{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T05:26:48Z","timestamp":1786685208720,"version":"build-2736575974"},"reference-count":69,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"crossref","award":["2022B1515130006"],"award-info":[{"award-number":["2022B1515130006"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Shenzhen Pengrui Young Faculty Program of Shenzhen Pengrui Foundation","award":["SZPR2023003"],"award-info":[{"award-number":["SZPR2023003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Vortex-induced vibration (VIV) is one of the main causes of fatigue failure in subsea pipelines and has recently attracted significant attention from researchers. Previous studies have mainly focused on idealized straight pipes, with limited consideration of gravity-induced slight curvature in free-spanning fluid-conveying pipes. In reality, the deformation configuration of a free-spanning fluid-conveying pipe is not fixed but varies with parameters such as internal flow velocity and tension, which in turn affect its dynamic behavior. A theoretical model, taking into account the axial stretching effect and the gravity-induced initial slight curvature, is developed to predict the VIV responses of free-spanning fluid-conveying pipes. The governing equations are derived based on Hamilton\u2019s principle. The interaction between the external flow and the pipe structure is simulated using the van der Pol equation. By combining the Galerkin method and the Runge\u2013Kutta method, the vibration responses of the pipe are obtained. The accuracy of the proposed model is validated by comparing the predicted VIV response curves and bifurcation diagrams with those reported in previous studies. The initial static deformation of the structure under different tensions and internal velocities is obtained through numerical calculations. It is found that the gravity-induced slight curvature leads to a reduction in the VIV response mode. The static deformation of the pipe decreases with increasing axial tension, while it increases with increasing internal flow velocity. Under the same external flow velocity, the gravity-induced initial deformation reduces the dominant vibration frequency and causes the vibration response to transition from quasi-periodic to periodic motion.<\/jats:p>","DOI":"10.3390\/ma19163426","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T16:17:52Z","timestamp":1786551472000},"page":"3426","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nonlinear Vortex-Induced Vibrations of Fluid-Conveying Pipes with Gravity-Induced Slight Initial Curvature"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9930-1810","authenticated-orcid":false,"given":"Bin","family":"Zhang","sequence":"first","affiliation":[{"name":"Offshore Oil Engineering Co., Ltd., Tianjin 300461, China"},{"name":"Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui-Feng","family":"Wang","sequence":"additional","affiliation":[{"name":"Offshore Oil Engineering Co., Ltd., Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9653-0097","authenticated-orcid":false,"given":"Zhen-Zhong","family":"Hu","sequence":"additional","affiliation":[{"name":"Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Offshore Oil Engineering Co., Ltd., Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zi-Qiang","family":"Ni","sequence":"additional","affiliation":[{"name":"Offshore Oil Engineering Co., Ltd., Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sun-Wei","family":"Li","sequence":"additional","affiliation":[{"name":"Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6253","DOI":"10.1007\/s11071-024-10486-1","article-title":"Recent progress on dynamics and control of pipes conveying fluid","volume":"113","author":"Tang","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2650299","DOI":"10.1142\/S0219455426502998","article-title":"Dynamic Behavior of a Fluid-Conveying Pipe with an Internal Nonlinear Support","volume":"26","author":"Yang","year":"2025","journal-title":"Int. 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