{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T17:19:30Z","timestamp":1763140770126,"version":"3.38.0"},"reference-count":25,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2015,6,1]],"date-time":"2015-06-01T00:00:00Z","timestamp":1433116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science"],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p> The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli\u2013Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack. <\/jats:p>","DOI":"10.1177\/0954406215589333","type":"journal-article","created":{"date-parts":[[2015,6,3]],"date-time":"2015-06-03T00:09:36Z","timestamp":1433290176000},"page":"34-54","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Vibrations of beams with a breathing crack and large amplitude displacements"],"prefix":"10.1177","volume":"230","author":[{"given":"Gon\u00e7alo","family":"Neves Carneiro","sequence":"first","affiliation":[{"name":"DEMec\/INEGI, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal"}]},{"given":"Pedro","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"DEMec\/INEGI, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2015,6,1]]},"reference":[{"key":"bibr1-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/0013-7944(94)00175-8"},{"key":"bibr2-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2012.04.007"},{"key":"bibr3-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2000.0717"},{"key":"bibr4-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7403(84)90017-1"},{"key":"bibr5-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.2001.3978"},{"key":"bibr6-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1115\/1.2893892"},{"key":"bibr7-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1996.0718"},{"key":"bibr8-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.2000.3156"},{"key":"bibr9-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2013.02.012"},{"key":"bibr10-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1994.1058"},{"key":"bibr11-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7949(99)00194-7"},{"key":"bibr12-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1115\/1.1452744"},{"key":"bibr13-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2010.08.032"},{"key":"bibr14-0954406215589333","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2006.08.007"},{"key":"bibr15-0954406215589333","unstructured":"Neves Carneiro G. An\u00e1lises de Vibra\u00e7\u00f5es N\u00e3o-Lineares de Vigas com Dano pelo M\u00e9todo dos Elementos Finitos tipo-p. DEMec. 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