Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method

Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method | 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 Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method Omid Mirali Yari, Saeed Jafari Mehrabadi, Mohammad Mahdi Najafizadeh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4966843/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 Background Magneto-rheological fluids (MRF) are considered smart materials with the principal characteristic being enhanced viscosity in the presence of magnetic fields. Sandwich MRF beams are able to minimize the effect of external vibrations by changing the structural hardness and damping properties in the presence of magnetic fields. Despite its importance in mechanical engineering, the behavior of such sandwich beams has not been investigated in response to free nonlinear vibration. Methods We investigated the behavior of a sandwich beam made of an MRF core and two functionally graded face layers exposed to free nonlinear vibration. Specifically, we examined the magnetic field intensity, power law components, the thickness of the fluid core and boundary layers, and the beam’s length versus the natural frequency and damping coefficient. Our analysis of the natural frequency and loss factor considered the Hamilton's principle, and Euler-Bernoulli (E-B) and Timoshenko (TS) beam theories, based on a generalized differential quadratic method. Finally, the findings were validated by comparison to reputable research publications. Results The structure’s natural frequency rose with increases in the beam’s maximal deflection, power law components, and the thickness of MRF core. Conversely, increases in the magnetic field intensity and the beam length reduced the beam behavior, while the effect of magnetic field intensity on the natural frequency and Loss factor was insignificant. Conclusions Increases in the maximal rise of the beam and natural frequency were greater based on the TS beam theory than on the E-B theory. Also, the maximal and minimal beam’s natural frequencies were observed based on simple and clamped support models of TS and E-B beam theories, respectively. The opposite was true with respect to the beam’s loss factor. Euler-Bernoulli’s and Timoschenko’s theories Free nonlinear vibration Generalized differential quadratic method Magneto-rheological fluid core Sandwich beam 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-4966843","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":344690731,"identity":"e9113b91-5754-4b2a-ae09-617d50d4df21","order_by":0,"name":"Omid Mirali Yari","email":"","orcid":"","institution":"Islamic Azad University, Arak","correspondingAuthor":false,"prefix":"","firstName":"Omid","middleName":"Mirali","lastName":"Yari","suffix":""},{"id":344690732,"identity":"c6ced369-ac21-448c-955c-53605d573455","order_by":1,"name":"Saeed Jafari Mehrabadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIie2QMQrCMBSGfwmkS7SrUqFXeMGpIJ7llYKrjoKDlUJcBC/gYRTBLh6gY8XVzUXQwYqLk6mbYL4pgXy87wVwOH4UQh+Q3jx9XUUtZVgpavuFgqeCNteMChcbjK88GLU6p/lFYRDCa5afow4MveQkMkGcBQqJToVHnxUwqHkVJIM4rRTBENIStiqh7zwj2dlmN4WZXUHB6CnekWw3TDVlZ1eoOKa9LuckVWyiNeXa2MOSvT7zlMJFfirOk2no+3tLGBrm7YOqo22TJ6Ks8cjhcDj+mQcIvDTlDjUNcwAAAABJRU5ErkJggg==","orcid":"","institution":"Islamic Azad University, Arak","correspondingAuthor":true,"prefix":"","firstName":"Saeed","middleName":"Jafari","lastName":"Mehrabadi","suffix":""},{"id":344690733,"identity":"b5d74757-c0ad-4420-881c-2cdffc10e1c2","order_by":2,"name":"Mohammad Mahdi Najafizadeh","email":"","orcid":"","institution":"Islamic Azad University, Arak","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Mahdi","lastName":"Najafizadeh","suffix":""}],"badges":[],"createdAt":"2024-08-24 02:36:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4966843/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4966843/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79677934,"identity":"55895f92-7c40-4979-9609-8df4d19443de","added_by":"auto","created_at":"2025-04-01 12:23:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1207615,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptFinalVersion8212024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4966843/v1_covered_9ab13db9-27ee-4ecc-a133-28f61b4ab46a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method","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":"Euler-Bernoulli’s and Timoschenko’s theories, Free nonlinear vibration, Generalized differential quadratic method, Magneto-rheological fluid core, Sandwich beam","lastPublishedDoi":"10.21203/rs.3.rs-4966843/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4966843/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eMagneto-rheological fluids (MRF) are considered smart materials with the principal characteristic being enhanced viscosity in the presence of magnetic fields. Sandwich MRF beams are able to minimize the effect of external vibrations by changing the structural hardness and damping properties in the presence of magnetic fields. Despite its importance in mechanical engineering, the behavior of such sandwich beams has not been investigated in response to free nonlinear vibration.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eWe investigated the behavior of a sandwich beam made of an MRF core and two functionally graded face layers exposed to free nonlinear vibration. Specifically, we examined the magnetic field intensity, power law components, the thickness of the fluid core and boundary layers, and the beam\u0026rsquo;s length versus the natural frequency and damping coefficient. Our analysis of the natural frequency and loss factor considered the Hamilton's principle, and \u003cem\u003eEuler-Bernoulli\u003c/em\u003e (E-B) and \u003cem\u003eTimoshenko\u003c/em\u003e (TS) beam theories, based on a generalized differential quadratic method. Finally, the findings were validated by comparison to reputable research publications.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe structure\u0026rsquo;s natural frequency rose with increases in the beam\u0026rsquo;s maximal deflection, power law components, and the thickness of MRF core. Conversely, increases in the magnetic field intensity and the beam length reduced the beam behavior, while the effect of magnetic field intensity on the natural frequency and Loss factor was insignificant.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eIncreases in the maximal rise of the beam and natural frequency were greater based on the \u003cb\u003eTS\u003c/b\u003e beam theory than on the \u003cb\u003eE-B\u003c/b\u003e theory. Also, the maximal and minimal beam\u0026rsquo;s natural frequencies were observed based on simple and clamped support models of TS and E-B beam theories, respectively. The opposite was true with respect to the beam\u0026rsquo;s loss factor.\u003c/p\u003e","manuscriptTitle":"Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-24 12:42:12","doi":"10.21203/rs.3.rs-4966843/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":"47fd7729-7903-4dc2-ab40-63fa744cea31","owner":[],"postedDate":"September 24th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-04-01T12:23:13+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-24 12:42:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4966843","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4966843","identity":"rs-4966843","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}