{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T10:40:37Z","timestamp":1719225637295},"reference-count":31,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,6,26]],"date-time":"2012-06-26T00:00:00Z","timestamp":1340668800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Numerical Analysis"],"published-print":{"date-parts":[[2012,6,26]]},"abstract":"<jats:p>Hyperelastic materials based on Signorini\u2019s strain energy density are studied by using Shannon wavelets. Cylindrical waves propagating in a nonlinear elastic material from the circular cylindrical cavity along the radius are analyzed in the following by focusing both on the main nonlinear effects and on the method of solution for the corresponding nonlinear differential equation. Cylindrical waves\u2019 solution of the resulting equations can be easily represented in terms of this family of wavelets. It will be shown that Hankel functions can be linked with Shannon wavelets, so that wavelets can have some physical meaning being a good approximation of cylindrical waves. The nonlinearity is introduced by Signorini elastic energy density and corresponds to the quadratic nonlinearity relative to displacements. The configuration state of elastic medium is defined through cylindrical coordinates but the deformation is considered as functionally depending only on the radial coordinate. The physical and geometrical nonlinearities arising from the wave propagation are discussed from the point of view of wavelet analysis.<\/jats:p>","DOI":"10.1155\/2012\/731591","type":"journal-article","created":{"date-parts":[[2012,6,27]],"date-time":"2012-06-27T14:54:52Z","timestamp":1340808892000},"page":"1-24","source":"Crossref","is-referenced-by-count":2,"title":["Signorini Cylindrical Waves and Shannon Wavelets"],"prefix":"10.1155","volume":"2012","author":[{"given":"Carlo","family":"Cattani","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Salerno, 84084 Fisciano (SA), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"issue":"2","key":"1","first-page":"97","volume":"1","year":"2008","journal-title":"Journal of Mathematics"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-69839-5_90"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s10778-006-0157-1"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s10778-006-0144-6"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10778-006-0170-4"},{"issue":"10","key":"6","first-page":"58","volume":"42","year":"2006","journal-title":"International Applied Mechanics"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02418157"},{"key":"8","first-page":"1","volume":"30","year":"1948","journal-title":"Annali di Matematica Pura ed Applicata, Series 4"},{"key":"9","series-title":"Series on Advances in Mathematics for Applied Sciences","volume":"74","year":"2007"},{"issue":"3","key":"10","first-page":"100","volume":"1","year":"2005","journal-title":"International Journal of Applied Mathematics and Mechanics"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1063\/1.1702365"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(92)90129-5"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/BF01170373"},{"key":"31"},{"key":"22","year":"2011"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620371602"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2005.07.001"},{"issue":"2","key":"18","first-page":"1","volume":"11","year":"2006","journal-title":"Mathematical Modelling and Analysis"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/164808"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/408418"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5562"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1996.0001"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1137\/0914010"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571732"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025710412031"},{"key":"11","year":"1973"},{"key":"12","year":"1974"},{"key":"13","year":"1994"},{"key":"14","year":"2009"},{"key":"15","year":"1997"},{"key":"16","year":"2000"}],"container-title":["Advances in Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/731591.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/731591.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/731591.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T05:01:00Z","timestamp":1607576460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ana\/2012\/731591\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,26]]},"references-count":31,"alternative-id":["731591","731591"],"URL":"https:\/\/doi.org\/10.1155\/2012\/731591","relation":{},"ISSN":["1687-9562","1687-9570"],"issn-type":[{"value":"1687-9562","type":"print"},{"value":"1687-9570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,26]]}}}