{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:58:10Z","timestamp":1773820690266,"version":"3.50.1"},"reference-count":25,"publisher":"Elsevier BV","issue":"24","content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2013,8]]},"DOI":"10.1016\/j.amc.2013.05.023","type":"journal-article","created":{"date-parts":[[2013,6,21]],"date-time":"2013-06-21T09:53:05Z","timestamp":1371808385000},"page":"11096-11109","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":26,"title":["Free vibration analysis of multiple-stepped beams by the discrete singular convolution"],"prefix":"10.1016","volume":"219","author":[{"given":"Guohui","family":"Duan","sequence":"first","affiliation":[]},{"given":"Xinwei","family":"Wang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.amc.2013.05.023_b0005","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/0022-460X(89)90561-0","article-title":"Free vibrations of stepped beams: exact and numerical solutions","volume":"130","author":"Jang","year":"1989","journal-title":"J. Sound Vib."},{"issue":"1","key":"10.1016\/j.amc.2013.05.023_b0010","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/0022-460X(89)90882-1","article-title":"Free vibrations of stepped beams: higher mode frequencies and effects of steps on frequency","volume":"132","author":"Jang","year":"1989","journal-title":"J. Sound Vib."},{"key":"10.1016\/j.amc.2013.05.023_b0015","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1016\/S0020-7403(02)00190-X","article-title":"Vibration of an Euler\u2013Bernoulli beam on elastic end supports and with up to three step changes in cross-section","volume":"44","author":"Naguleswaran","year":"2002","journal-title":"Int. J. Mech. Sci."},{"key":"10.1016\/j.amc.2013.05.023_b0020","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1016\/j.jsv.2008.11.041","article-title":"Vibration analysis of multiple-stepped beams with the composite element model","volume":"322","author":"Lu","year":"2009","journal-title":"J. Sound Vib."},{"key":"10.1016\/j.amc.2013.05.023_b0025","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1016\/j.mcm.2011.03.019","article-title":"Free vibration analysis of multiple-stepped beams by using adomian decomposition method","volume":"54","author":"Mao","year":"2011","journal-title":"Math. Comput. Model."},{"key":"10.1016\/j.amc.2013.05.023_b0030","doi-asserted-by":"crossref","first-page":"5802","DOI":"10.1016\/j.amc.2012.12.037","article-title":"Free vibration analysis of multiple-stepped beams by the differential quadrature element method","volume":"219","author":"Wang","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2013.05.023_b0035","doi-asserted-by":"crossref","first-page":"8930","DOI":"10.1063\/1.478812","article-title":"Discrete singular convolution for the solution of the Fokker\u2013Planck equations","volume":"190","author":"Wei","year":"1999","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.amc.2013.05.023_b0040","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1006\/jsvi.2002.5055","article-title":"A novel approach for the analysis of high-frequency vibrations","volume":"257","author":"Wei","year":"2002","journal-title":"J. Sound Vib."},{"key":"10.1016\/j.amc.2013.05.023_b0045","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0020-7683(01)00183-4","article-title":"Discrete singular convolution for the prediction of high frequency vibration of plates","volume":"39","author":"Zhao","year":"2002","journal-title":"Int. J. Solids Struct."},{"key":"10.1016\/j.amc.2013.05.023_b0050","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/nme.1179","article-title":"DSC-Ritz method for the high frequency mode analysis of thick shallow shells","volume":"62","author":"Lim","year":"2005","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.amc.2013.05.023_b0055","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/S0020-7683(01)00241-4","article-title":"Plate vibration under irregular internal supports","volume":"39","author":"Zhao","year":"2002","journal-title":"Int. J. Solids Struct."},{"key":"10.1016\/j.amc.2013.05.023_b0060","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1016\/j.ijmecsci.2006.10.002","article-title":"Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method","volume":"49","author":"Civalek","year":"2007","journal-title":"Int. J. Mech. Sci."},{"key":"10.1016\/j.amc.2013.05.023_b0065","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.jsv.2008.01.061","article-title":"Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification","volume":"315","author":"Secgin","year":"2008","journal-title":"J. Sound Vib."},{"key":"10.1016\/j.amc.2013.05.023_b0070","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.cam.2006.05.001","article-title":"Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach","volume":"205","author":"Civalek","year":"2007","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"10.1016\/j.amc.2013.05.023_b0075","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.apm.2007.11.003","article-title":"Four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates","volume":"33","author":"Civalek","year":"2009","journal-title":"Appl. Math. Model."},{"key":"10.1016\/j.amc.2013.05.023_b0080","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.euromechsol.2009.12.007","article-title":"DSC-Ritz element method for vibration analysis of rectangular Mindlin plates with mixed edge supports","volume":"29","author":"Xiang","year":"2010","journal-title":"Eur. J. Mech. A Solids"},{"key":"10.1016\/j.amc.2013.05.023_b0085","doi-asserted-by":"crossref","first-page":"3493","DOI":"10.1016\/j.apm.2010.02.037","article-title":"The discrete singular convolution for analyses of elastic wave propagations in one-dimensional structures","volume":"34","author":"Wang","year":"2010","journal-title":"Appl. Math. Model."},{"key":"10.1016\/j.amc.2013.05.023_b0090","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1016\/j.apm.2005.11.023","article-title":"Nonlinear analysis of thin rectangular plates on Winkler\u2013Pasternak elastic foundations by DSC\u2013HDQ methods","volume":"31","author":"Civalek","year":"2007","journal-title":"Appl. Math. Model."},{"issue":"6","key":"10.1016\/j.amc.2013.05.023_b0095","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.ijnonlinmec.2011.11.008","article-title":"Non-linear buckling analysis of inclined circular cylinder-in-cylinder by the discrete singular convolution","volume":"47","author":"Yuan","year":"2012","journal-title":"Int. J. Nonlinear Mech."},{"key":"10.1016\/j.amc.2013.05.023_b0100","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.jcp.2006.03.027","article-title":"On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method","volume":"219","author":"Zhou","year":"2006","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2013.05.023_b0105","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.jcp.2007.08.003","article-title":"Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities","volume":"227","author":"Yu","year":"2007","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2013.05.023_b0110","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1016\/S0020-7403(01)00021-2","article-title":"The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution","volume":"43","author":"Wei","year":"2001","journal-title":"Int. J. Mech. Sci."},{"key":"10.1016\/j.amc.2013.05.023_b0115","doi-asserted-by":"crossref","first-page":"1780","DOI":"10.1016\/j.jsv.2009.12.006","article-title":"Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution","volume":"319","author":"Wang","year":"2010","journal-title":"J. Sound Vib."},{"key":"10.1016\/j.amc.2013.05.023_b0120","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1016\/j.advengsoft.2011.05.019","article-title":"Free vibration analyses of Timoshenko beams with free edges by using the discrete singular convolution","volume":"42","author":"Xu","year":"2011","journal-title":"Adv. Eng. Software"},{"key":"10.1016\/j.amc.2013.05.023_b0125","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.jsv.2007.11.010","article-title":"Free vibration of a cantilevered beam with multiple steps: comparison of several theoretical methods with experiment","volume":"312","author":"Jaworski","year":"2008","journal-title":"J. Sound Vib."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0096300313005432?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0096300313005432?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,10,14]],"date-time":"2018-10-14T23:50:04Z","timestamp":1539561004000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300313005432"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":25,"journal-issue":{"issue":"24","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["S0096300313005432"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1016\/j.amc.2013.05.023","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2013,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Free vibration analysis of multiple-stepped beams by the discrete singular convolution","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1016\/j.amc.2013.05.023","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2013 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}