Non-Linear Dynamics and Controls of Non-Local Strain Gradient Beam with Harmonic Balance, Sliding Mode and Feedback Linearization Methods

Non-Linear Dynamics and Controls of Non-Local Strain Gradient Beam with Harmonic Balance, Sliding Mode and Feedback Linearization Methods | 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 Non-Linear Dynamics and Controls of Non-Local Strain Gradient Beam with Harmonic Balance, Sliding Mode and Feedback Linearization Methods Alireza Babaei, Hedieh Mir Mohammad Rezaei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8450365/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 nonlinear dynamic analysis and active control framework for an Euler–Bernoulli nanobeam modeled using the Nonlocal Strain Gradient Theory (NSGT). The governing sixth-order nonlinear partial differential equation is derived using Hamilton’s principle with von Kármán geometric strain assumptions and reduced to a Duffing-type single-mode model through the Galerkin method. Bifurcation analysis is conducted to examine the effects of nonlocal and strain-gradient length-scale parameters on resonance behavior, stability boundaries, and hysteresis. Two advanced nonlinear control strategies: Sliding Mode Control (SMC) and Feedback Linearization with Proportional–Derivative and Feed-Forward compensation (FBL-PD-FF) are designed and evaluated under deterministic harmonic excitation and stochastic white-noise disturbances. Numerical simulations demonstrate that SMC offers superior robustness, disturbance rejection, and overshoot suppression, while FBL-PD-FF achieves fast response but suffers from higher sensitivity to nonlinearities and noise. The results provide theoretical insight and practical guidance for designing stable, high-precision MEMS/NEMS resonators operating under nonlinear and stochastic conditions. Nonlinear Controls Non-Local Strain Gradient Theory Sliding Mode Control Feed-Back Linearization PD-Stiffness FF Control Nonlinear Analysis Micro/Nano-Systems 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-8450365","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":574373401,"identity":"0bf60e65-78e2-4847-b50b-1fa479d0551a","order_by":0,"name":"Alireza 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Methods","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 Controls, Non-Local Strain Gradient Theory, Sliding Mode Control, Feed-Back Linearization 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The governing sixth-order nonlinear partial differential equation is derived using Hamilton\u0026rsquo;s principle with von K\u0026aacute;rm\u0026aacute;n geometric strain assumptions and reduced to a Duffing-type single-mode model through the Galerkin method. Bifurcation analysis is conducted to examine the effects of nonlocal and strain-gradient length-scale parameters on resonance behavior, stability boundaries, and hysteresis. Two advanced nonlinear control strategies: Sliding Mode Control (SMC) and Feedback Linearization with Proportional\u0026ndash;Derivative and Feed-Forward compensation (FBL-PD-FF) are designed and evaluated under deterministic harmonic excitation and stochastic white-noise disturbances. Numerical simulations demonstrate that SMC offers superior robustness, disturbance rejection, and overshoot suppression, while FBL-PD-FF achieves fast response but suffers from higher sensitivity to nonlinearities and noise. 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