Limit Imposed Loads on SSSS Rectangular Panels Forced to Vibrate Under a Uniformly Distributed Load

Limit Imposed Loads on SSSS Rectangular Panels Forced to Vibrate Under a Uniformly Distributed Load | 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 Limit Imposed Loads on SSSS Rectangular Panels Forced to Vibrate Under a Uniformly Distributed Load Njoku, Fidelis Chidiebere, Ibearugbulem, Owuamanam Mathias, Okere, Chinenye Elizabeth, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4113008/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 the determination of limit imposed loads on ssss rectangular panel that is forced to vibrate under uniformly distributed load. By employing the principles of elasticity, the total potential energy functional of a rectangular plate under forced vibration is obtained. This functional is minimized with respect to the deflection function. The minimization gives the governing equation of the plate. A general deflection function that satisfies the governing equation is obtained after integrating the governing equation. With the general deflection, the boundary conditions of ssss plate are satisfied and a peculiar deflection function for ssss plate is obtained. This deflection function is substituted into the total potential energy functional earlier obtained and the outcome minimized with respect to the coefficient of the deflection to get the formula for the deflection coefficient. The obtained deflection coefficient is substituted into stress formulas and the outcomes rearranged to get formulas for limit imposed loads that satisfied the requirements of allowable deflection and yield stress. Using these formulas limit imposed loads for various aspect ratios, forcing frequency ratio and thicknesses are calculated and presented in tables. From the obtained results it is obvious that square panels are stronger than rectangular panels. It is also obvious that strength of panels reduces as the forced frequency ratio increase from zero to 1. It is also seen that panels whose spans are up to 1m should be designed with thickness less than 8mm. Civil Engineering Limit Loads SSSS Rectangular Panels Forced Vibration Uniformly Distributed Loads and Imposed Loads Full Text Additional Declarations The authors declare no competing interests. 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. 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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-4113008","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":280297800,"identity":"36ae7a0e-c123-4a39-ae9d-4f91c2eda8f1","order_by":0,"name":"Njoku, Fidelis Chidiebere","email":"","orcid":"","institution":"Federal University of Technology, Owerri","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fidelis","middleName":"Chidiebere","lastName":"Njoku","suffix":""},{"id":280297801,"identity":"6001eec9-c931-4894-b162-3c9c99185481","order_by":1,"name":"Ibearugbulem, Owuamanam 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By employing the principles of elasticity, the total potential energy functional of a rectangular plate under forced vibration is obtained. This functional is minimized with respect to the deflection function. The minimization gives the governing equation of the plate. A general deflection function that satisfies the governing equation is obtained after integrating the governing equation. With the general deflection, the boundary conditions of ssss plate are satisfied and a peculiar deflection function for ssss plate is obtained. This deflection function is substituted into the total potential energy functional earlier obtained and the outcome minimized with respect to the coefficient of the deflection to get the formula for the deflection coefficient. The obtained deflection coefficient is substituted into stress formulas and the outcomes rearranged to get formulas for limit imposed loads that satisfied the requirements of allowable deflection and yield stress. 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