{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:59:06Z","timestamp":1760785146400,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000},"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":["12272011","2022YFB3806000"],"award-info":[{"award-number":["12272011","2022YFB3806000"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["12272011","2022YFB3806000"],"award-info":[{"award-number":["12272011","2022YFB3806000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In this paper, an H\u221e optimization problem of a novel three-element-type DVA model including an inerter device and a grounded negative stiffness spring is studied by combining a traditional theory and an intelligent algorithm. Firstly, to ensure the system\u2019s stability, the specific analytical expressions of the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio with regard to the mass ratio and inerter\u2013mass ratio are determined through fixed-point theory, which provides an iterative range for algorithm optimization. Secondly, the particle swarm optimization (PSO) algorithm is used to further optimize the four parameters of DVA simultaneously. The effects of the traditional fixed-point theory and the intelligent PSO algorithm are comprehensively compared and analyzed. The results verify that the effect of the coupling of the traditional theory and the intelligent algorithm is better than that of fixed-point theory alone and can make the two resonance peaks on the amplitude\u2013frequency response curves almost equal, which is difficult to achieve using fixed-point theory alone. Finally, we compare the proposed model with other DVA models under harmonic and random excitation. By comparing the amplitude\u2013frequency curves, stroke lengths, mean square responses, time history diagrams, variances and decrease ratios, it is clear that the established DVA has a good vibration absorption effect. The research results provide theoretical and algorithm support for designing more effective DVA models of the same type in engineering applications.<\/jats:p>","DOI":"10.3390\/e25071048","type":"journal-article","created":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T01:43:22Z","timestamp":1689212602000},"page":"1048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["H\u221e Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm"],"prefix":"10.3390","volume":"25","author":[{"given":"Ting","family":"Gao","sequence":"first","affiliation":[{"name":"Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7278-2764","authenticated-orcid":false,"given":"Jing","family":"Li","sequence":"additional","affiliation":[{"name":"Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Shaotao","family":"Zhu","sequence":"additional","affiliation":[{"name":"Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China"},{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0073-0823","authenticated-orcid":false,"given":"Xiaodong","family":"Yang","sequence":"additional","affiliation":[{"name":"Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Hongzhen","family":"Zhao","sequence":"additional","affiliation":[{"name":"Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,12]]},"reference":[{"key":"ref_1","unstructured":"Frahm, H. 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