Investigation of Non-linear Characteristics of Electrostatically Coupled MEMS Resonator Arrays

Investigation of Non-linear Characteristics of Electrostatically Coupled MEMS Resonator Arrays | 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 Investigation of Non-linear Characteristics of Electrostatically Coupled MEMS Resonator Arrays Uma Shankar, Anand Bhushan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7843275/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 paper presents an investigation of non-linear static and dynamic characteristics of electrostatically coupled n-microbeam MEMS resonator arrays, to understand their collective behavior. We develop a novel reduced-order model using a single-mode Galerkin approximation to derive the governing dynamic equations for an arbitrary number of microbeams, 'n'. Our comprehensive investigation reveals that while the first natural frequency remains constant irrespective of 'n', the system's pull-in voltage converges to an asymptotic value as the array size increases. We systematically explore the intricate influence of inter-beam and electrode-beam gap distances, microbeam thickness variations, and both tensile and compressive axial stresses on natural frequencies, mode shapes, and the operational tuning range. A key finding is that the highest-order mode consistently exhibits all microbeams vibrating in-phase. Furthermore, we demonstrate that strategic non-uniformities in gaps, thickness, or axial stress can be used to significantly tune system stability and dynamic response. The theoretical framework is rigorously validated against Finite Element Analysis (FEA) using COMSOL Multiphysics across various array sizes and complex asymmetric scenarios, confirming the model's accuracy and robustness. This research provides crucial insights for the advanced design and optimization of MEMS devices that leverage complex non-linear and emergent behaviors. Nonlinear Dynamics MEMS Electrostatic Coupling Reduced-Order Modeling Finite Element Analysis Microbeam Arrays Multi-Microbeam Systems Mode Shapes Axial Stress 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. 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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-7843275","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545841876,"identity":"d1ba4836-ec04-407a-8343-dd341da6f80d","order_by":0,"name":"Uma Shankar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVRIiWNgGAWjYBADHn4Q+YFBAso3IKxFRrKBgYFxBoOEBNFabAwOMDAw8zDArcENDK4dfvyBcUctj2QDd+Jj2x0WdeYMzA8/MBTcwa3ldpqZBOOZ40C/8G42zj0jIWHZwGYswWDwDI+WBDMGxrZjQFt4t0nntklIAF1oBhQ/jEdL+ucPIC0GB3i3/7YEa2H/RkBLjoEEY1sNSMs2ZkawFh78tkjezimTSDxzgEeymXezZG+bhOTOZp5iiQQ8Wvhup2/+8HFHnT0/e+/GDz/b6vjN2ds3fvjwB7cWMEhsACpghjkVxEjArwEY6w11SL4jpHoUjIJRMApGHAAAkTpOLVHqBz8AAAAASUVORK5CYII=","orcid":"","institution":"National Institute of Technology Patna","correspondingAuthor":true,"prefix":"","firstName":"Uma","middleName":"","lastName":"Shankar","suffix":""},{"id":545841877,"identity":"8b1b7e53-8d45-443c-8ff7-3eee17af0a8c","order_by":1,"name":"Anand Bhushan","email":"","orcid":"","institution":"National Institute of Technology Patna","correspondingAuthor":false,"prefix":"","firstName":"Anand","middleName":"","lastName":"Bhushan","suffix":""}],"badges":[],"createdAt":"2025-10-13 00:23:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7843275/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7843275/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96207155,"identity":"ade5c63d-7ebb-4d59-8e3c-8f8edf9f16c8","added_by":"auto","created_at":"2025-11-18 17:34:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13110557,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7843275/v1/277355454c847335cc43eae8.pdf"},{"id":96207154,"identity":"519ad137-4836-44db-84f4-3bbd6e0bd1b2","added_by":"auto","created_at":"2025-11-18 17:34:36","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4149,"visible":true,"origin":"","legend":"","description":"","filename":"4de25763fd574a9aa17d32c36cabaf6e.json","url":"https://assets-eu.researchsquare.com/files/rs-7843275/v1/ab79d6a4dd7b62dd6d4ebb81.json"},{"id":103020247,"identity":"f5040ba9-9c16-42eb-b6f9-56c87a498b25","added_by":"auto","created_at":"2026-02-19 17:40:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":13004069,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7843275/v1_covered_fe78d302-9c04-483c-9fb2-cab268f5bfba.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigation of Non-linear Characteristics of Electrostatically Coupled MEMS Resonator Arrays","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 Dynamics, MEMS, Electrostatic Coupling, Reduced-Order Modeling, Finite Element Analysis, Microbeam Arrays, Multi-Microbeam Systems, Mode Shapes, Axial Stress","lastPublishedDoi":"10.21203/rs.3.rs-7843275/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7843275/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents an investigation of non-linear static and dynamic characteristics of electrostatically coupled n-microbeam MEMS resonator arrays, to understand their collective behavior. We develop a novel reduced-order model using a single-mode Galerkin approximation to derive the governing dynamic equations for an arbitrary number of microbeams, 'n'. Our comprehensive investigation reveals that while the first natural frequency remains constant irrespective of 'n', the system's pull-in voltage converges to an asymptotic value as the array size increases. We systematically explore the intricate influence of inter-beam and electrode-beam gap distances, microbeam thickness variations, and both tensile and compressive axial stresses on natural frequencies, mode shapes, and the operational tuning range. A key finding is that the highest-order mode consistently exhibits all microbeams vibrating in-phase. Furthermore, we demonstrate that strategic non-uniformities in gaps, thickness, or axial stress can be used to significantly tune system stability and dynamic response. The theoretical framework is rigorously validated against Finite Element Analysis (FEA) using COMSOL Multiphysics across various array sizes and complex asymmetric scenarios, confirming the model's accuracy and robustness. 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