Nonlinear Dynamics of a Beam on an Elastomeric Foundation: Coupled Effects of Inertia, Shear, and Nonlinear Interactions

Nonlinear Dynamics of a Beam on an Elastomeric Foundation: Coupled Effects of Inertia, Shear, and Nonlinear Interactions | 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 Dynamics of a Beam on an Elastomeric Foundation: Coupled Effects of Inertia, Shear, and Nonlinear Interactions Anna Kashcheeva, Alyona Zamyshlyaeva1, Saber Azizi, Ghader Rezazadeh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6571462/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 nonlinear dynamic analysis of a beam resting on a viscoelastic elastomeric foundation, incorporating shear deformations, viscoelastic damping, foundation inertia, and nonlinear strains to capture the full elasto-dynamic interaction. Conventional models that prioritize stiffness and damping are contrasted with the present study's comprehensive framework, which considers the material-dependent response and the influence of excitation amplitude on stability and bifurcation. The governing equations are solved in the frequency domain using a continuation-based method, revealing a strong dependence of the system behavior on both the material properties of the foundation and the amplitude of the external excitation. For low-amplitude base inputs, the system manifests approximately linear behavior, with resonance peaks following classical vibrational characteristics. However, as the excitation amplitude increases, the response deviates significantly due to nonlinear interactions, leading to complex phenomena such as period-doubling bifurcations, Neimark-Sacker bifurcations, branch-point cycles, and limit-point cycles. The veracity of the frequency response findings, in certain instances, is substantiated by time domain response, FFT analysis, phase portrait trajectories, and Poincaré section maps. The findings demonstrate that, contingent on material characteristics, system response can vary not only quantitatively but also qualitatively due to substantial nonlinearities, resulting in bifurcation and instability within specific frequency ranges. These findings underscore the imperative for judicious material selection and meticulous control of excitation amplitude to avert undesirable dynamic behavior. The knowledge gained from this work is crucial for the design of wearable sensors, MEMS devices, and vibration isolation systems to ensure stable and predictable performance under dynamic loading conditions. Nonlinear analysis Stability Wearable Sensors Bifurcation tracking MEMS Elastomeric foundation 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-6571462","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":454455251,"identity":"7761ac55-4f51-4db4-bd61-9a10178c9579","order_by":0,"name":"Anna Kashcheeva","email":"","orcid":"","institution":"South Ural State University","correspondingAuthor":false,"prefix":"","firstName":"Anna","middleName":"","lastName":"Kashcheeva","suffix":""},{"id":454455252,"identity":"d28115aa-d0cf-4ec5-9137-bd5a99047233","order_by":1,"name":"Alyona Zamyshlyaeva1","email":"","orcid":"","institution":"South Ural State University","correspondingAuthor":false,"prefix":"","firstName":"Alyona","middleName":"","lastName":"Zamyshlyaeva1","suffix":""},{"id":454455253,"identity":"f5e701b1-e691-4c7d-9a69-f4e14f775dff","order_by":2,"name":"Saber Azizi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIiWNgGAWjYFACHgjFxsDY+ABFQoIILc0GpGkB6UJVhEuLfPvZg48rGOzs+fgPt1X+bLPLk29vfsDwo4YhcWYDdi0GZ/KSDc8wJDOzMRxsu83bllxscOaYAWPPMYbE2ThsMWDIMZNsYGBmY2NsbLvNuI05cYNEggEDbwND4jxcDut/Y/6zgaGeh42Zsa3w57b6xPnzn39g/ItHC8ONHDPGBobDEkBr2hh4tx1ObLjBY8AMsgWnw268S5ZsMDhuwMbD2CzN++944oYzOQWHZY5JGOPyvnx/7sGPDRXV9vL9xx9+/HGmOnF++/GND9/U2MjOOIDLZZBAQAUH8EXkKBgFo2AUjALCAAAPYFXjM6wV8gAAAABJRU5ErkJggg==","orcid":"","institution":"Swansea University","correspondingAuthor":true,"prefix":"","firstName":"Saber","middleName":"","lastName":"Azizi","suffix":""},{"id":454455254,"identity":"34b16e3a-b54d-4264-8604-304cd5bb661b","order_by":3,"name":"Ghader Rezazadeh","email":"","orcid":"","institution":"Urmia University","correspondingAuthor":false,"prefix":"","firstName":"Ghader","middleName":"","lastName":"Rezazadeh","suffix":""}],"badges":[],"createdAt":"2025-05-01 11:23:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6571462/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6571462/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91795768,"identity":"4470410e-4ae1-48b0-a386-8b52053448bd","added_by":"auto","created_at":"2025-09-21 15:16:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":915564,"visible":true,"origin":"","legend":"","description":"","filename":"ABABeamonViscoelasticPolymericfoundationD15.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6571462/v1_covered_c3c02218-bab6-481b-9326-d2c7c6739ec9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear Dynamics of a Beam on an Elastomeric Foundation: Coupled Effects of Inertia, Shear, and Nonlinear Interactions","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 analysis, Stability, Wearable Sensors, Bifurcation tracking, MEMS, Elastomeric foundation","lastPublishedDoi":"10.21203/rs.3.rs-6571462/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6571462/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study presents a nonlinear dynamic analysis of a beam resting on a viscoelastic elastomeric foundation, incorporating shear deformations, viscoelastic damping, foundation inertia, and nonlinear strains to capture the full elasto-dynamic interaction. Conventional models that prioritize stiffness and damping are contrasted with the present study's comprehensive framework, which considers the material-dependent response and the influence of excitation amplitude on stability and bifurcation. The governing equations are solved in the frequency domain using a continuation-based method, revealing a strong dependence of the system behavior on both the material properties of the foundation and the amplitude of the external excitation. For low-amplitude base inputs, the system manifests approximately linear behavior, with resonance peaks following classical vibrational characteristics. However, as the excitation amplitude increases, the response deviates significantly due to nonlinear interactions, leading to complex phenomena such as period-doubling bifurcations, Neimark-Sacker bifurcations, branch-point cycles, and limit-point cycles. 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