{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T17:58:31Z","timestamp":1762624711677,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Natural Science Foundation of China","award":["No. E51508102"],"award-info":[{"award-number":["No. E51508102"]}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["No. 2019J05128","No. 2019J01233"],"award-info":[{"award-number":["No. 2019J05128","No. 2019J01233"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The interaction between multiple loops and string cables complicates the dynamic response of triple square loops-string dome structures under seismic excitation. The internal connection between the multiple square loops-string cables and the grid beams was studies to provide a favorable reference for an anti-seismic structure. With a finite element model of the Fuzhou Strait Olympic Sports Center Gymnasium, established by SAP2000 software, the structural dynamic characteristic parameters were obtained first, and then this study adopted a time-history analysis method to study the internal force response of the cables and the roof grid beams of the multiple square loops-string dome (MSLSD) under three types of seismic array excitation. The influence of two factors, namely the seismic pulse and the near and far seismic fields, on the dynamic response of this structure was analyzed by three groups of different types of seismic excitation (PNF, NNF, PFF). As shown from the results, the first three-order vibration modes were torsional deformations caused by cables, the last five were mainly the overall roof plane vibration and antisymmetric vibration. Under the excitation of the three seismic arrays, the internal force responses of stay cables, square cables in the outer ring and the string cables were largest, while the maximum internal force response of the struts changed with the direction of seismic excitation. The largest internal force response of the roof grid beams occurred in local components such as BX3, BX7 and BY7, and the largest deformation of the beam nodes occurred in JX7, JX12 and JY4. In general, the seismic pulse and the near seismic field weakened the internal force response of the struts and cables but increased the internal force response and deformation of the dome beams, while the near and far seismic fields outweighed the seismic pulse. All the above provides an important reference for structural monitoring and seismic resistance.<\/jats:p>","DOI":"10.3390\/sym13112062","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"2062","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Response Analysis of a Multiple Square Loops-String Dome under Seismic Excitation"],"prefix":"10.3390","volume":"13","author":[{"given":"Zhenwei","family":"Lin","sequence":"first","affiliation":[{"name":"College of Civil Engineering, Yango University, Fuzhou 350017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7722-7428","authenticated-orcid":false,"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jucan","family":"Dong","sequence":"additional","affiliation":[{"name":"Shenzhen Expressway Engineering Consultant Co., Ltd., Shenzhen 518029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianliang","family":"Ou","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Yango University, Fuzhou 350017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Yu","sequence":"additional","affiliation":[{"name":"Gemdale Properties & Investment, Kunshan 215399, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,1]]},"reference":[{"key":"ref_1","first-page":"210","article-title":"Research Review of String Dome Structure","volume":"31","author":"Chen","year":"2010","journal-title":"J. Build. Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.2174\/1874149501711010131","article-title":"Suspen-Dome System: A Fascinating Space Structure","volume":"11","author":"Olofin","year":"2017","journal-title":"Open Civ. Eng. J."},{"key":"ref_3","first-page":"47","article-title":"New String Structure System Design of Shenzhen South Railway Station Canopy","volume":"45","author":"Fu","year":"2015","journal-title":"Build. Struct."},{"key":"ref_4","first-page":"41","article-title":"Construction Technology of Square Loop-String Structure of Fuzhou Strait Olympic Sports Center Gymnasium","volume":"44","author":"Tuo","year":"2015","journal-title":"Constr. Technol."},{"key":"ref_5","unstructured":"Rao, P.X. (2016). Seismic Response and Dynamic Stability Analysis of Long-Span Cavit-Square String Dome Structure under Multi-dimensional and Multi-Point Excitation. [Marster\u2019s Thesis, Nanchang University]."},{"key":"ref_6","unstructured":"Yu, L. (2017). Study on Anti-Seismic Performance and Cable Breakage of Multiple Square Loop-String Dome Structure. [Marster\u2019s Thesis, Fuzhou University]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jcsr.2017.06.024","article-title":"Finite element Analysis of the Static Properties and Stability of a 800 m Kiewitt Type Mega-latticed Structure","volume":"137","author":"Zhang","year":"2017","journal-title":"J. Constr. Steel Res."},{"key":"ref_8","unstructured":"Zhao, R.X. (2020). Static Stability and Dynamic Response Analysis of String Dome Structure. [Marster\u2019s Thesis, Hebei University]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1080\/10168664.2019.1634983","article-title":"Influence of Friction on Buckling and Dynamic Behavior of Suspen-Dome Structures","volume":"30","author":"Zhao","year":"2020","journal-title":"Struct. Eng. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1177\/1369433217693629","article-title":"Model updating of suspended-dome using artificial neural networks","volume":"20","author":"Guo","year":"2017","journal-title":"Adv. Struct. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"209","DOI":"10.4028\/www.scientific.net\/AMR.430-432.209","article-title":"Dynamic Stability of Long-span Suspen-Domessubjected to Seismic Excitations","volume":"378","author":"Liu","year":"2012","journal-title":"Adv. Mater. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/0266351117736649","article-title":"Optimal Design of Nonlinear Large-scale Suspen Dome Using Cascade Optimization","volume":"33","author":"Kaveh","year":"2018","journal-title":"Int. J. Space Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1108\/EC-11-2014-0235","article-title":"Particle Swarm Optimization Algorithm for Suspendome Structure under Multiple Loading Cases","volume":"33","author":"Liu","year":"2016","journal-title":"Eng. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shen, X.H., Zhang, Q., and Lee, D.S.H. (2021). Static Behavior of a Retractable Suspen-Dome Structure. Symmetry, 13.","DOI":"10.3390\/sym13071105"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2174\/1874149501711010303","article-title":"Mechanical Properties Research on Suspended-dome Structure with Discontinuous Support under Different Parameters","volume":"11","author":"Yu","year":"2017","journal-title":"Open Civ. Eng. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1007\/s12205-017-0879-0","article-title":"Investigation on Simulation Methods of Initial Geometric Imperfection Distribution in Elasto-plastic Stability Analysis of Single-layer Reticulated Shells","volume":"22","author":"He","year":"2018","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s40996-020-00345-5","article-title":"Cable Tension Estimation for Suspen-Dome Structures Based on Numerical Method","volume":"44","author":"Yang","year":"2020","journal-title":"Iran J. Sci. Technol. Trans. Civ. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Itu, C., Bratu, P., Borza, P.N., Vlase, S., and Lixandroiu, D. (2020). Design and analysis of inertial platform insulation of the eli-np project of laser and gamma beam systems. Symmetry, 12.","DOI":"10.3390\/sym12121972"},{"key":"ref_19","first-page":"595","article-title":"Static and dynamic behavior of steel-reinforced epoxy granite CNC lathe bed using finite element analysis","volume":"234","author":"Chinnuraj","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part L"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1504\/IJMRI.2018.089058","article-title":"Finite element thrust line analysis of cracked axisymmetric masonry domes reinforced with tension rings","volume":"3","author":"Varma","year":"2018","journal-title":"Int. J. Mason. Res. Innov."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"012050","DOI":"10.1088\/1757-899X\/242\/1\/012050","article-title":"The research of Suspen-dome Structure","volume":"242","author":"Gong","year":"2017","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_22","first-page":"30","article-title":"Dynamic Performance Analysis of String Dome Structure under Soil-structure Interaction","volume":"45","author":"Li","year":"2015","journal-title":"Ind. Constr."},{"key":"ref_23","first-page":"191","article-title":"Analysis of Nonlinear Buckling of a Long-Span Elliptic Paraboloid Suspended Dome Structure","volume":"639","author":"Jiang","year":"2013","journal-title":"Adv. Mater. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1007\/s10518-019-00774-2","article-title":"A practical approach for estimating the floor deformability in existing RC buildings: Evaluation of the effects in the structural response and seismic fragility","volume":"18","author":"Ruggieri","year":"2020","journal-title":"Bull. Earthq. Eng."},{"key":"ref_25","first-page":"1","article-title":"A New Approach to Predict the Fundamental Period of Vibration for Newly-designed Reinforced Concrete Buildings","volume":"4","author":"Ruggieri","year":"2021","journal-title":"J. Earthq. Eng."},{"key":"ref_26","first-page":"797","article-title":"Monitoring and Numerical Simulation Analysis of Multiple Square Loop-String Roof Cable Tension Construction Process","volume":"40","author":"Zhang","year":"2016","journal-title":"J. Wuhan Univ. Technol."},{"key":"ref_27","unstructured":"GB 50011-2010 (2016). Code for Seismic Design of Buildings, China Architectural Engineering Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2062\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:24:23Z","timestamp":1760167463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,1]]},"references-count":27,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["sym13112062"],"URL":"https:\/\/doi.org\/10.3390\/sym13112062","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,11,1]]}}}