{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T17:29:16Z","timestamp":1767374956059,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,7]],"date-time":"2022-10-07T00:00:00Z","timestamp":1665100800000},"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":["12171287","ZR2021MA063"],"award-info":[{"award-number":["12171287","ZR2021MA063"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["12171287","ZR2021MA063"],"award-info":[{"award-number":["12171287","ZR2021MA063"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper discusses the Crank\u2013Nicolson compact difference method for the time-fractional damped plate vibration problems. For the time-fractional damped plate vibration equations, we introduce the second-order space derivative and the first-order time derivative to convert fourth-order differential equations into second-order differential equation systems. We discretize the space derivative via compact difference and approximate the time-integer-order derivative and fraction-order derivative via central difference and L1 interpolation, respectively, to obtain the compact difference formats with fourth-order space precision and 3\u2212\u03b1(1&lt;\u03b1&lt;2)-order time precision. We apply the energy method to analyze the stability and convergence of this difference format. We provide numerical cases, which not only validate the convergence order and feasibility of the given difference format, but also simulate the influence of the damping coefficient on the amplitude of plate vibration.<\/jats:p>","DOI":"10.3390\/axioms11100535","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T00:07:43Z","timestamp":1665187663000},"page":"535","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Crank\u2013Nicolson Compact Difference Method for Time-Fractional Damped Plate Vibration Equations"],"prefix":"10.3390","volume":"11","author":[{"given":"Cailian","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Congcong","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ailing","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,7]]},"reference":[{"key":"ref_1","first-page":"109","article-title":"Recent advances in research and applications of viscoelastically damped structure","volume":"26","author":"Wang","year":"2006","journal-title":"J. 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