{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T10:10:12Z","timestamp":1775815812186,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62073114"],"award-info":[{"award-number":["62073114"]}]},{"name":"National Natural Science Foundation of China","award":["11971032"],"award-info":[{"award-number":["11971032"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>Viscoelastic (VE) dampers show good performance in dissipating energy, being widely used for reducing vibration in engineering structures caused by earthquakes and winds. Experimental studies have shown that ambient temperature has great influence on the mechanical behavior of VE dampers. Therefore, it is important to accurately model VE dampers considering the effect of temperature. In this paper, a new fractional-order Zener (AEF-Zener) model of VE dampers is proposed. Firstly, the important influence of fractional orders on the energy dissipation ability of materials is analyzed. Secondly, an equivalent AEF-Zener model is developed that incorporates the ambient temperature and fractional-order equivalence principle. Finally, the chaotic fractional-order particle swarm optimization (CFOPSO) algorithm is used to determine the model\u2019s parameters. The accuracy of the AEF-Zener model is verified by comparing model simulations with experimental results. This study is helpful for designing and analyzing vibration reduction techniques for civil structures with VE dampers under the influence of temperature.<\/jats:p>","DOI":"10.3390\/fractalfract7100714","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T07:50:26Z","timestamp":1695887426000},"page":"714","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Fractional-Order Zener Model with Temperature-Order Equivalence for Viscoelastic Dampers"],"prefix":"10.3390","volume":"7","author":[{"given":"Kang","family":"Xu","sequence":"first","affiliation":[{"name":"School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8110-5378","authenticated-orcid":false,"given":"Liping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5680-5199","authenticated-orcid":false,"given":"Mingwu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Ranchao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Anhui University, Hefei 230601, China"}]},{"given":"Min","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2163","DOI":"10.1177\/1369433220906225","article-title":"Generalized algorithms for the identification of seismic ground excitations to building structures based on generalized Kalman filtering under unknown input","volume":"23","author":"Huang","year":"2020","journal-title":"Adv. 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