{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:40:21Z","timestamp":1753886421409,"version":"3.41.2"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,1,17]],"date-time":"2012-01-17T00:00:00Z","timestamp":1326758400000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single\u2010edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height, <jats:italic>a\/h<\/jats:italic>. The mathematical model of this single\u2010edge open crack beam is considered as an Euler\u2010Bernoulli beam. The modified factor, <jats:italic>f(a\/h)<\/jats:italic>, derived in this paper is in good agreement with previous researchers\u2032 results for crack depth ratio <jats:italic>a\/h<\/jats:italic> less than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single\u2010edge open crack beams can then be evaluated by applying this modified factor <jats:italic>f(a\/h)<\/jats:italic>. Using the compatibility conditions on the crack and the analytical transfer matrix method, the numerical solutions for natural frequencies of the cracked beam are obtained. The natural frequencies and the mode shapes with crack at different locations are obtained and compared with the latest research literature. The numerical results of the proposed cracked beam model obtained by this method can be extended to construct frequency contour. The natural frequencies measured from field can be used in solving the inverse problem to identify cracks in structures.<\/jats:p>","DOI":"10.1155\/2012\/543828","type":"journal-article","created":{"date-parts":[[2012,1,17]],"date-time":"2012-01-17T21:00:48Z","timestamp":1326834048000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modified and Simplified Sectional Flexibility of a Cracked Beam"],"prefix":"10.1155","volume":"2012","author":[{"given":"Chih-Shiung","family":"Wang","sequence":"first","affiliation":[]},{"given":"Lin-Tsang","family":"Lee","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,1,17]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2260-5","volume-title":"Method of Fracture Analysis and Solutions of Crack Problems","author":"Sih G. 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F.","year":"1966"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/543828.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/543828.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/543828","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:47:04Z","timestamp":1718088424000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/543828"}},"subtitle":[],"editor":[{"given":"George","family":"Jaiani","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/543828"],"URL":"https:\/\/doi.org\/10.1155\/2012\/543828","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-04-25","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-09-27","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"543828"}}