Response of irregularly ribbed elastic structures, under fluid loading, to localized excitation

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Cooper A. J. and Crighton D. G. 1999Response of irregularly ribbed elastic structures, under fluid loading, to localized excitationProc. R. Soc. Lond. A.4551083–1105http://doi.org/10.1098/rspa.1999.0350SectionRestricted accessResponse of irregularly ribbed elastic structures, under fluid loading, to localized excitation A. J. Cooper A. J. Cooper Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author and D. G. Crighton D. G. Crighton Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author A. J. Cooper A. J. Cooper Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author and D. G. Crighton D. G. Crighton Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 1999https://doi.org/10.1098/rspa.1999.0350AbstractThis paper investigates the response to excitation of a fluid–loaded elastic membrane supported by a finite array of irregularly spaced ribs. Fluid loading is assumed to provide the only mechanism for the transmission of energy along the structure. This gives rise to two forms of coupling, local surface wave coupling and long–range fluid coupling, which are determined by the Green'function of the unribbed membrane. When the Green'function consists only of the dominant subsonic surface wave component, irregularity gives rise to the phenomenon of Anderson localization whereby energy becomes exponentially localized around the source at all frequencies, in contrast to the pass/stop–band structure generated when the ribs are arranged strictly periodically. This, however, neglects the effect of the second, acoustic component of the Green'function which provides long–range coupling and taken alone gives rise to algebraic decay at all frequencies along a regularly ribbed membrane. It is shown, analytically and numerically that, when the Green'function consists only of the acoustic component, this algebraic decay is essentially insensitive to any degree of disorder. Similar techniques are used to show that the stop band response, when only local coupling is accounted for, can show slight delocalization in comparison with the response for the regular array. When the full Green'function is used, consisting of both components, it is shown that the exponential decay induced by irregularity in the pass bands becomes short–circuited by the much slower algebraic decay so that the energy transmission levels become significantly higher. This, with similar behaviour in the stop bands, suggests that the effect of long–range coupling would frustrate any attempt at exploiting either the Anderson localization phenomenon or stop–band localization in fluid–loaded structures. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Liu W (2022) Effect of reducing the vibration of a frame-spacing arrangement, Journal of Vibroengineering, 10.21595/jve.2022.22547, 24:8, (1428-1444), Online publication date: 31-Dec-2022. Legault J, Mejdi A and Atalla N (2011) Vibro-acoustic response of orthogonally stiffened panels: The effects of finite dimensions, Journal of Sound and Vibration, 10.1016/j.jsv.2011.07.017, 330:24, (5928-5948), Online publication date: 1-Nov-2011. Metcalfe P (2005) Ribbed elastic structures under a mean flow, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461:2056, (913-931), Online publication date: 8-Apr-2005. This Issue08 March 1999Volume 455Issue 1983 Article InformationDOI:https://doi.org/10.1098/rspa.1999.0350Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/1999Published in print08/03/1999 License: Citations and impact Keywordsirregular rib arraylong–range couplingensemble averagefluid–loaded structureAnderson localizationalgebraic decay