Vibration of Circular Microplate of Silicon Under Refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson Theorems of Thermoelasticity

Vibration of Circular Microplate of Silicon Under Refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson Theorems of Thermoelasticity | 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 Vibration of Circular Microplate of Silicon Under Refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson Theorems of Thermoelasticity Hamdy M. Youssef, Alaa A. El-Bary This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7104926/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 work presents novel unified mathematical models for analyzing the heat conduction of a circular micro-plate that is isotropic, homogenous, and thermoelastic. The models are based on Kirchhoff's Love of plate theory. The refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson theorems of generalized thermoelasticity have been used under unified governing differential equations. The study demonstrates the application of scaled thermoelasticity to a circular microplate that is simply supported on the outer bounding surface. The microplate's bounding surface has been subjected to thermal loading using ramp-type heating, and the Laplace transform has been applied to the governing equations. Numerical calculations have been performed to determine the inverse of the Laplace transform by the iteration method of Tzou. The study included graphical comparisons between the studied models. The ramp-time heat, plate thickness, and parameters can be used as a tuner for the propagation of the thermomechanical waves through the silicon microplate. The closest models to each other in the mechanical behaviour are Green-Naghdi Type-III and Moore–Gibson–Thompson models, and then Biot of coupled thermoelasticity and Lord-Sulman of generalized thermoelasticity models. Microplate resonator Thermoelasticity Silicon Kirchhoff's Love plate Ramp-type heat Refined Green-Lindsay Biot Lord-Sulman Green-Naghdi T Moore–Gibson–Thompson 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-7104926","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":498386355,"identity":"1b0bb22c-0469-4b07-83a7-7b5f7b48bfd1","order_by":0,"name":"Hamdy M. 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The models are based on Kirchhoff's Love of plate theory. The refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore\u0026ndash;Gibson\u0026ndash;Thompson theorems of generalized thermoelasticity have been used under unified governing differential equations. The study demonstrates the application of scaled thermoelasticity to a circular microplate that is simply supported on the outer bounding surface. The microplate's bounding surface has been subjected to thermal loading using ramp-type heating, and the Laplace transform has been applied to the governing equations. Numerical calculations have been performed to determine the inverse of the Laplace transform by the iteration method of Tzou. The study included graphical comparisons between the studied models. The ramp-time heat, plate thickness, and \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e parameters can be used as a tuner for the propagation of the thermomechanical waves through the silicon microplate. The closest models to each other in the mechanical behaviour are Green-Naghdi Type-III and Moore\u0026ndash;Gibson\u0026ndash;Thompson models, and then Biot of coupled thermoelasticity and Lord-Sulman of generalized thermoelasticity models.\u003c/p\u003e","manuscriptTitle":"Vibration of Circular Microplate of Silicon Under Refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson Theorems of Thermoelasticity","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-12 07:57:34","doi":"10.21203/rs.3.rs-7104926/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":"81e00328-d416-4dda-8bbe-ac4697c940e7","owner":[],"postedDate":"August 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-05T15:53:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-12 07:57:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7104926","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7104926","identity":"rs-7104926","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}