{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T06:18:59Z","timestamp":1762409939161,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:00:00Z","timestamp":1636502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper studies the vibration response of an elastic solid that has geometric symmetries. These determine special properties of the equations of motion of such a system, presented in the case of a cylindrical body (hollow cylinder). The properties of the eigenvalues and eigenmodes of these systems are theoretically established. A validation of these results is made using the finite element method. The use of the obtained results can lead to an easing of the vibration analysis of such a system and, consequently, to the decrease of the cost related to the design and manufacture of such a structure. The properties presented and demonstrated in the paper can simplify the numerical calculation and experimental verifications of such a structure. Serving these symmetries, the computation cost decrease substantially and will depend not in the number of the identical parts.<\/jats:p>","DOI":"10.3390\/sym13112145","type":"journal-article","created":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T23:07:21Z","timestamp":1636672041000},"page":"2145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Use of the Symmetries in the Study of Vibration Response of a Hollow Cylinder"],"prefix":"10.3390","volume":"13","author":[{"given":"C\u0103lin","family":"Itu","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 20, 500036 Bra\u0219ov, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2579","authenticated-orcid":false,"given":"Sorin","family":"Vlase","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 20, 500036 Bra\u0219ov, Romania"},{"name":"Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Transilvania University of Bra\u0219ov, B-dul Eroilor 20, 500036 Bra\u0219ov, Romania"}]},{"given":"Ana","family":"Toderi\u021b\u0103","sequence":"additional","affiliation":[{"name":"Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5477","DOI":"10.1016\/S0020-7683(03)00279-8","article-title":"Free and forced vibration of repetitive structure","volume":"40","author":"Wang","year":"2003","journal-title":"Int. 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