Bifurcation and Chaos of Hyperelastic Spherical Membrane under Structural Damping

Bifurcation and Chaos of Hyperelastic Spherical Membrane under Structural Damping | 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 Bifurcation and Chaos of Hyperelastic Spherical Membrane under Structural Damping Minfu Ma, Gangxiong Wu, Deli Cao, Ma Chi, Yangyang Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7649806/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 investigates the dynamic responses of spherical membrane composed of an incompressible hyperelastic material following the Yeoh model, under the simultaneous influence of periodic disturbance loads and structural damping. Based on the energy variational principle, a strongly nonlinear differential equation is established to provide an approximate description of the radially symmetric motion of a spherical membrane. Through qualitative analysis of the solution, some meaningful conclusions are obtained for the spherical membrane: (1) For constant loading without damping, the influence of constant load on the equilibrium points of the system was analyzed through the equilibrium point curves and potential energy curves, and the critical parameter E0 that determines the motion trajectory of the spherical membranes was obtained. Periodic motion and amplitude jumping phenomena are discussed by analyzing the system's potential wells. (2) For loading of periodic disturbance loads without damping, the quasi-periodic and chaotic motions of the spherical membranes in the secondary steering bifurcation scenario have been detailed. The effects of the periodic disturbance load on the chaotic motions of the membrane have been further analyzed. (3) For combined loading of periodic disturbance loads and structural damping, the effects of factors such as the damping coefficient and periodic disturbance loads on the chaotic motion of the spherical membrane are analyzed primarily using Poincaré sections. Especially, the motion of the membrane under structural damping generates a strange attractor, which provides significant implications for its practical applications in engineering fields. Hyperelastic materials Spherical membrane Structural damping Periodic disturbance load Bifurcation and chaos Strange attractor 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-7649806","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":526146421,"identity":"17c8d1b3-ec84-4ec5-a444-660cf21cace8","order_by":0,"name":"Minfu Ma","email":"","orcid":"","institution":"Zhaotong Health Vocational College","correspondingAuthor":false,"prefix":"","firstName":"Minfu","middleName":"","lastName":"Ma","suffix":""},{"id":526146423,"identity":"bd5efa34-1aca-4212-be97-c290308d2c5d","order_by":1,"name":"Gangxiong Wu","email":"","orcid":"","institution":"Zhaotong Health Vocational 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Based on the energy variational principle, a strongly nonlinear differential equation is established to provide an approximate description of the radially symmetric motion of a spherical membrane. Through qualitative analysis of the solution, some meaningful conclusions are obtained for the spherical membrane: (1) For constant loading without damping, the influence of constant load on the equilibrium points of the system was analyzed through the equilibrium point curves and potential energy curves, and the critical parameter E0 that determines the motion trajectory of the spherical membranes was obtained. Periodic motion and amplitude jumping phenomena are discussed by analyzing the system's potential wells. (2) For loading of periodic disturbance loads without damping, the quasi-periodic and chaotic motions of the spherical membranes in the secondary steering bifurcation scenario have been detailed. The effects of the periodic disturbance load on the chaotic motions of the membrane have been further analyzed. (3) For combined loading of periodic disturbance loads and structural damping, the effects of factors such as the damping coefficient and periodic disturbance loads on the chaotic motion of the spherical membrane are analyzed primarily using Poincaré sections. 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