{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:19Z","timestamp":1740134539099,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51205159","20090061110022","20126001","20121097"],"award-info":[{"award-number":["51205159","20090061110022","20126001","20121097"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Doctoral Program of Higher Education","award":["51205159","20090061110022","20126001","20121097"],"award-info":[{"award-number":["51205159","20090061110022","20126001","20121097"]}]},{"name":"Major Program of Science and Technology Development Plan of Jilin Province of China","award":["51205159","20090061110022","20126001","20121097"],"award-info":[{"award-number":["51205159","20090061110022","20126001","20121097"]}]},{"name":"Graduate Innovation Fund of Jilin University","award":["51205159","20090061110022","20126001","20121097"],"award-info":[{"award-number":["51205159","20090061110022","20126001","20121097"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>Derivatives of eigenvectors with respect to structural parameters play an important role in structural design, identification, and optimization. Particularly, calculation of eigenvector sensitivity is considered when the eigenvalues are repeated. A relaxation factor embedded in the combined approximations (CA) method makes it effective to the structural response at various modified designs. The proposed method is feasible after overcoming the defection of irreversibility of the characteristic matrix. Numerical examples show that it is easy to implement the computational procedure, and the method presented in this paper is efficient for the general linear vibration damped systems with repeated frequencies.<\/jats:p>","DOI":"10.1155\/2013\/810147","type":"journal-article","created":{"date-parts":[[2013,1,30]],"date-time":"2013-01-30T16:03:03Z","timestamp":1359561783000},"page":"1-7","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Procedures of Sensitivity Analysis for Structural Vibration Systems with Repeated Frequencies"],"prefix":"10.1155","volume":"2013","author":[{"given":"Shijia","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China"}]},{"given":"Tao","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China"}]},{"given":"Guikai","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China"}]},{"given":"Dongkai","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1993.1340"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1998.1728"},{"year":"1965","key":"3"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.2514\/3.5008"},{"key":"5","doi-asserted-by":"crossref","first-page":"943","DOI":"10.2514\/3.5795","volume":"8","year":"1970","journal-title":"The American Institute of Aeronautics and Astronautics"},{"issue":"9","key":"6","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.2514\/3.7211","volume":"14","year":"1976","journal-title":"The American Institute of Aeronautics and Astronautics"},{"issue":"3","key":"7","doi-asserted-by":"crossref","first-page":"361","DOI":"10.2514\/3.9897","volume":"26","year":"1988","journal-title":"The American Institute of Aeronautics and Astronautics"},{"issue":"7","key":"8","doi-asserted-by":"crossref","first-page":"867","DOI":"10.2514\/3.9980","volume":"26","year":"1988","journal-title":"The American Institute of Aeronautics and Astronautics"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.2514\/3.10137"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.2514\/3.48905"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1996.9989"},{"year":"2007","key":"12"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s001580050141"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1080\/03052150601128329"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/810147.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/810147.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/810147.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T02:41:37Z","timestamp":1498012897000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/810147\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":14,"alternative-id":["810147","810147"],"URL":"https:\/\/doi.org\/10.1155\/2013\/810147","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}