designs aim for a 25% increase in natural frequencies and 15-20% 1 weight reduction compared to conventional FG beams. The proposed framework highlights the effectiveness of dual-directional grading and controlled porosity in balancing stiffness-to-weight trade-offs. The optimized design can be applied in aerospace, civil infrastructure, and mechanical systems. Bi-directional porous FG beams HSDT Gradient-based optimization Natural frequency Porosity factor Wave propagation analysis Quasi-Newton Hessian algorithm. 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. 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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-7411138","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511727159,"identity":"edf88c56-fbd0-40f6-97ad-5f407cb3bb15","order_by":0,"name":"Slimane Debbaghi","email":"data:image/png;base64,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","orcid":"","institution":"Univerity of Adrar","correspondingAuthor":true,"prefix":"","firstName":"Slimane","middleName":"","lastName":"Debbaghi","suffix":""},{"id":511727161,"identity":"6a8d18a5-e197-4c7d-8fcc-d5aedd0a04ff","order_by":1,"name":"Mouloud Dahmane","email":"","orcid":"","institution":"Higher National School of Hydraulics","correspondingAuthor":false,"prefix":"","firstName":"Mouloud","middleName":"","lastName":"Dahmane","suffix":""},{"id":511727166,"identity":"84b452eb-e283-493d-9b4c-4125e702e9a4","order_by":2,"name":"Abderrahim Boussaid","email":"","orcid":"","institution":"Université Tahri Mohamed Bechar","correspondingAuthor":false,"prefix":"","firstName":"Abderrahim","middleName":"","lastName":"Boussaid","suffix":""}],"badges":[],"createdAt":"2025-08-19 18:23:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7411138/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7411138/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92345477,"identity":"1facd874-ac13-4a39-b987-5e59d3e1ac5e","added_by":"auto","created_at":"2025-09-28 08:46:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":699287,"visible":true,"origin":"","legend":"","description":"","filename":"snarticleGA.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7411138/v1_covered_e56a6b72-ef7d-4028-9441-8053c8fc8702.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Gradient-Based Optimization of Wave Propagation in Dual Directional Porous Functionally Graded Beams","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":"Bi-directional porous FG beams, HSDT, Gradient-based optimization, Natural frequency, Porosity factor, Wave propagation analysis, Quasi-Newton Hessian algorithm.","lastPublishedDoi":"10.21203/rs.3.rs-7411138/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7411138/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study presents a gradient-driven optimization framework to enhance the dynamic performance of bi-directional porous functionally graded (FG) beams. 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