{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T17:59:13Z","timestamp":1778954353161,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T00:00:00Z","timestamp":1703203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NNSFC)","award":["12202018"],"award-info":[{"award-number":["12202018"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["12332001"],"award-info":[{"award-number":["12332001"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["12322202"],"award-info":[{"award-number":["12322202"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["20190123083"],"award-info":[{"award-number":["20190123083"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["27170123038"],"award-info":[{"award-number":["27170123038"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["2021TQ0021"],"award-info":[{"award-number":["2021TQ0021"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["2022M710280"],"award-info":[{"award-number":["2022M710280"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["12202018"],"award-info":[{"award-number":["12202018"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["12332001"],"award-info":[{"award-number":["12332001"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["12322202"],"award-info":[{"award-number":["12322202"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["20190123083"],"award-info":[{"award-number":["20190123083"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["27170123038"],"award-info":[{"award-number":["27170123038"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["2021TQ0021"],"award-info":[{"award-number":["2021TQ0021"]}]},{"name":"Funding Projects of the Beijing Institute of Graphic Communication","award":["2022M710280"],"award-info":[{"award-number":["2022M710280"]}]},{"name":"China Postdoctoral Science Foundation","award":["12202018"],"award-info":[{"award-number":["12202018"]}]},{"name":"China Postdoctoral Science Foundation","award":["12332001"],"award-info":[{"award-number":["12332001"]}]},{"name":"China Postdoctoral Science Foundation","award":["12322202"],"award-info":[{"award-number":["12322202"]}]},{"name":"China Postdoctoral Science Foundation","award":["20190123083"],"award-info":[{"award-number":["20190123083"]}]},{"name":"China Postdoctoral Science Foundation","award":["27170123038"],"award-info":[{"award-number":["27170123038"]}]},{"name":"China Postdoctoral Science Foundation","award":["2021TQ0021"],"award-info":[{"award-number":["2021TQ0021"]}]},{"name":"China Postdoctoral Science Foundation","award":["2022M710280"],"award-info":[{"award-number":["2022M710280"]}]},{"name":"Funding Project for Postdoctoral Research","award":["12202018"],"award-info":[{"award-number":["12202018"]}]},{"name":"Funding Project for Postdoctoral Research","award":["12332001"],"award-info":[{"award-number":["12332001"]}]},{"name":"Funding Project for Postdoctoral Research","award":["12322202"],"award-info":[{"award-number":["12322202"]}]},{"name":"Funding Project for Postdoctoral Research","award":["20190123083"],"award-info":[{"award-number":["20190123083"]}]},{"name":"Funding Project for Postdoctoral Research","award":["27170123038"],"award-info":[{"award-number":["27170123038"]}]},{"name":"Funding Project for Postdoctoral Research","award":["2021TQ0021"],"award-info":[{"award-number":["2021TQ0021"]}]},{"name":"Funding Project for Postdoctoral Research","award":["2022M710280"],"award-info":[{"award-number":["2022M710280"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>New three-phase composite structures reinforced synergistically by nano-fillers and macroscopic fibers have great application potential. This paper presents a general framework for material properties calculation and the free vibration analysis of three-phase composite shell structures. Based on this methodological system, the free vibration characteristics of three types of nano-enhanced functionally graded three-phase composite cylindrical shells are investigated. First, the equivalent mechanical properties of these three three-phase composites were evaluated using the Halpin\u2013Tsai and Mori\u2013Tanaka models. The governing equations for the cylindrical shells were derived based on the first-order shear deformation theory (FSDT) and Hamilton\u2019s principle. The equations were discretized using Galerkin\u2019s method and solved to obtain the natural frequencies and mode shapes. The finite element simulation results and existing literature verified the accuracy and reliability of the method in this paper. The synergistic effects of nano-reinforced fillers and macroscopic fibers on the free vibrations of these structures were also analyzed. Among them, the natural frequency of the three-phase composite cylindrical shells was the highest when graphene platelets (GPLs) were used as the nano-reinforced fillers, which was 150.32% higher than that of fiber-reinforced epoxy composite cylindrical shells. These studies provide theoretical guidance for the design and manufacture of such symmetric or antisymmetric structures in the future.<\/jats:p>","DOI":"10.3390\/sym16010020","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:44:15Z","timestamp":1703450655000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A General Framework for Material Properties Calculation and the Free Vibration Analysis of New Three-Phase Composite Cylindrical Shell Structures"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0210-5642","authenticated-orcid":false,"given":"Wei","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, Beijing 100124, China"},{"name":"School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinqiu","family":"Duan","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2576-8123","authenticated-orcid":false,"given":"Tao","family":"Liu","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Institute of Graphic Communication, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingjing","family":"Qian","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7570","DOI":"10.1016\/j.jmrt.2023.04.267","article-title":"The effects of nano-additives on the mechanical, impact, vibration, and buckling\/post-buckling properties of composites: A review","volume":"24","author":"Shan","year":"2023","journal-title":"J. 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