{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:53:21Z","timestamp":1787028801203,"version":"build-2736575974"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51705537, 11902368"],"award-info":[{"award-number":["51705537, 11902368"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["2018JJ3661"],"award-info":[{"award-number":["2018JJ3661"]}]},{"name":"Innovation Driven Program of Central South University","award":["2019CX006"],"award-info":[{"award-number":["2019CX006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.<\/jats:p>","DOI":"10.3390\/ma13041010","type":"journal-article","created":{"date-parts":[[2020,2,25]],"date-time":"2020-02-25T04:21:26Z","timestamp":1582604486000},"page":"1010","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions"],"prefix":"10.3390","volume":"13","author":[{"given":"Bin","family":"Qin","sequence":"first","affiliation":[{"name":"Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic &amp; Transportation Engineering, Central South University, Changsha 410075, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha 410075, China"},{"name":"National &amp; Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, Changsha 410075, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xing","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huifang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic &amp; Transportation Engineering, Central South University, Changsha 410075, China"},{"name":"Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha 410075, China"},{"name":"National &amp; Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, Changsha 410075, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongge","family":"Yu","sequence":"additional","affiliation":[{"name":"Overall R&amp;D Department, CRRC Changchun Railway Vehicles Co. LTD, Changchun 130062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingshan","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Huu Quoc, T., Minh Tu, T., and Van Tham, V. (2019). Free vibration analysis of smart laminated functionally graded CNT reinforced composite plates via new four-variable refined plate theory. Materials, 12.","DOI":"10.3390\/ma12223675"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tornabene, F., Fantuzzi, N., and Bacciocchi, M. (2017). Linear static behavior of damaged laminated composite plates and shells. 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