{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T03:42:21Z","timestamp":1773373341119,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T00:00:00Z","timestamp":1753488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Science and Technology Major Program","award":["GuikeAA23062040-4"],"award-info":[{"award-number":["GuikeAA23062040-4"]}]},{"name":"Guangxi Science and Technology Major Program","award":["XJ2022001101"],"award-info":[{"award-number":["XJ2022001101"]}]},{"name":"Hubei University of Technology Doctoral Research Startup Fund","award":["GuikeAA23062040-4"],"award-info":[{"award-number":["GuikeAA23062040-4"]}]},{"name":"Hubei University of Technology Doctoral Research Startup Fund","award":["XJ2022001101"],"award-info":[{"award-number":["XJ2022001101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The subject of ship structural dynamics has faced new technological obstacles due to scientific and technological advancements, and one of the main concerns in related sectors is how to effectively reduce the vibration levels of different ships. This article focuses on the application scenarios of ship floating raft isolation systems, establishing a wave propagation model for acoustic black hole (ABH) structures based on the idea of the ABH effect. Then, a transfer matrix model for serially connected ABH structures is derived, which serves as a basis for subsequent structural designs. Second, the finite element method is used to study the energy distribution and vibration characteristics of a symmetrically distributed periodic non-uniform multi-level ABH structure. Meanwhile, it examines its bandgap distribution under a one-dimensional periodic arrangement and then investigates the vibration properties of non-uniform multi-level ABH thin-plate constructions with different periods from the perspective of engineering applications. Moreover, parameter optimization studies of non-uniform multi-level ABH structures with finite periods are carried out with an emphasis on engineering applications. The first step is to use the design space to determine the range of values for the parameters that need to be optimized. The hyper Latin cubic sampling method is then employed to select samples, and the EI criterion and PSO optimization algorithm are applied to add new samples to improve the Kriging surrogate model\u2019s accuracy. When the optimal structural parameters have been determined, they are applied to the raft rib plate to verify the isolation effect of the non-uniform multi-level ABH structure by analyzing the vibration level difference at specific raft positions before and after embedding it.<\/jats:p>","DOI":"10.3390\/sym17081196","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T07:57:24Z","timestamp":1753689444000},"page":"1196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Research on Vibration Reduction Characteristics and Optimization of an Embedded Symmetric Distribution Multi-Level Acoustic Black Hole Floating Raft Isolation System"],"prefix":"10.3390","volume":"17","author":[{"given":"Xipeng","family":"Luo","sequence":"first","affiliation":[{"name":"Hubei Key Laboratory of Modern Manufacturing Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Wang","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Modern Manufacturing Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiyuan","family":"Fan","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Modern Manufacturing Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0208-2316","authenticated-orcid":false,"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Modern Manufacturing Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Shi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaqi","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7117-6255","authenticated-orcid":false,"given":"Yizhe","family":"Huang","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Modern Manufacturing Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China"},{"name":"Dongfeng Liuzhou Motor Co., Ltd., Liuzhou 545005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,26]]},"reference":[{"key":"ref_1","first-page":"110","article-title":"Development review on mechanical-noise control for submarine","volume":"7","author":"Yu","year":"2003","journal-title":"J. Ship Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1539\/joh.K10004","article-title":"Occupational Risks and Challenges of Seafaring","volume":"52","author":"Oldenburg","year":"2010","journal-title":"J. Occup. Health"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Huang, Y., Yan, B., Zhang, H., Wang, C., Wang, J., Zhang, Z., Huang, Q., and Zhan, X. (2024). Transmission Loss Characteristics of Dual Cavity Impedance Composite Mufflers for Non-Planar Wave Cavity Resonance. Appl. Sci., 14.","DOI":"10.3390\/app14166879"},{"key":"ref_4","first-page":"128","article-title":"Naval vessel machinery mounting technology and its recent advances","volume":"38","author":"Lin","year":"2013","journal-title":"J. Acta Acust."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"112863","DOI":"10.1016\/j.oceaneng.2022.112863","article-title":"Underwater radiated noise from marine vessels: A review of noise reduction methods and technology","volume":"266","author":"Smith","year":"2022","journal-title":"J. Ocean Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1061\/(ASCE)0733-9445(2003)129:7(845)","article-title":"State of the art of structural control","volume":"129","author":"Spencer","year":"2003","journal-title":"J. Struct. Eng."},{"key":"ref_7","unstructured":"Sakai, F. (1989, January 25\u201327). Tuned liquid column damper-new type device for suppression of building vibration. Proceedings of the International Conference on High-Rise Buildings, Nanjing, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Rijken, O., Spillane, M., and Leverette, S.J. (2010, January 6\u201311). Vibration absorber technology and conceptual design of vibration absorber for TLP in ultradeep water. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, Shanghai, China.","DOI":"10.1115\/OMAE2010-21013"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bian, X.S., Leverette, S.J., and Rijken, O.R. (2010, January 6\u201311). A TLP solution for 8000 Ft water depth. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, Shanghai, China.","DOI":"10.1115\/OMAE2010-20409"},{"key":"ref_10","unstructured":"Spillane, M.W., Rijken, O.R., and Leverette, S. (2007, January 1\u20136). Vibration Absorbers For Deepwater TLP\u2019s. Proceedings of the International Ocean and Polar Engineering Conference, Lisbon, Portugal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112886","DOI":"10.1016\/j.oceaneng.2022.112886","article-title":"Research on acoustic reconstruction methods of the hull vibration based on the limited vibration monitor data","volume":"266","author":"Ye","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.compositesb.2007.03.004","article-title":"Advanced shock-resistant and vibration damping of nanoparticle-reinforced composite material","volume":"39","author":"Kireitseu","year":"2008","journal-title":"Compos. Part B Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/0022-460X(66)90123-4","article-title":"High-frequency vibration isolation","volume":"4","author":"Ungar","year":"1966","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1121\/1.1909014","article-title":"Isolation from Vibration with a Mounting Utilizing Low-and High-Damping Rubberlike Materials","volume":"34","author":"Snowdon","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1076935","DOI":"10.1155\/2024\/1076935","article-title":"Review of lightweight vibration isolation technologies for marine power devices","volume":"2024","author":"Qiu","year":"2024","journal-title":"Shock Vib."},{"key":"ref_16","first-page":"581","article-title":"The dynamic instability of FG orthotropic conical shells within the SDT","volume":"25","author":"Sofiyev","year":"2017","journal-title":"Steel Compos. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"481","DOI":"10.12989\/sem.2007.25.4.481","article-title":"Dynamic combination resonance characteristics of doubly curved panels subjected to non-uniform tensile edge loading with damping","volume":"25","author":"Udar","year":"2007","journal-title":"Struct. Eng. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1142\/S1758825111001263","article-title":"Parametric instability of laminated composite cylindrical panels subjected to periodic non-uniform in-plane loads","volume":"3","author":"Panda","year":"2011","journal-title":"Int. J. Appl. Mech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1080\/15376494.2019.1572841","article-title":"Dynamic instability characteristic of damped laminated composite conical shell panel under periodic axial compression","volume":"28","author":"Kumar","year":"2021","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"115316","DOI":"10.1016\/j.jsv.2020.115316","article-title":"The acoustic black hole: A review of theory and applications","volume":"476","author":"Pelat","year":"2020","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1177\/1077546320980570","article-title":"Numerical simulation of characteristics of wave propagation and reflection coefficient in a helix-acoustic black hole","volume":"28","author":"Kim","year":"2022","journal-title":"J. Vib. Control"},{"key":"ref_22","first-page":"318","article-title":"Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval","volume":"34","author":"Mironov","year":"1988","journal-title":"Sov. Phys. Acoust."},{"key":"ref_23","first-page":"176","article-title":"Conditions for validity of the geometrical-acoustics approximation in application to waves in an acute-angle solid wedge","volume":"35","author":"Krylov","year":"1989","journal-title":"Sov. Phys. Acoust."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"061003","DOI":"10.1115\/1.4003591","article-title":"Experimental study of vibration damping in a modified elastic wedge of power-law profile","volume":"133","author":"Bayod","year":"2011","journal-title":"J. Vib. Acoust."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"114838","DOI":"10.1016\/j.jsv.2019.07.004","article-title":"Experimental validation of vibration damping using an Archimedean spiral acoustic black hole","volume":"459","author":"Park","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1515\/rams-2022-0235","article-title":"Application research of acoustic black hole in floating raft vibration isolation system","volume":"61","author":"Gao","year":"2022","journal-title":"Rev. Adv. Mater. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"194901","DOI":"10.1063\/1.4983459","article-title":"Broadband locally resonant band gaps in periodic beam structures with embedded acoustic black holes","volume":"121","author":"Tang","year":"2017","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"104304","DOI":"10.1103\/PhysRevB.91.104304","article-title":"Phononic thin plates with embedded acoustic black holes","volume":"91","author":"Zhu","year":"2015","journal-title":"Phys. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1177\/1045389X211011679","article-title":"Dynamic analysis and optimization of a cantilevered beam with both the acoustic black hole and the nonlinear energy sink","volume":"33","author":"He","year":"2022","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"EL227","DOI":"10.1121\/1.4961735","article-title":"Multi-objective optimization of acoustic black hole vibration absorbers","volume":"140","author":"Shepherd","year":"2016","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"140831","DOI":"10.1109\/ACCESS.2020.3013616","article-title":"Cost-efficient bi-layer modeling of antenna input characteristics using gradient kriging surrogates","volume":"8","author":"Koziel","year":"2020","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Nikas, I.A., Georgopoulos, V.P., and Loukopoulos, V.C. (2025). Selective Multistart Optimization Based on Adaptive Latin Hypercube Sampling and Interval Enclosures. Mathematics, 13.","DOI":"10.3390\/math13111733"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"113468","DOI":"10.1016\/j.ijsolstr.2025.113468","article-title":"Exact solutions of the Euler\u2013Bernoulli equation for selected polynomially non-uniform beams used for acoustic black holes","volume":"320","author":"Krpensky","year":"2025","journal-title":"Int. J. Solids Struct."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1304","DOI":"10.1007\/BF02438287","article-title":"Analysis on transverse impact response of an unrestrained Timoshenko beam","volume":"25","author":"Chen","year":"2004","journal-title":"Appl. Math. Mech."},{"key":"ref_35","first-page":"75","article-title":"Vibration isolation performance of distributed acoustic black hole floating raft system","volume":"41","author":"Zhao","year":"2022","journal-title":"J. Vib. Shock"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6721","DOI":"10.1007\/s00521-024-09424-4","article-title":"SRIME a strengthened RIME with Latin hypercube sampling and embedded distance-based selection for engineering optimization problems","volume":"36","author":"Zhong","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_37","first-page":"6647573","article-title":"Study on vibration damping mechanism of shoe sole with alternating lattice structure using vibration level difference","volume":"2021","author":"Wang","year":"2021","journal-title":"Math. Probl. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1196\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:16:34Z","timestamp":1760033794000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,26]]},"references-count":37,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081196"],"URL":"https:\/\/doi.org\/10.3390\/sym17081196","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,26]]}}}