{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:18:08Z","timestamp":1777630688116,"version":"3.51.4"},"reference-count":88,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T00:00:00Z","timestamp":1678665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>The dynamic buckling of circular rings is a pervasive instability problem with a major impact in various fields, such as structural, nuclear and offshore engineering, robotics, electromechanics, and biomechanics. This phenomenon may be simply seen as the complex motion that occurs deviating from the original circular shape under, for instance, any kind of time-dependent forcing load. Despite the fact that this topic has progressively gained importance since the mid-20th century, it seems that the same points have not been made completely clear. In fact, even some subtleties in the derivation of classical static buckling load may still give rise to misinterpretations and lead to misleading results. A fortiori, research concerning the nonlinear dynamics of rings still suffers the inherent difficulties associated with different possible analytical formulations of post-buckling dynamics. Advancement in this respect would be relevant, both from a theoretical and a practical point of view, since the applications are endless, with countless possibilities, especially in the biomedical and biotechnological fields: buckling-driven transformations of thin-film materials for applications in electronic microsystems, self-excited oscillations in collapsible tubes and pliable fluid-carrying shells, vocal-fold oscillations during phonation and snoring, pulse wave propagation in arteries, closure and reopening of pulmonary airways, stability of cardiac and venous valves during vascular surgery, stability of annuloplasty devices, flow-induced deformation and ultimate rupture of a cerebral aneurysm, and much more. The present article, in the framework of a critical review of the classic formulation of elastic ring buckling, proposes a straightforward approach for the nonlinear dynamics of an elastic ring that leads to a Mathieu\u2013Duffing equation. In such a manner, some possible evolutions of the system under pulsing loads are analyzed and discussed, showing the inherent complexity of its dynamic behavior.<\/jats:p>","DOI":"10.3389\/fams.2023.1115227","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T05:42:34Z","timestamp":1678686154000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["From static buckling to nonlinear dynamics of circular rings"],"prefix":"10.3389","volume":"9","author":[{"given":"Enrico","family":"Babilio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ida","family":"Mascolo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Guarracino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"111001","DOI":"10.1115\/1.4031456","article-title":"A perspective on the revival of structural (in)stability with novel opportunities for function: from Buckliphobia to Buckliphilia","volume":"82","author":"Reis","year":"2015","journal-title":"J Appl Mech."},{"key":"B2","doi-asserted-by":"publisher","first-page":"34","DOI":"10.3389\/fams.2019.00034","article-title":"Happy catastrophe: recent progress in analysis and exploitation of elastic instability","volume":"5","author":"Champneys","year":"2019","journal-title":"Front Appl Math Stat."},{"key":"B3","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.tws.2015.07.020","article-title":"An investigation into the plastic buckling paradox for circular cylindrical shells under non-proportional loading","volume":"95","author":"Shamass","year":"2015","journal-title":"Thin Walled Struct."},{"key":"B4","doi-asserted-by":"publisher","first-page":"514267","DOI":"10.1155\/2015\/514267","article-title":"An analytical insight into the buckling paradox for circular cylindrical shells under axial and lateral loading","volume":"2015","author":"Shamass","year":"2015","journal-title":"Math Probl Eng."},{"key":"B5","doi-asserted-by":"publisher","first-page":"1750072","DOI":"10.1142\/S0219455417500729","article-title":"On elastoplastic buckling analysis of cylinders under nonproportional loading by differential quadrature method","volume":"17","author":"Shamass","year":"2017","journal-title":"Int J Struct Stabil Dyn."},{"key":"B6","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/978-1-4612-4866-8_24","article-title":"Self-excited oscillation of a collapsible tube conveying fluid","volume-title":"Frontiers in Biomechanics","author":"Matsuzaki","year":"1986"},{"key":"B7","doi-asserted-by":"publisher","first-page":"106241","DOI":"10.1016\/j.ast.2020.106241","article-title":"Aeroelastic stability analysis of aircraft wings with initial curvature","volume":"107","author":"Amoozgar","year":"2020","journal-title":"Aerospace Sci Technol."},{"key":"B8","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.tws.2012.10.007","article-title":"Towards an accurate assessment of UOE pipes under external pressure: effects of geometric imperfection and material inhomogeneity","volume":"63","author":"Fraldi","year":"2013","journal-title":"Thin Walled Struct."},{"key":"B9","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.ijmecsci.2014.05.021","article-title":"Postbuckling of FGM rings","volume":"85","author":"Kerdegarbakhsh","year":"2014","journal-title":"Int J Mech Sci."},{"key":"B10","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1016\/j.jash.2015.09.011","article-title":"The origin of Korotkoff sounds and the accuracy of auscultatory blood pressure measurements","volume":"9","author":"Babbs","year":"2015","journal-title":"J Am Soc Hypertens."},{"key":"B11","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.smrv.2009.06.002","article-title":"The acoustics of snoring","volume":"14","author":"Pevernagie","year":"2010","journal-title":"Sleep Med Rev."},{"key":"B12","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1098\/rspa.2005.1453","article-title":"Surface-tension-induced buckling of liquid-lined elastic tubes: a model for pulmonary airway closure","volume":"461","author":"Hazel","year":"2005","journal-title":"Pro. of the Royal Soc. 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