首页 期刊 论文 学科刊群 资讯 加盟 关于
EN
image
Article(id=1243306316983283929, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243306309064442584, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.05.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1732204800000, receivedDateStr=2024-11-22, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774356925482, onlineDateStr=2026-03-24, pubDate=1747670400000, pubDateStr=2025-05-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774356925482, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774356925482, creator=13701087609, updateTime=1774356925482, updator=13701087609, issue=Issue{id=1243306309064442584, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='5', pageStart='681', pageEnd='848', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1774356923595, creator=13701087609, updateTime=1774357065180, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243306902965301262, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243306309064442584, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243306902965301263, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243306309064442584, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=790, endPage=806, ext={EN=ArticleExt(id=1243306317243330792, articleId=1243306316983283929, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Uncertainty analysis of large flared ship slamming response based on CFD-FEM two-way fluid-structure interaction, columnId=1242129251223274417, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanics, runingTitle=null, highlight=null, articleAbstract=

The accurate assessment and analysis of nonlinear wave loads on ships and the high-frequency vibrational response of ship structures are requisites for determining the safety of ship structures. However, the reliability of numerical simulation and the analysis of their uncertainties have received relatively little attention. This paper presents a segmented keel beam hydroelastic model CFD-FEM simulation and experimental research to simulate and analyze the high-frequency response of a ship model in waves. Uncertainty analysis was performed on the simulation results to evaluate the reliability of the simulation model. The calculation results of numerical uncertainties can provide criteria for judging the convergence of results under different influencing factors and the level of uncertainty. The uncertainty levels of the impact pressure on the ship’s bow, the motion of the ship model, and the high and low-frequency wave bending moments of the ship hull are also clarified. A comparison between numerical simulation and experimental testing reveals that CFD-FEM two-way fluid-structure coupling simulation can accurately capture the high-frequency response of ship structures. The high-frequency bending moment component of the ship under cruising conditions can account for more than 49.95% of the low-frequency wave bending moment. The dynamic response of ships induced by impact loads cannot be ignored, and their influence must be considered in the structural design and safety assessment of such ships. This paper can provide a reference for the uncertainty analysis of high-frequency structural dynamic responses such as ship impact vibration.

, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Guang-yu TIAN, Yi-wen WANG, Han-tao ZHANG, Wei-guo WU), CN=ArticleExt(id=1243306335417250467, articleId=1243306316983283929, tenantId=1146029695717560320, journalId=1240685776644648972, language=CN, title=基于CFD-FEM双向流固耦合的大外飘型船舶砰击颤振响应不确定度研究, columnId=1241023038926410098, journalTitle=船舶力学, columnName=结构力学, runingTitle=null, highlight=null, articleAbstract=

船舶非线性波浪载荷及结构高频颤振响应的准确评估与分析，是明确船舶结构安全性的前提，然而其数值仿真计算的可靠性及其不确定度分析则较少得到关注。本文开展分段龙骨梁水弹性模型CFD-FEM双向流固耦合仿真以及试验研究，对船模在波浪下的高频响应进行仿真分析，并对仿真结果开展不确定度分析，评估仿真模型的可靠性。数值不确定度的计算结果，能够提供不同影响因素下结果是否收敛的判别依据和不确定度水平，并明确船艏的砰击压力、船模的运动和船体高低频波浪弯矩的不确定度水平。对比数值仿真与试验测试可知，CFD-FEM双向流固耦合仿真能够精确地捕捉到船舶结构高频响应，船舶在巡航工况下高频弯矩成分能够占到低频波浪弯矩的49.95%以上，砰击载荷诱发的舰船高频颤振动态响应不容忽视，此类舰船的结构设计及安全评估中须考虑其影响。本文可为船舶砰击颤振此类高频结构动态响应的不确定度分析提供参考。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
通讯作者；E-mail：
, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=XK587P7ly5zE6poRLCHYfQ==, magXml=5fLedt0df0l331AC7QOUSg==, pdfUrl=null, pdf=FbsXoK/kwX/HGqGyK9Idow==, pdfFileSize=14151654, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=H71ezkFlg6sOC5eYTBKYMA==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=KEVDkUX0uXz0m1374Q2v7A==, mapNumber=null, authorCompany=null, fund=null, authors=

田光钰（1999-），男，硕士研究生

王一雯（1990-），女，博士，副研究员，通讯作者；E-mail：。

, authorsList=田光钰, 王一雯, 张涵韬, 吴卫国)}, authors=[Author(id=1243306335887012542, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1243306336017035973, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306335887012542, language=EN, stringName=Guang-yu TIAN, firstName=Guang-yu, middleName=null, lastName=TIAN, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, b, address=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China
b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1243306336121893577, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306335887012542, language=CN, stringName=田光钰, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, b, address=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063
b.武汉理工大学　船海与能源动力工程学院，武汉　430063, bio={"content":"

田光钰（1999-），男，硕士研究生

"}, bioImg=null, bioContent=

田光钰（1999-），男，硕士研究生

, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1243306335647937195, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=a., ext=[AuthorCompanyExt(id=1243306335656325804, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335664714413, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063)]), AuthorCompany(id=1243306335782154933, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=b., ext=[AuthorCompanyExt(id=1243306335790543541, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335798932151, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.武汉理工大学　船海与能源动力工程学院，武汉　430063)])]), Author(id=1243306337627648719, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, orderNo=1, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=yiwenwang90@whut.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1243306337707340503, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306337627648719, language=EN, stringName=Yi-wen WANG, firstName=Yi-wen, middleName=null, lastName=WANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, address=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1243306337782837978, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306337627648719, language=CN, stringName=王一雯, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, address=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063, bio={"content":"

王一雯（1990-），女，博士，副研究员，通讯作者；E-mail：。

"}, bioImg=null, bioContent=

王一雯（1990-），女，博士，副研究员，通讯作者；E-mail：。

, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1243306335647937195, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=a., ext=[AuthorCompanyExt(id=1243306335656325804, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335664714413, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063)])]), Author(id=1243306337866724064, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, orderNo=2, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1243306337975775975, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306337866724064, language=EN, stringName=Han-tao ZHANG, firstName=Han-tao, middleName=null, lastName=ZHANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, b, address=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China
b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1243306338063856363, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306337866724064, language=CN, stringName=张涵韬, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, b, address=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063
b.武汉理工大学　船海与能源动力工程学院，武汉　430063, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1243306335647937195, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=a., ext=[AuthorCompanyExt(id=1243306335656325804, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335664714413, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063)]), AuthorCompany(id=1243306335782154933, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=b., ext=[AuthorCompanyExt(id=1243306335790543541, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335798932151, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.武汉理工大学　船海与能源动力工程学院，武汉　430063)])]), Author(id=1243306338160325362, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, orderNo=3, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1243306338248405748, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306338160325362, language=EN, stringName=Wei-guo WU, firstName=Wei-guo, middleName=null, lastName=WU, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, address=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1243306338332291834, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, authorId=1243306338160325362, language=CN, stringName=吴卫国, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=a, address=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1243306335647937195, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=a., ext=[AuthorCompanyExt(id=1243306335656325804, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335664714413, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063)])])], keywords=[Keyword(id=1243306338437149439, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, orderNo=1, keyword=hydroelastic model experiment), Keyword(id=1243306338554589955, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, orderNo=2, keyword=slamming-induced flutter), Keyword(id=1243306338667836169, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, orderNo=3, keyword=CFD-FEM), Keyword(id=1243306338739139339, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, orderNo=4, keyword=uncertainty analysis), Keyword(id=1243306338823025425, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, orderNo=1, keyword=水弹性模型试验), Keyword(id=1243306338923688724, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, orderNo=2, keyword=砰击颤振), Keyword(id=1243306339020157719, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, orderNo=3, keyword=CFD-FEM双向流固耦合), Keyword(id=1243306339104043799, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, orderNo=4, keyword=不确定度分析)], refs=[Reference(id=1243306347207439322, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2020, volume=96, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=Lakshmynarayanana P A, Temarel P, journalName=Applied Ocean Research, refType=null, unstructuredReference=Lakshmynarayanana P A, Temarel P. Application of a two-way partitioned method for predicting the wave-induced loads of a flexible containership[J]. Applied Ocean Research, 2020, 96:102052., articleTitle=Application of a two-way partitioned method for predicting the wave-induced loads of a flexible containership, refAbstract=null), Reference(id=1243306347299714014, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2019, volume=65, issue=1, pageStart=308, pageEnd=325, url=null, language=null, rfNumber=[2], rfOrder=1, authorNames=Lakshmynarayanana P A, Temarel P, journalName=Marine Structures, refType=null, unstructuredReference=Lakshmynarayanana P A, Temarel P. Application of CFD and FEA coupling to predict dynamic behaviour of a flexible barge in regular head waves[J]. Marine Structures, 2019, 65(1): 308-325., articleTitle=Application of CFD and FEA coupling to predict dynamic behaviour of a flexible barge in regular head waves, refAbstract=null), Reference(id=1243306347366822879, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2020, volume=203, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[3], rfOrder=2, authorNames=Lakshmynarayanana P A, Hirdaris S, journalName=Ocean Engineering, refType=null, unstructuredReference=Lakshmynarayanana P A, Hirdaris S. Comparison of nonlinear one- and two-way FFSI methods for the prediction of the symmetric response of a containership in waves[J]. Ocean Engineering, 2020, 203:107179., articleTitle=Comparison of nonlinear one- and two-way FFSI methods for the prediction of the symmetric response of a containership in waves, refAbstract=null), Reference(id=1243306347467486178, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2021, volume=117, issue=102919, pageStart=117, pageEnd=139, url=null, language=null, rfNumber=[4], rfOrder=3, authorNames=Jiao J L, Huang S X, Wang S, journalName=Applied Ocean Research, refType=null, unstructuredReference=Jiao J L, Huang S X, Wang S, et al. A CFD-FEA two-way coupling method for predicting ship wave loads and hydroelastic responses[J]. Applied Ocean Research, 2021, 117(102919): 117-139., articleTitle=A CFD-FEA two-way coupling method for predicting ship wave loads and hydroelastic responses, refAbstract=null), Reference(id=1243306347576538084, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=1998, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[5], rfOrder=4, authorNames=Roache P J, journalName=Verification and validation in computational science and engineering, refType=null, unstructuredReference=Roache P J. Verification and validation in computational science and engineering[M]. Hermvsa, 1998., articleTitle=null, refAbstract=null), Reference(id=1243306347664618472, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2007, volume=37, issue=2, pageStart=279, pageEnd=288, url=null, language=null, rfNumber=[6], rfOrder=5, authorNames=邓小刚, 宗文刚, 张来平, journalName=力学进展, refType=null, unstructuredReference=邓小刚，宗文刚，张来平，等. 计算流体力学中的验证与确认[J]. 力学进展，2007, 37(2):279-288., articleTitle=计算流体力学中的验证与确认, refAbstract=null), Reference(id=1243306347735921641, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2007, volume=37, issue=2, pageStart=279, pageEnd=288, url=null, language=null, rfNumber=[6], rfOrder=6, authorNames=Deng X G, Zong W G, Zhang L P, journalName=Advance in Mechanics, refType=null, unstructuredReference=Deng X G, Zong W G, Zhang L P, et al. Verification and validation in computational fluid dynamics[J]. Advance in Mechanics, 2007, 37(2): 279-288. (in Chinese), articleTitle=Verification and validation in computational fluid dynamics, refAbstract=null), Reference(id=1243306347815613420, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2004, volume=8, issue=5, pageStart=52, pageEnd=61, url=null, language=null, rfNumber=[7], rfOrder=7, authorNames=马向能, 孙张群, 冯骏, journalName=船舶力学, refType=null, unstructuredReference=马向能，孙张群，冯骏. 测量不确定度分析在操纵性试验中的应用[J]. 船舶力学，2004, 8(5):52-61., articleTitle=测量不确定度分析在操纵性试验中的应用, refAbstract=null), Reference(id=1243306347903693808, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2004, volume=8, issue=5, pageStart=52, pageEnd=61, url=null, language=null, rfNumber=[7], rfOrder=8, authorNames=Ma X N, Sun Z Q, Feng J, journalName=Journal of Ship Mechanics, refType=null, unstructuredReference=Ma X N, Sun Z Q, Feng J. Uncertainty analysis in captive model test[J]. Journal of Ship Mechanics, 2004, 8(5): 52-61. (in Chinese), articleTitle=Uncertainty analysis in captive model test, refAbstract=null), Reference(id=1243306347979191281, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2011, volume=55, issue=2, pageStart=100, pageEnd=123, url=null, language=null, rfNumber=[8], rfOrder=9, authorNames=Zhu S J, Wu M K, Moan T, journalName=Journal of Ship Research, refType=null, unstructuredReference=Zhu S J, Wu M K, Moan T. Experimental and numerical study of wave-induced load effects of open ships in oblique seas[J]. Journal of Ship Research, 2011, 55(2): 100-123., articleTitle=Experimental and numerical study of wave-induced load effects of open ships in oblique seas, refAbstract=null), Reference(id=1243306348058883059, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2014, volume=35, issue=null, pageStart=1, pageEnd=25, url=null, language=null, rfNumber=[9], rfOrder=10, authorNames=Zhu S J, Moan T, journalName=Marine Structures, refType=null, unstructuredReference=Zhu S J, Moan T. Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large container ship model in severe head and oblique seas[J]. Marine Structures, 2014, 35:1-25., articleTitle=Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large container ship model in severe head and oblique seas, refAbstract=null), Reference(id=1243306348205683701, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2022, volume=26, issue=2, pageStart=202, pageEnd=214, url=null, language=null, rfNumber=[10], rfOrder=11, authorNames=司海龙, 顾学康, 胡嘉骏, journalName=船舶力学, refType=null, unstructuredReference=司海龙，顾学康，胡嘉骏，等. 船模波浪载荷试验不确定度分析方法研究[J]. 船舶力学，2022, 26(2):202-214., articleTitle=船模波浪载荷试验不确定度分析方法研究, refAbstract=null), Reference(id=1243306348289569783, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2022, volume=26, issue=2, pageStart=202, pageEnd=214, url=null, language=null, rfNumber=[10], rfOrder=12, authorNames=Si H L, Gu X K, Hu J J, journalName=Journal of Ship Mechanics, refType=null, unstructuredReference=Si H L, Gu X K, Hu J J, et al. Uncertainty analysis of ship model wave-induced load experiment[J]. Journal of Ship Mechanics, 2022, 26(2): 202-214. (in Chinese), articleTitle=Uncertainty analysis of ship model wave-induced load experiment, refAbstract=null), Reference(id=1243306348352484344, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=1991, volume=18, issue=4, pageStart=329, pageEnd=362, url=null, language=null, rfNumber=[11], rfOrder=13, authorNames=Guedes Soares C, journalName=Ocean Engineering, refType=null, unstructuredReference=Guedes Soares C. Effect of transfer function uncertainty on short-term ship responses[J]. Ocean Engineering, 1991, 18(4): 329-362., articleTitle=Effect of transfer function uncertainty on short-term ship responses, refAbstract=null), Reference(id=1243306348423787514, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2007, volume=22, issue=3, pageStart=363, pageEnd=370, url=null, language=null, rfNumber=[12], rfOrder=14, authorNames=朱德祥, 张志荣, 吴乘胜, journalName=水动力学研究与进展A辑, refType=null, unstructuredReference=朱德祥，张志荣，吴乘胜，等. 船舶CFD不确定度分析及ITTC临时规程的初步应用[J]. 水动力学研究与进展A辑，2007, 22(3):363-370., articleTitle=船舶CFD不确定度分析及ITTC临时规程的初步应用, refAbstract=null), Reference(id=1243306348503479292, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2007, volume=22, issue=3, pageStart=363, pageEnd=370, url=null, language=null, rfNumber=[12], rfOrder=15, authorNames=Zhu D X, Zhang Z R, Wu C S, journalName=Journal of Hydrodynamics, refType=null, unstructuredReference=Zhu D X, Zhang Z R, Wu C S, et al. Uncertainty analysis in ship CFD and the primary application of ITTC procedures[J]. Journal of Hydrodynamics, 2007, 22(3): 363-370. (in Chinese), articleTitle=Uncertainty analysis in ship CFD and the primary application of ITTC procedures, refAbstract=null), Reference(id=1243306348578976766, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2014, volume=86, issue=null, pageStart=3, pageEnd=10, url=null, language=null, rfNumber=[13], rfOrder=16, authorNames=Drummen I, Holtmann M, journalName=Ocean Engineering, refType=null, unstructuredReference=Drummen I, Holtmann M. Benchmark study of slamming and whipping[J]. Ocean Engineering, 2014, 86:3-10., articleTitle=Benchmark study of slamming and whipping, refAbstract=null), Reference(id=1243306348641891328, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2022, volume=82, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[14], rfOrder=17, authorNames=Huang S X, Jiao J L, Guedes S C, journalName=Marine Structures, refType=null, unstructuredReference=Huang S X, Jiao J L, Guedes S C. Uncertainty analyses on the CFD-FEA co-simulations of ship wave loads and whipping responses[J]. Marine Structures, 2022, 82:103129., articleTitle=Uncertainty analyses on the CFD-FEA co-simulations of ship wave loads and whipping responses, refAbstract=null), Reference(id=1243306348704804865, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[15], rfOrder=18, authorNames=ITTC, journalName=null, refType=null, unstructuredReference=ITTC. 7.5-03-01-01, Uncertainty analysis in CFD verification and validation methodology and procedures[S]. 2021., articleTitle=null, refAbstract=null), Reference(id=1243306348771913731, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2004, volume=126, issue=4, pageStart=704, pageEnd=706, url=null, language=null, rfNumber=[16], rfOrder=19, authorNames=Wilson R, Shao J, Stern F, journalName=ASME J. Fluids Eng, refType=null, unstructuredReference=Wilson R, Shao J, Stern F. Discussion: Criticism of the “correction factor verification” method[J]. ASME J. Fluids Eng, 2004, 126(4): 704-706., articleTitle=Discussion: Criticism of the “correction factor verification” method, refAbstract=null), Reference(id=1243306348839022597, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2010, volume=132, issue=6, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[17], rfOrder=20, authorNames=Xing T, Stern F, journalName=Journal of Fluids Engineering, refType=null, unstructuredReference=Xing T, Stern F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Engineering, 2010, 132(6): 061403., articleTitle=Factors of safety for Richardson extrapolation, refAbstract=null), Reference(id=1243306348914520071, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, doi=null, pmid=null, pmcid=null, year=2020, volume=96, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[18], rfOrder=21, authorNames=Lakshmynarayanana P A, Temarel P, journalName=Applied Ocean Research, refType=null, unstructuredReference=Lakshmynarayanana P A, Temarel P. Application of a two-way partitioned method for predicting the wave-induced loads of a flexible container ship[J]. Applied Ocean Research, 2020, 96:102052., articleTitle=Application of a two-way partitioned method for predicting the wave-induced loads of a flexible container ship, refAbstract=null)], funds=[Fund(id=1243306347035472852, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, awardId=8091B03012406, language=CN, fundingSource=装备预先研究教育部联合基金青年人才项目(8091B03012406), fundOrder=null, country=null), Fund(id=1243306347110970328, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, awardId=2023010201020318, language=CN, fundingSource=武汉市知识创新专项曙光计划项目(2023010201020318), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1243306335647937195, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=a., ext=[AuthorCompanyExt(id=1243306335656325804, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335664714413, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335647937195, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063)]), AuthorCompany(id=1243306335782154933, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, xref=b., ext=[AuthorCompanyExt(id=1243306335790543541, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China), AuthorCompanyExt(id=1243306335798932151, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, companyId=1243306335782154933, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=b.武汉理工大学　船海与能源动力工程学院，武汉　430063)])], figs=[ArticleFig(id=1243306339326341918, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.1, caption=Shape and dimensions of backbone beam with variable sections, figureFileSmall=tg7bZqOc56lhA3K8kplb3w==, figureFileBig=H71ezkFlg6sOC5eYTBKYMA==, tableContent=null), ArticleFig(id=1243306339422810914, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图1, caption=龙骨梁变截面型式及尺寸示意图（单位：mm）, figureFileSmall=tg7bZqOc56lhA3K8kplb3w==, figureFileBig=H71ezkFlg6sOC5eYTBKYMA==, tableContent=null), ArticleFig(id=1243306339636720426, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.2, caption=Towing tank test of ship model, figureFileSmall=afgdkI59I+A7RP516WP6bw==, figureFileBig=Wn1v+Lt9HU3t4DNfiX/H4w==, tableContent=null), ArticleFig(id=1243306339724800814, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图2, caption=拖曳水池模型试验, figureFileSmall=afgdkI59I+A7RP516WP6bw==, figureFileBig=Wn1v+Lt9HU3t4DNfiX/H4w==, tableContent=null), ArticleFig(id=1243306339821269810, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.3, caption=CFD-FEM two-way fluid-structure interaction calculation principle, figureFileSmall=xYMAuHQwGKpOoKfJJ008Aw==, figureFileBig=AUi/tJ9+Ov+PSYbjdok3xw==, tableContent=null), ArticleFig(id=1243306339909350198, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图3, caption=CFD-FEM双向流固耦合仿真计算原理, figureFileSmall=xYMAuHQwGKpOoKfJJ008Aw==, figureFileBig=AUi/tJ9+Ov+PSYbjdok3xw==, tableContent=null), ArticleFig(id=1243306340022596409, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.4, caption=Hydrodynamic calculation domain and boundary conditions, figureFileSmall=4GTKifUCv1QAlwpI3+CfMQ==, figureFileBig=9D5RLS01PaRFjQSJ4fDbFw==, tableContent=null), ArticleFig(id=1243306340123259709, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图4, caption=水动力计算域和边界条件, figureFileSmall=4GTKifUCv1QAlwpI3+CfMQ==, figureFileBig=9D5RLS01PaRFjQSJ4fDbFw==, tableContent=null), ArticleFig(id=1243306340211340098, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.5, caption=Fluid domain grid in the center plane, figureFileSmall=qEDjohojU0AITSLtQmQbYQ==, figureFileBig=fxnVSGrQjcPrI0LZGw7Uww==, tableContent=null), ArticleFig(id=1243306340316197702, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图5, caption=水动力计算域网格示意图, figureFileSmall=qEDjohojU0AITSLtQmQbYQ==, figureFileBig=fxnVSGrQjcPrI0LZGw7Uww==, tableContent=null), ArticleFig(id=1243306340412666698, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.6, caption=Finite element model of ship hull, figureFileSmall=sPms3gvsDB33x3Jvp0pbiQ==, figureFileBig=qbGY87Xzq7RHxy5mdW1Xbg==, tableContent=null), ArticleFig(id=1243306340496552779, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图6, caption=船舶结构有限元模型, figureFileSmall=sPms3gvsDB33x3Jvp0pbiQ==, figureFileBig=qbGY87Xzq7RHxy5mdW1Xbg==, tableContent=null), ArticleFig(id=1243306340584633169, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.7, caption=Free surface waveform for fluid domains with different sizes, figureFileSmall=Kb8Ui52Q+JyFBcgx3Okl1g==, figureFileBig=vUS2Yd9s5gnPqPLPMM6Mqw==, tableContent=null), ArticleFig(id=1243306342069416786, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图7, caption=不同水域大小的自由面波形, figureFileSmall=Kb8Ui52Q+JyFBcgx3Okl1g==, figureFileBig=vUS2Yd9s5gnPqPLPMM6Mqw==, tableContent=null), ArticleFig(id=1243306342144914259, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.8, caption=Time histories of ship motions for different fluid-domain sizes, figureFileSmall=Uqh9ym00xy2+1D3tEiupzA==, figureFileBig=98Ku1CBQ+mNqmnUMvIT03g==, tableContent=null), ArticleFig(id=1243306342241383255, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图8, caption=不同水域尺寸下船舶运动的时间历程曲线, figureFileSmall=Uqh9ym00xy2+1D3tEiupzA==, figureFileBig=98Ku1CBQ+mNqmnUMvIT03g==, tableContent=null), ArticleFig(id=1243306342312686426, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.9, caption=Calculated results of ship-bottom pressure under different time steps (t=4.5 s), figureFileSmall=31iiNmWs2L6rbpT/cpm3eA==, figureFileBig=P5/bbW+nnoHmoQWJzC6rnA==, tableContent=null), ArticleFig(id=1243306342400766811, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图9, caption=不同时间步长下船底压力云图（t=4.5 s）, figureFileSmall=31iiNmWs2L6rbpT/cpm3eA==, figureFileBig=P5/bbW+nnoHmoQWJzC6rnA==, tableContent=null), ArticleFig(id=1243306342480458588, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.10, caption=VBM results in the time and frequency domain for different time steps, figureFileSmall=uQHM9QYgim53AH8q5Nis2Q==, figureFileBig=VEH8o0pKFWs9LY3zH3ndRw==, tableContent=null), ArticleFig(id=1243306342547567456, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图10, caption=不同时间步长下的垂向弯矩时域和频域对比图, figureFileSmall=uQHM9QYgim53AH8q5Nis2Q==, figureFileBig=VEH8o0pKFWs9LY3zH3ndRw==, tableContent=null), ArticleFig(id=1243306342627259233, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.11, caption=Grid density under different grid sizes, figureFileSmall=or/IFEGQHxZzXKfrCPPCsQ==, figureFileBig=ropNhqoSiLHuzyIC2y/Ing==, tableContent=null), ArticleFig(id=1243306342702756707, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图11, caption=不同密度的网格, figureFileSmall=or/IFEGQHxZzXKfrCPPCsQ==, figureFileBig=ropNhqoSiLHuzyIC2y/Ing==, tableContent=null), ArticleFig(id=1243306342769865573, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.12, caption=VBM results in the time and frequency domain for three different size of grids, figureFileSmall=XvJh5SYFGsjkdnj+hzQVkg==, figureFileBig=8PvDIA0wNX7wDAzTZ4P0AQ==, tableContent=null), ArticleFig(id=1243306342849557352, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图12, caption=不同网格大小方案下的船中垂向弯矩的时间历程曲线和频域曲线, figureFileSmall=XvJh5SYFGsjkdnj+hzQVkg==, figureFileBig=8PvDIA0wNX7wDAzTZ4P0AQ==, tableContent=null), ArticleFig(id=1243306342916666219, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.13, caption=VBM results in the time and frequency domain for different structural damping, figureFileSmall=Z8Yr80a76D689klAjGP0PQ==, figureFileBig=0r9w+WzF8niJqjcyAq0mXw==, tableContent=null), ArticleFig(id=1243306343008940911, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图13, caption=不同结构阻尼下的垂向弯矩时域和频域曲线, figureFileSmall=Z8Yr80a76D689klAjGP0PQ==, figureFileBig=0r9w+WzF8niJqjcyAq0mXw==, tableContent=null), ArticleFig(id=1243306343084438386, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.14, caption=Bow pressure measuring point P3, figureFileSmall=k2KVPJZO0H3cpH0X5KPjfQ==, figureFileBig=mRo5yDAeIsfYENIW1R5cWA==, tableContent=null), ArticleFig(id=1243306343151547253, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图14, caption=船艏砰击压力测点图, figureFileSmall=k2KVPJZO0H3cpH0X5KPjfQ==, figureFileBig=mRo5yDAeIsfYENIW1R5cWA==, tableContent=null), ArticleFig(id=1243306343218656121, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.15, caption=Time histories of bow slamming pressure under different schemes, figureFileSmall=FA3xIQyuCGF2/3H3x4NKJg==, figureFileBig=x2xBoliS4KzzZpxoKWCXBQ==, tableContent=null), ArticleFig(id=1243306343306736506, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图15, caption=不同影响因素下船艏砰击压力时域曲线, figureFileSmall=FA3xIQyuCGF2/3H3x4NKJg==, figureFileBig=x2xBoliS4KzzZpxoKWCXBQ==, tableContent=null), ArticleFig(id=1243306343394816893, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.16, caption=Comparison of wave heights between calculation and experiment, figureFileSmall=qQ+ildo6ENqWDTJ5q+InsQ==, figureFileBig=//0m9rmwsDEM62VdLlbg2A==, tableContent=null), ArticleFig(id=1243306343474508673, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图16, caption=遭遇波浪高度的时域变化对比图（计算值与试验结果）, figureFileSmall=qQ+ildo6ENqWDTJ5q+InsQ==, figureFileBig=//0m9rmwsDEM62VdLlbg2A==, tableContent=null), ArticleFig(id=1243306343537423236, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.17, caption=Spectrum diagram of the VBM at Section 1 and Section 4 for H=0.083 m, figureFileSmall=MubJPsJPzEX0zApwZoxdeA==, figureFileBig=che15eqfexzduK9uyKOH8g==, tableContent=null), ArticleFig(id=1243306343600337797, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图17, caption=Mv1与Mv4的垂向弯矩频谱图（H=0.083 m）, figureFileSmall=MubJPsJPzEX0zApwZoxdeA==, figureFileBig=che15eqfexzduK9uyKOH8g==, tableContent=null), ArticleFig(id=1243306343663252359, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.18, caption=Time history and spectrogram of VBM at Section 1 and 2, figureFileSmall=FZnj/TFvU+lwAuAJJ3eADQ==, figureFileBig=KfYlEqcC/zBB71dSKQ6lTg==, tableContent=null), ArticleFig(id=1243306343717778313, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图18, caption=截面1和2的垂向弯矩响应时域曲线与频谱图, figureFileSmall=FZnj/TFvU+lwAuAJJ3eADQ==, figureFileBig=KfYlEqcC/zBB71dSKQ6lTg==, tableContent=null), ArticleFig(id=1243306343801664397, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Fig.19, caption=Time history of VBM components at Sections 1 and 2, figureFileSmall=NmHpGu5SbCrOVWN33h5XDQ==, figureFileBig=HWazdyb6dzADJCG/SGvI7A==, tableContent=null), ArticleFig(id=1243306343881356176, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=图19, caption=船模截面1和2垂向弯矩成分时域对比, figureFileSmall=NmHpGu5SbCrOVWN33h5XDQ==, figureFileBig=HWazdyb6dzADJCG/SGvI7A==, tableContent=null), ArticleFig(id=1243306343952659347, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.1, caption=

Principal particulars of ship and model

, figureFileSmall=null, figureFileBig=null, tableContent=
物理量符号/单位实船船模
缩尺比λ130
总长LOA/m154.45.146
垂线间长L/m1424.733
型宽B/m17.80.592
型深h/m9.840.325
设计吃水d/m5.040.167
水密度γ/（t·m-3）1.0251.000
排水量Δ/t62000.229
), ArticleFig(id=1243306344028156823, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表1, caption=

实船及船模主要参数

, figureFileSmall=null, figureFileBig=null, tableContent=
物理量符号/单位实船船模
缩尺比λ130
总长LOA/m154.45.146
垂线间长L/m1424.733
型宽B/m17.80.592
型深h/m9.840.325
设计吃水d/m5.040.167
水密度γ/（t·m-3）1.0251.000
排水量Δ/t62000.229
), ArticleFig(id=1243306344095265692, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.2, caption=

Dimensions of backbone beam with variable sections

, figureFileSmall=null, figureFileBig=null, tableContent=
站号内壁宽/mm内壁高/mm左右壁面厚/mm上下壁面厚/mm长度/mm
1~432535
4~6806056473
6~161092356
16~1932796
), ArticleFig(id=1243306344179151776, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表2, caption=

龙骨梁变截面尺寸

, figureFileSmall=null, figureFileBig=null, tableContent=
站号内壁宽/mm内壁高/mm左右壁面厚/mm上下壁面厚/mm长度/mm
1~432535
4~6806056473
6~161092356
16~1932796
), ArticleFig(id=1243306344271426469, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.3, caption=

Size information of three different fluid domains

, figureFileSmall=null, figureFileBig=null, tableContent=
水域水域宽度ai/m水域长度bi/m
大尺寸20.0830.12
中尺寸14.2021.30
小尺寸10.0415.06
), ArticleFig(id=1243306344372089770, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表3, caption=

三种不同大小水域尺寸信息

, figureFileSmall=null, figureFileBig=null, tableContent=
水域水域宽度ai/m水域长度bi/m
大尺寸20.0830.12
中尺寸14.2021.30
小尺寸10.0415.06
), ArticleFig(id=1243306344435004333, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.4, caption=

Uncertainty analysis of VBM and ship motions for three different fluid-domain sizes

, figureFileSmall=null, figureFileBig=null, tableContent=
参数/单位三种不同水域大小计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SZ1SZ2SZ3ɛ21ɛ23RGPkCkδREUZUZCUZ/SZ2SC
纵摇/°3.2893.3013.3200.0120.0190.6321.3260.5830.0210.0380.0090.0123.339
垂荡/mm29.80130.01830.6220.2170.6040.3602.9491.7790.1220.3130.0950.01030.331
1阶波浪弯矩/（N·m）27.87828.02628.3020.1480.2760.5341.8100.8730.1690.2120.0220.00828.238
2阶倍频弯矩/（N·m）11.90412.00012.2880.0960.2880.3333.1702.0000.0480.1440.0480.01212.144
二节点弯矩/（N·m）0.74580.7550.76560.00920.01060.8680.4080.1520.0600.1630.05120.2160.918
), ArticleFig(id=1243306344510501810, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表4, caption=

三种不同水域尺寸下的垂向弯矩和船模运动的不确定度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
参数/单位三种不同水域大小计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SZ1SZ2SZ3ɛ21ɛ23RGPkCkδREUZUZCUZ/SZ2SC
纵摇/°3.2893.3013.3200.0120.0190.6321.3260.5830.0210.0380.0090.0123.339
垂荡/mm29.80130.01830.6220.2170.6040.3602.9491.7790.1220.3130.0950.01030.331
1阶波浪弯矩/（N·m）27.87828.02628.3020.1480.2760.5341.8100.8730.1690.2120.0220.00828.238
2阶倍频弯矩/（N·m）11.90412.00012.2880.0960.2880.3333.1702.0000.0480.1440.0480.01212.144
二节点弯矩/（N·m）0.74580.7550.76560.00920.01060.8680.4080.1520.0600.1630.05120.2160.918
), ArticleFig(id=1243306344569222068, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.5, caption=

Uncertainty analysis of VBM and motions under different time steps

, figureFileSmall=null, figureFileBig=null, tableContent=
不同时间步长下计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
ST1ST2ST3ɛ21ɛ23RGPkCkδREUTUTCUT/ST2SC
纵摇/°3.3323.3013.267-0.031-0.0340.9000.3040.111-0.2750.2750.2450.0834.066
垂荡/mm30.50530.01829.217-0.487-0.8010.6081.4370.646-0.7540.7540.2670.02531.307
1阶波浪弯矩/（N·m）28.19428.02626.481-0.168-1.5450.1096.4038.198-0.0200.3160.1480.01128.342
2阶倍频弯矩/（N·m）12.15312.00010.763-0.153-1.2370.1246.0317.086-0.0220.2840.1310.02412.284
二节点弯矩/（N·m）0.8560.7550.608-0.101-0.1470.6871.0830.455-0.2220.2220.1210.2941.218
), ArticleFig(id=1243306344648913847, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表5, caption=

不同时间步长下的垂向弯矩和船模运动的不确定度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
不同时间步长下计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
ST1ST2ST3ɛ21ɛ23RGPkCkδREUTUTCUT/ST2SC
纵摇/°3.3323.3013.267-0.031-0.0340.9000.3040.111-0.2750.2750.2450.0834.066
垂荡/mm30.50530.01829.217-0.487-0.8010.6081.4370.646-0.7540.7540.2670.02531.307
1阶波浪弯矩/（N·m）28.19428.02626.481-0.168-1.5450.1096.4038.198-0.0200.3160.1480.01128.342
2阶倍频弯矩/（N·m）12.15312.00010.763-0.153-1.2370.1246.0317.086-0.0220.2840.1310.02412.284
二节点弯矩/（N·m）0.8560.7550.608-0.101-0.1470.6871.0830.455-0.2220.2220.1210.2941.218
), ArticleFig(id=1243306344736994232, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.6, caption=

Base size and total number of grids for three different cases

, figureFileSmall=null, figureFileBig=null, tableContent=
网格方案基础尺寸/m网格总数
大网格0.035286.43万
中网格0.025328.38万
小网格0.018482.18万
), ArticleFig(id=1243306344804103099, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表6, caption=

三种不同网格大小的基础尺寸和网格总数

, figureFileSmall=null, figureFileBig=null, tableContent=
网格方案基础尺寸/m网格总数
大网格0.035286.43万
中网格0.025328.38万
小网格0.018482.18万
), ArticleFig(id=1243306344871211965, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.7, caption=

Uncertainty analysis of VBM and ship motion under three different types of sizes

, figureFileSmall=null, figureFileBig=null, tableContent=
三种不同网格大小方案计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SG1SG2SG3ε21ε23RGPkCkδREUGUGCUG/SG2SC
纵摇/°3.4133.3013.160-0.112-0.1410.7940.6640.259-0.4330.4330.3530.1313.746
垂荡/mm30.82330.01829.030-0.805-0.9880.8150.5910.227-3.5411.3940.8890.04631.412
1阶波浪弯矩/（N·m）28.31028.02627.500-0.284-0.5260.5401.7780.852-0.3330.3330.0490.01228.359
2阶倍频弯矩/（N·m）12.60012.00011.150-0.600-0.8500.7061.0050.417-1.4401.4400.8400.12013.440
二节点弯矩/（N·m）0.8560.7550.612-0.101-0.1430.7061.0030.416-0.2430.2430.1420.3220.998
), ArticleFig(id=1243306344984458177, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表7, caption=

不同网格大小方案下的垂向弯矩和船模运动的不确定度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
三种不同网格大小方案计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SG1SG2SG3ε21ε23RGPkCkδREUGUGCUG/SG2SC
纵摇/°3.4133.3013.160-0.112-0.1410.7940.6640.259-0.4330.4330.3530.1313.746
垂荡/mm30.82330.01829.030-0.805-0.9880.8150.5910.227-3.5411.3940.8890.04631.412
1阶波浪弯矩/（N·m）28.31028.02627.500-0.284-0.5260.5401.7780.852-0.3330.3330.0490.01228.359
2阶倍频弯矩/（N·m）12.60012.00011.150-0.600-0.8500.7061.0050.417-1.4401.4400.8400.12013.440
二节点弯矩/（N·m）0.8560.7550.612-0.101-0.1430.7061.0030.416-0.2430.2430.1420.3220.998
), ArticleFig(id=1243306345072538564, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.8, caption=

Uncertainty analysis of VBM with different stractural damping

, figureFileSmall=null, figureFileBig=null, tableContent=
三种不同结构阻尼计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SR1SR2SR3ε21ε23RGPkCkδREURURCUR/SR2SC
1阶波浪弯矩/（N·m）27.94928.13728.4510.1880.3130.6011.4710.6650.2830.4720.1040.01728.609
2阶倍频弯矩/（N·m）12.34012.49112.7180.1510.2270.6651.1790.5050.3000.5950.2060.04813.086
二节点弯矩/（N·m）0.8320.8770.9770.0450.1000.4542.2781.2020.0380.0530.0070.0600.930
), ArticleFig(id=1243306346586682311, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表8, caption=

三种不同结构阻尼下的垂向弯矩的不确定度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
三种不同结构阻尼计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SR1SR2SR3ε21ε23RGPkCkδREURURCUR/SR2SC
1阶波浪弯矩/（N·m）27.94928.13728.4510.1880.3130.6011.4710.6650.2830.4720.1040.01728.609
2阶倍频弯矩/（N·m）12.34012.49112.7180.1510.2270.6651.1790.5050.3000.5950.2060.04813.086
二节点弯矩/（N·m）0.8320.8770.9770.0450.1000.4542.2781.2020.0380.0530.0070.0600.930
), ArticleFig(id=1243306346674762697, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.9, caption=

Uncertainty analysis of pressure with different factors

, figureFileSmall=null, figureFileBig=null, tableContent=
方案类型三种不同方案计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SJ1SJ2SJ3ɛ21ɛ23RGPkCkδ*REUJUJCUJ/SJ2SC
网格1.5201.5991.7250.0790.1260.6251.3550.5990.1320.1320.0640.0831.730
水域1.6351.5991.510-0.036-0.0890.4042.6171.477-0.0240.0480.0160.0301.646
时间步长1.6031.5991.592-0.004-0.0070.6111.4220.637-0.0060.0060.0030.0041.605
), ArticleFig(id=1243306346767037388, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表9, caption=

不同影响因素下的砰击压力不确定度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
方案类型三种不同方案计算结果差值收敛比准确度修正因子数值误差不确定度校正不确定度不确定度占比结果修正
SJ1SJ2SJ3ɛ21ɛ23RGPkCkδ*REUJUJCUJ/SJ2SC
网格1.5201.5991.7250.0790.1260.6251.3550.5990.1320.1320.0640.0831.730
水域1.6351.5991.510-0.036-0.0890.4042.6171.477-0.0240.0480.0160.0301.646
时间步长1.6031.5991.592-0.004-0.0070.6111.4220.637-0.0060.0060.0030.0041.605
), ArticleFig(id=1243306346850923470, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=EN, label=Tab.10, caption=

Values and proportions of VBM of different orders at Sections 1 and 2

, figureFileSmall=null, figureFileBig=null, tableContent=
倍频阶级截面1（Mv1）截面2（Mv2）
垂向弯矩/（N·m）各阶波浪弯矩占比（%）垂向弯矩/（N·m）各阶波浪弯矩占比（%）
试验结果CFD-FEM试验结果CFD-FEM试验结果CFD-FEM试验结果CFD-FEM
128.21128.893100.00100.0088.59191.71100.00100.00
214.08812.78549.9444.2527.18726.77230.6929.19
33.5334.06212.5214.066.7877.0117.667.65
42.8852.45610.238.504.2143.8424.764.19
51.6851.0565.973.652.952.0363.332.22
60.7470.7012.652.431.472.1491.662.34
71.2860.7144.562.473.1752.4193.582.64
), ArticleFig(id=1243306346930615249, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306316983283929, language=CN, label=表10, caption=

截面1和2处不同阶倍频垂向弯矩大小及占比

, figureFileSmall=null, figureFileBig=null, tableContent=
倍频阶级截面1（Mv1）截面2（Mv2）
垂向弯矩/（N·m）各阶波浪弯矩占比（%）垂向弯矩/（N·m）各阶波浪弯矩占比（%）
试验结果CFD-FEM试验结果CFD-FEM试验结果CFD-FEM试验结果CFD-FEM
128.21128.893100.00100.0088.59191.71100.00100.00
214.08812.78549.9444.2527.18726.77230.6929.19
33.5334.06212.5214.066.7877.0117.667.65
42.8852.45610.238.504.2143.8424.764.19
51.6851.0565.973.652.952.0363.332.22
60.7470.7012.652.431.472.1491.662.34
71.2860.7144.562.473.1752.4193.582.64
)], attaches=null, journal=Journal(id=1240685663704625163, delFlag=0, nameCn=船舶力学, nameEn=Journal of Ship Mechanics, nameHistory1=null, nameHistory2=null, issn=1007-7294, eissn=null, cn=32-1468/U, coden=null, periodic=0, language=CN, oaType=null, ccby=null, superviseOffice=null, ownerOffice=null, pubOffice=null, editorOffice=null, officeType=null, aims=null, clcCode=null, officeProv=null, officeCity=null, officeAddr=null, officeZip=null, officeEmail=null, officePhone=null, editDirector=null, officeDirector=null, officeDirectorPhone=null, officeStaffNum=null, officeEmpNum=null, coverPicUrl=8VABIsgSw5I4HF/4goaIlA==, journalPrice=null, startedYear=null, abbrevIsoEn=Journal of Ship Mechanics, journalRemark=null, publicationField=null, createdTime=1773732113054, updatedTime=1773732336269, createdBy=18614031015, updatedBy=13701087609, firstLetterCn=J, firstLetterEn=J, subjectCode=Engineering, subjectName=null, subjectCodeEn=Engineering, subjectNameEn=null, picCn=8VABIsgSw5I4HF/4goaIlA==, picEn=Ve/8A/FRYceS/z8o7GCJ5g==, jcr=null, cjcr=null, exts=[JournalExt(id=1240686600003318325, language=CN, name=船舶力学, nameHistory1=null, nameHistory2=null, managedBy=, sponsoredBy=, publishedBy=, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=, createdTime=1773732336283, updatedTime=1773732336283, createdBy=13701087609, updatedBy=13701087609, submissionGuidelinesUrl=, submissionAuthorUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=1, submissionEditorUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=3, submissionReviewUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=2, submissionCeEditorUrl=, submissionAeEditorUrl=, option={"copyright":""}), JournalExt(id=1240686600041067062, language=EN, name=Journal of Ship Mechanics, nameHistory1=null, nameHistory2=null, managedBy=, sponsoredBy=, publishedBy=, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=, createdTime=1773732336292, updatedTime=1773732336292, createdBy=13701087609, updatedBy=13701087609, submissionGuidelinesUrl=, submissionAuthorUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=1, submissionEditorUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=3, submissionReviewUrl=https://cblx.cbpt.cnki.net/EditorD3N/index.aspx?t=2, submissionCeEditorUrl=, submissionAeEditorUrl=, option={"copyright":""})], databaseList=null, tenantJournalId=1240685776644648972, websiteList=[Website(id=1240686760611607145, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1240685776644648972, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/cblx/CN, language=CN, createTime=1773732374576, createBy=18614031015, updateTime=1773732394922, updateBy=18614031015, name=船舶力学-中文, tplId=1146099689490845704, title=船舶力学, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1240687166741869216, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=articleTextType, value=kx, createTime=1773732471404, updateTime=1773732471404, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166725091997, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=banner, value=null, createTime=1773732471400, updateTime=1773732471400, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166758646435, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=grayFlag, value=0, createTime=1773732471408, updateTime=1773732471408, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166716703388, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=logo, value=https://castjournals.cast.org.cn/joweb/cblx/CN/file/pic?fileId=/ZVjg3ao2vf5wYxw5Kn1Uw==, createTime=1773732471398, updateTime=1773732471398, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166771229349, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=minRunFlag, value=0, createTime=1773732471411, updateTime=1773732471411, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166737674911, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/cblx/CN/file/pic, createTime=1773732471403, updateTime=1773732471403, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166767035044, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=silenceFlag, value=0, createTime=1773732471410, updateTime=1773732471410, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166729286302, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_cn_619/, createTime=1773732471401, updateTime=1773732471401, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166750257825, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=themeColor, value=null, createTime=1773732471406, updateTime=1773732471406, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687166754452130, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760611607145, code=themeStyle, value=null, createTime=1773732471407, updateTime=1773732471407, creator=18614031015, updator=18614031015)]), Website(id=1240686760674521707, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1240685776644648972, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/cblx/EN, language=EN, createTime=1773732374590, createBy=18614031015, updateTime=1773732413338, updateBy=18614031015, name=船舶力学-英文, tplId=1146101810881728533, title=Journal of Ship Mechanics, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1240687194269078438, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=articleTextType, value=kx, createTime=1773732477967, updateTime=1773732477967, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194248106915, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=banner, value=null, createTime=1773732477962, updateTime=1773732477962, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194285855657, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=grayFlag, value=0, createTime=1773732477971, updateTime=1773732477971, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194239718306, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=logo, value=https://castjournals.cast.org.cn/joweb/cblx/EN/file/pic?fileId=/ZVjg3ao2vf5wYxw5Kn1Uw==, createTime=1773732477960, updateTime=1773732477960, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194302632875, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=minRunFlag, value=0, createTime=1773732477975, updateTime=1773732477975, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194260689829, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/cblx/EN/file/pic, createTime=1773732477965, updateTime=1773732477965, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194294244266, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=silenceFlag, value=0, createTime=1773732477973, updateTime=1773732477973, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194256495524, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_en_623/, createTime=1773732477964, updateTime=1773732477964, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194277467047, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=themeColor, value=null, createTime=1773732477969, updateTime=1773732477969, creator=18614031015, updator=18614031015), WebsiteProps(id=1240687194281661352, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1240686760674521707, code=themeStyle, value=null, createTime=1773732477970, updateTime=1773732477970, creator=18614031015, updator=18614031015)])], journalTitle=船舶力学, weixinUrl=null, journalUrl=https://cblx.cbpt.cnki.net/, iacademicId=null, status=1, seqNo=null, journalTitleEn=Journal of Ship Mechanics, journalPhotoCn=8VABIsgSw5I4HF/4goaIlA==, journalPhotoEn=Ve/8A/FRYceS/z8o7GCJ5g==, journalFirstLetter=J, journalRecommend=null, journalNew=null, journalCollection=null, jcrJf=null, cjcrJf=null, jcrJfStr=null, cjcrJfStr=null, submissionFirstDecision=null, sciSubjectClassification=null, casSubjectClassification=null, citeScore=null, totalCitationFrequency=null, icpCode=null, psCode=null, advertisingLicenseCode=null, copyrightInformation=null, country=null, option=, provinceCode=null, provinceName=null, collectFlag=false), detailUrlCn=https://castjournals.cast.org.cn/joweb/cblx/CN/10.3969/j.issn.1007-7294.2025.05.011, detailUrlEn=https://castjournals.cast.org.cn/joweb/cblx/EN/10.3969/j.issn.1007-7294.2025.05.011, pdfUrlCn=https://castjournals.cast.org.cn/joweb/cblx/CN/PDF/10.3969/j.issn.1007-7294.2025.05.011, pdfUrlEn=https://castjournals.cast.org.cn/joweb/cblx/EN/PDF/10.3969/j.issn.1007-7294.2025.05.011, aliStartDate=null, aliEndDate=null, collectionFlag=false, citedCount=null, citedUrl=null, reference=null)
收藏切换
基于CFD-FEM双向流固耦合的大外飘型船舶砰击颤振响应不确定度研究
收藏切换
PDF下载
田光钰 a, b , 王一雯 a , 张涵韬 a, b , 吴卫国 a
船舶力学 | 结构力学 2025,29(5): 790-806
收起
收藏切换
船舶力学 | 结构力学 2025, 29(5): 790-806
基于CFD-FEM双向流固耦合的大外飘型船舶砰击颤振响应不确定度研究
全屏
田光钰a, b, 王一雯a , 张涵韬a, b, 吴卫国a
作者信息
  • a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063
  • b.武汉理工大学　船海与能源动力工程学院，武汉　430063

    • 田光钰（1999-），男，硕士研究生

    王一雯（1990-），女，博士，副研究员，通讯作者；E-mail：。

通讯作者:

通讯作者；E-mail：
Uncertainty analysis of large flared ship slamming response based on CFD-FEM two-way fluid-structure interaction
Guang-yu TIANa, b, Yi-wen WANGa , Han-tao ZHANGa, b, Wei-guo WUa
Affiliations
  • a.Green & Smart River-Sea-Going Ship Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China
  • b.School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China
出版时间: 2025-05-20 doi: 10.3969/j.issn.1007-7294.2025.05.011
文章导航
收藏切换
摘要
收起

船舶非线性波浪载荷及结构高频颤振响应的准确评估与分析，是明确船舶结构安全性的前提，然而其数值仿真计算的可靠性及其不确定度分析则较少得到关注。本文开展分段龙骨梁水弹性模型CFD-FEM双向流固耦合仿真以及试验研究，对船模在波浪下的高频响应进行仿真分析，并对仿真结果开展不确定度分析，评估仿真模型的可靠性。数值不确定度的计算结果，能够提供不同影响因素下结果是否收敛的判别依据和不确定度水平，并明确船艏的砰击压力、船模的运动和船体高低频波浪弯矩的不确定度水平。对比数值仿真与试验测试可知，CFD-FEM双向流固耦合仿真能够精确地捕捉到船舶结构高频响应，船舶在巡航工况下高频弯矩成分能够占到低频波浪弯矩的49.95%以上，砰击载荷诱发的舰船高频颤振动态响应不容忽视，此类舰船的结构设计及安全评估中须考虑其影响。本文可为船舶砰击颤振此类高频结构动态响应的不确定度分析提供参考。

水弹性模型试验  /  砰击颤振  /  CFD-FEM双向流固耦合  /  不确定度分析

The accurate assessment and analysis of nonlinear wave loads on ships and the high-frequency vibrational response of ship structures are requisites for determining the safety of ship structures. However, the reliability of numerical simulation and the analysis of their uncertainties have received relatively little attention. This paper presents a segmented keel beam hydroelastic model CFD-FEM simulation and experimental research to simulate and analyze the high-frequency response of a ship model in waves. Uncertainty analysis was performed on the simulation results to evaluate the reliability of the simulation model. The calculation results of numerical uncertainties can provide criteria for judging the convergence of results under different influencing factors and the level of uncertainty. The uncertainty levels of the impact pressure on the ship’s bow, the motion of the ship model, and the high and low-frequency wave bending moments of the ship hull are also clarified. A comparison between numerical simulation and experimental testing reveals that CFD-FEM two-way fluid-structure coupling simulation can accurately capture the high-frequency response of ship structures. The high-frequency bending moment component of the ship under cruising conditions can account for more than 49.95% of the low-frequency wave bending moment. The dynamic response of ships induced by impact loads cannot be ignored, and their influence must be considered in the structural design and safety assessment of such ships. This paper can provide a reference for the uncertainty analysis of high-frequency structural dynamic responses such as ship impact vibration.

hydroelastic model experiment  /  slamming-induced flutter  /  CFD-FEM  /  uncertainty analysis
田光钰, 王一雯, 张涵韬, 吴卫国. 基于CFD-FEM双向流固耦合的大外飘型船舶砰击颤振响应不确定度研究. 船舶力学, 2025 , 29 (5) : 790 -806 . DOI: 10.3969/j.issn.1007-7294.2025.05.011
Guang-yu TIAN, Yi-wen WANG, Han-tao ZHANG, Wei-guo WU. Uncertainty analysis of large flared ship slamming response based on CFD-FEM two-way fluid-structure interaction[J]. Journal of Ship Mechanics, 2025 , 29 (5) : 790 -806 . DOI: 10.3969/j.issn.1007-7294.2025.05.011
正文
收起
0　引言
收起
水面舰船装备向着大型化、快速化、多功能化的方向发展，而且在深远海航行过程中所处环境愈发复杂恶劣，舰船高速航行时不可避免地会伴随着剧烈的船波相对运动，使得船艏易遭遇强非线性瞬态高幅值砰击载荷作用。不仅会使得船艏结构产生弹塑性变形或局部损伤，也会诱发全船结构的高频动态响应成分即砰击颤振，其与低频波浪载荷耦合叠加后的结构应力水平激增，成为影响船舶结构极限强度的重要因素之一。因此，对恶劣海况下船舶非线性波浪载荷以及砰击颤振的准确评估与分析，是明确舰船结构安全性的前提。
在研究砰击颤振这类结构动态响应较大且流固耦合效应显著的水弹性问题时一般使用双向流固耦合仿真方法，可模拟实际现象并较好地求解水弹性问题。Lakshmynarayanana等[1-3]采用CFD-FEM方法针对规则波下的驳船运动响应开展双向流固耦合仿真计算，并与试验测量结果和二维水弹性计算进行对比，还采用相同方法研究了S175集装箱船的对称运动和波浪载荷，将规则波中的迎浪运动和波浪载荷与其他人的试验测量结果以及二维线性水弹性程序计算结果进行比较，其CFD-FEM方法预测船舯弯矩的精度与线性和非线性切片理论相当，结果表明该方法能够较好地捕捉模型的非线性波浪载荷特征。Jiao等[4]基于CFD-FEM流固耦合模型分析了船舶在波浪条件下的非线性水弹性效应、砰击和甲板上浪，对其提出的CFD-FEM双向流固耦合方法在船舶水弹性模拟中的可行性进行验证，通过所提方法可以再现船舶耐波性和水弹性范围内的非线性大振幅运动、加速度、波浪载荷、砰击载荷、甲板上浪载荷以及颤振和波激振动响应。
伴随着数值仿真技术的广泛应用和不断更新，对其可靠性的研究也逐渐开展起来。20世纪末，Roache等[5]提出并开始数值仿真计算的不确定度分析研究。近年来有关船模波浪载荷试验和数值仿真的不确定度分析与研究也初步发展。不确定度分析是验证CFD计算可靠性与准确性的一种方法，包含“验证”和“确认”两大过程[6]。
模型试验中的测量不确定度分析能够以定量的形式给出试验的质量和可信度，是模型试验报告必要的一个组成部分，国内外学者已经分别将不确定度分析方法应用到了船模操纵性等试验中[7]。目前国际ITTC-ISSC联合委员会致力于促成对波浪载荷不确定度分析的发展，诸多学者也为此开展大量工作。Zhu等[8]在进行分段水弹性模型试验的不确定度分析时，以多个波浪载荷测量数据的有效段为研究对象，将各组有效段数据的标准差与其平均值的比值用于量化各物理量的随机误差，发现拖曳速度、航向角和拖曳力均会对波浪弯矩测量结果的不确定度有一定影响。对13000 TEU分段船模在不规则波中结构响应的试验数据分析中发现[9]，试验中目标波浪谱与实际波浪谱的差异、斜浪航行时的浪向角和航速是试验不确定度的重要来源。司海龙等[10]开展了集装箱船波浪载荷模型试验，针对船体线型、转动惯量、重心高、测量梁标定系数等影响因素进行了不确定度分析，并建立了波浪载荷模型试验的不确定度分析方法，明确了模型试验不确定度的影响因素。
Guedes Soares[11]研究了不同波浪载荷预测理论对短期船舶运动和载荷结果的影响，并对模型的不确定度进行了定量分析，以修正理论预测模型；朱德祥等[12]对ITTC关于CFD的不确定度分析流程进行了介绍，并对SUBOFF艇体的表面压力系数进行了不确定度分析，进行了初步的应用实践；Drummen等[13]使用滚装渡轮的不同试验和数值仿真数据对砰击和砰击载荷进行了基准研究，对流体动力学特性的建模不确定度和结构响应进行了研究；Huang等[14]采用CFD-FEM流固耦合方法对标准S175集装箱船模型的运动和波浪载荷进行了全面计算，对流体网格密度、流体区域大小、流体粘度等因素计算船舶响应的结果进行了不确定度分析，与S175模型相关的试验和数值计算数据进行了对比。
目前，在计算船舶的波浪载荷和全船结构的高频响应成分时，较少关注其数值仿真计算结果的可靠性并进行不确定度分析，而是否能够量化不确定度，对于结构强度评估的影响和研究其可靠性方法的应用都是十分重要的。由于载荷和模型的复杂性，本文开展分段龙骨梁水弹性模型CFD-FEM双向流固耦合的仿真以及试验研究，对船模在波浪下的高频响应进行仿真分析，并对仿真结果开展不确定度分析，评估仿真模型的可靠性。通过两种方法的结合，能够量化仿真中的不确定度对于结构强度评估的影响，给出多个因素下船艏的砰击压力、船模的运动和船体高低频波浪弯矩的不确定度水平，可为船舶砰击颤振此类高频结构动态响应的不确定度分析提供参考，且能够较好地揭示船模砰击颤振高频响应的影响规律。
1　变截面龙骨梁水弹性船模试验
收起
通过变截面龙骨梁的水弹性模型试验，针对大外飘型船舶非线性波浪载荷、船艏瞬时砰击载荷以及高频砰击颤振响应开展研究。本试验于武汉理工大学拖曳水池内开展，水池长132 m，宽10.8 m，水深2 m。水池末端布置有液压式造波机，可模拟不同波高、不同周期的规则波与不规则波。
为明确实船于波浪下的相对运动和非线性波浪载荷特性，进行模型试验时，需使船模满足与实船的几何相似、流体边界相似、流体动力相似和结构刚度相似等相似条件。综合考虑试验水池尺寸、造波能力、拖车航速等因素，选用船模缩尺比为λ=30，实船及船模的主要参数如表1所示。大外飘型船模重量分布与重心位置等参数通过特制设备进行调整从而与实船保持相似。此外，为充分体现模型高频响应特性，将整体船模进行分段设计，分段截面1~7分别位于#3、#5、#7.5、#10、#12.5、#15、#17处，8分段船模通过铝制变截面龙骨梁进行连接，以探究大外飘型船舶高频砰击颤振响应特性。
由于实船刚度沿船长方向变化较大，通过变截面龙骨梁型式使得船模满足实船结构动态特性相似，其龙骨梁的型式及结构尺寸如图1及表2所示。通过应变片测量上述各分段截面1~7站号处的垂向弯矩即Mv1~Mv7，通过船艏布置的高精度高频压力传感器测量波浪下的砰击压力时间历程。
通过模型试验模拟实船的巡航工况，船模试验的航速V=1.408 m/s，入射波浪频率（ω）范围为2.688~5.853 rad/s，波高H=0.0833~0.167 m，拖曳水池模型试验如图2所示。
2　CFD-FEM双向流固耦合仿真计算
收起
基于CFD-FEM双向流固耦合仿真方法，对变截面龙骨梁分段船模开展水弹性数值仿真研究，分析波浪下船舶非线性波浪载荷及高频砰击颤振响应。根据结构变形对流场的影响程度，可以分成两种类型即单向流固耦合与双向流固耦合。当结构变形被认为对流体具有较小可忽略的影响时，可使用单向耦合，单向耦合使用CFD计算流体载荷，假定结构是刚性的，将水压力作为载荷施加到结构模型计算结构响应；结构变形较大且对流场存在较大影响时，则使用CFD-FEM双向流固耦合仿真方法。
对于结构动态响应较大且流固耦合效应显著的水弹性问题，一般使用双向流固耦合方法开展时域仿真分析，采用的是双向隐式耦合法。流体与结构分别单独求解，CFD计算采用的数值方法为有限体积方法，假定流动受RANS（平均雷诺N-S）方程控制，通过求解流体质量和动量守恒方程来得到船体表面压力。其中流动的RANS控制守恒方程为
式中，ρ代表流体密度，代表平均压力，ν为动力粘度，和为速度法向分量的平均值，为雷诺应力张量系数。
流体自由表面的流动采用流体体积法（Volume of Fluid, VOF）来实现，VOF方法可以有效地模拟两相流体交界处自由液面的状态，明确不同流体介质的分布，以获取自由液面的变形信息。VOF方法通过求解计算域内流体体积分数的输运方程来捕捉界面运动。流体体积分数的输运方程表示如下：
式中，α表示流体体积分数，u为速度矢量，∇为梯度算子，S(α)为描述表面张力和影响体积分数的力。
CFD计算中采用的湍流模型的物理控制方程为标准k-ε模型，通过求解湍流动能和湍流耗散率两个输运方程的分布来模拟湍流流动，两个输运方程的形式为
式中，k代表湍动能，ε代表湍动耗散率，是密度的时间平均值，为动力粘度，Pk为湍动能的产生项，C1ε和C2ε为经验常数。
FEM计算则通过在船体外表面上施加流体水压力载荷，基于有限元法得到结构的应力、位移和变形。CFD-FEM双向流固耦合通过设定船体同一表面为耦合交界面进行数据交换，CFD计算得到压力数据传递给FEM模型使结构模型产生变形，反过来将结构变形数据反馈到流场中以更新流体网格。采用隐式耦合方案，在每一个时间步长内多次进行数据交换迭代使得双向耦合仿真结果达到收敛。CFD-FEM双向流固耦合仿真计算原理如图3所示。
仿真计算模型的主尺度参数设置与试验模型保持一致，保证两种模型的重量分布、龙骨梁刚度分布以及波浪参数相同。流体计算模型中计算域原点位于船底中横剖面和中纵剖面的交点处，范围为−2.5L<x<2L，0<y<1.5L，−2L<z<1.2L，划分为空气域和水域。沿船舶中纵面设置对称平面边界，以降低计算域网格数量，从而提高计算效率，船体计算域和边界条件如图4所示。
采用五阶斯托克斯波模型模拟入射波浪，在液面网格划分时为保证入射波浪稳定性，沿船长纵向方向单个波浪周期至少由40个网格单元组成，垂向方向至少由16个网格单元构成。本文流体仿真模型的液面区域，在完整周期波浪的纵向方向设置160个单元，垂向设置40个单元，从而能精准捕捉自由液面和船波交界处的运动。水动力计算域的网格划分示意如图5所示。
结构仿真模型中三维龙骨梁采用线性梁单元B31，保证变截面型式与试验模型一致。通过瑞利阻尼考虑龙骨梁刚度阻尼的影响，满足船模试验中的龙骨梁刚度特征相似。梁模型相对位置于重心高度处，船模分段的总体质量集中分布于船长方向的梁单元之上。船模的外壳由面单元建模，单元类型为SFM4D4。外壳单元与梁单元的节点采用运动耦合约束连接，外壳单元将流体载荷通过约束连接，传递到龙骨梁结构单元进行结构响应分析。船舶结构有限元模型如图6所示。
3　CFD-FEM双向流固耦合仿真不确定度分析
收起
基于ITTC相关指南中不确定度分析的相关要求[15]，不确定度分析由验证（Verification）和确认（Validation）组成，并分别计算数值不确定度和建模不确定度。数值不确定度的计算须明确计算模型的影响参数，诸如时间步长、网格尺寸、迭代次数等。数值不确定度USN计算可表示为
式中，UG、UI、UT、Uo分别为网格、迭代次数、时间步和其他因素引起的不确定度。
一般选用n(n≥3)个影响参数来进行不确定度分析，每次只改变一个参数的大小，保持所有其他参数不变，保证被改变的参数其扩大和缩小的比率相同。并对改变后的不同参数结果进行收敛性研究，一般设置至少i(i≥3)个解来进行，本文中选取3个不同的参数解来进行收敛性分析，不同解之间的差值εi以及收敛比Ri分别为
式中，i=1、2、3分别对应三个不同输入参数计算的解。收敛比存在三种不同的误差形式，Ⅰ：0<Ri<1，单调收敛（Monotonic Convergence, MC）；Ⅱ：Ri<0，振荡收敛（Oscillatory Convergence, OC）；Ⅲ：>1，发散（Monotonic Divergence, MD)。对于第Ⅰ种迭代误差，使用广义Richardson外推法来预测误差和准确度，定义为数值误差，pi为准确度阶数，计算公式如下：
在估计不确定度时还需要引入一个修正因子Ci（Correction Factor, CF），修正因子是从基于一维波动方程、二维拉普拉斯方程和Blasius边界层分析的基准研究中提出的，修正因子可作为确定数值计算解和渐近范围的可靠定量度量，Ci的计算公式为
式中，Piest为改进后准确度（精度）阶数的估计值，一般取Piest=2。当Ci趋近于1时，意味着计算解接近于渐近范围；当Ci远离1时，意味着计算的解远离渐进范围。根据修正因子Ci来估计不确定度[16]，不确定度Ui公式为
上述方法为广义Richardson外推法的应用，当Ci趋近于1时仅估计50%的不确定度。对不确定度公式进行修正得到在不同修正因子Ci下的修正不确定度Uic为
至于建模不确定度则是通过试验数据来评估。引入对比误差E，它由基准试验数据和仿真数据得到。若D为试验值结果，S为仿真计算结果，UD为试验的不确定度，则对比误差和建模不确定度分别为
当E的绝对值小于建模不确定度UV时则可以确认，数值计算结果可靠，反之则需要对模型进行修正。本章将针对仿真计算船模在波浪下的高频响应开展不确定度分析，由于Xing等[17]在研究中发现，迭代不确定度至少比网格大小和时间步长的不确定度小一个数量级，故本文对迭代次数这一影响因素不做分析，仅针对网格大小、流体域尺寸、时间步长和结构阻尼比等影响因素开展分析。
3.1　流体域尺寸的影响分析
船模水弹性试验结果会受到拖曳水池壁面效应影响，当船模尺度较大时，池底和侧壁的存在使得水流的流动被限制，回流速度增大而引起阻塞效应。因此进行仿真计算时应关注水域尺寸对计算结果的影响，以保证结果的准确性。为了确定最合适可靠的流体域尺寸，需进行水域大小的不确定度分析，采用三个大小不同的水域尺寸进行对比，以相同的放大比例改变水域的长度和宽度，而空气域大小和水域的深度保持不变，详细参数如表3所示。
上述三种不同的水域大小下仿真计算得到的船模自由面波形如图7所示，计算的船舶垂向运动的时域曲线对比如图8所示。由图中可以看出，小尺寸水域与中尺寸水域计算的船模垂荡运动和纵摇运动的时域曲线非常接近，大尺寸水域结果有细微偏差。表4中列举的是计算三种不同尺寸流体域的垂向弯矩和船模运动的不确定度UZ过程和结果。
根据表4数据计算可得，用上述方法估计的船模纵摇和垂荡运动的不确定度UZ分别为SZ2的1.15%和1.04%。船模首部截面1的Mv1的一阶波浪弯矩的不确定度UZ为SZ2的0.76%，校正后的不确定度UZC量级较小，为SZ2的0.08%；二节点弯矩的不确定度UZ为SZ2的21.59%，校正后不确定度UZC为SZ2的6.78%。结果表明纵摇和垂荡运动的不确定度均处于较低水平，一阶波浪弯矩的不确定度处于较小的量级，小于仿真结果的1%，但反映砰击颤振特性的船模二节点弯矩的不确定度处于相对较高的水平。水域尺寸的变化对于船舶运动和低阶波浪载荷存在相当小的影响，但对于高频响应成分会产生影响。综合考虑计算精度和计算资源，在后续分析中选择中等大小水域。
3.2　迭代时间步长影响分析
在CFD-FEM双向流固耦合仿真方法计算砰击颤振这类涉及到高频振动的问题时，计算模型设置的时间步长是影响结果收敛的重要因素。如果时间步长取值较大，那么在计算的各个阶段都可能会出现崩溃并导致压力发散的现象。因为在耦合时，流体和结构模型的网格变形位移数据在每个时间步中进行多次传递，较小的时间步长能防止网格变形过快，减小发散几率。在计算船舶水弹性分析这类特殊问题时，时间步长一般设置为小于2节点固有周期的1/100，以便计算收敛和较好地反映高频现象。
为探究时间步长因素的不确定度，以的放大比例设置三个不同的时间步长：0.0007 s、0.001 s、0.0014 s，保持水域尺寸、网格大小和网格数量不变。采用上述三种时间步长分别开展仿真计算，仿真时长为10 s，并根据计算结果分别计算不确定度UT。
三种不同时间步长下船模t=4.5 s时刻的船底压力云图如图9所示，垂向弯矩的对比如图10所示。表5中列举的是三种不同时间步长下的垂向弯矩和船模运动的不确定度计算过程。根据图10和表5可以看出，不同时间步长下计算得到的船模中部的垂向弯矩较为接近；小时间步长的结果有一定偏差。船模截面1处Mv1的一阶波浪、二阶倍频和二节点弯矩的不确定度UT分别为ST2的1.13%、2.37%、29.27%。上述结果表明，时间步长大小对船体-阶波浪弯矩的影响较小，对反映砰击颤振特性的二节点波浪弯矩影响更显著。
3.3　网格尺寸的影响分析
开展网格密度大小的不确定度分析，只改变重叠区域网格的密度大小，不改变背景区域的网格大小。设置重叠区域的网格基础尺寸为0.025 m（其他网格以此大小按照参数加细化进行变化），根据参数放大比例划分，重叠网格基础尺寸大小分别为0.035 m、0.025 m、0.018 m。
在仿真模拟过程中，包括时间步长在内的其他参数保持不变，并且保证三种网格方案在计算域中能产生高质量的波，分别计算三种不同尺寸网格类型的λ/L=1.0（λ为波长）工况下的运动及载荷响应。每组网格方案的网格基础尺寸和计算域的网格总数见表6，不同大小网格密度如图11所示。
根据图12和表7结果可知，不同网格大小方案计算得到的船模截面1处Mv1的一阶、二阶和二节点弯矩不确定度UG为SG2的1.18%、12.00%、32.18%。修正后的校正不确定度分别为1.18%、7.00%、18.80%。且截面1处的弯矩分量收敛方式均为单调收敛。网格大小的变化对低阶波浪弯矩的影响较小，对反映砰击颤振特性的高阶波浪弯矩影响逐渐增大。
3.4　结构阻尼影响分析
Lakshmynarayanana等[18]采用流固耦合仿真方法分析了瑞利（Rayleigh）结构阻尼对船舯非线性波浪载荷的影响，与无阻尼情况相比，有结构阻尼时船舯弯矩幅值下降了约60%。本文中的水弹性模型试验，采用变截面连续弹性龙骨梁连接船模的各个分段，在建立结构耦合模型时，考虑了瑞利阻尼系数，更加接近于船模试验模型的结构阻尼。
瑞利阻尼在结构动力分析中广泛应用，瑞利阻尼假设结构的阻尼矩阵是质量矩阵和刚度矩阵的组合。结构阻尼会对分段船模砰击颤振的高频响应产生影响，针对仿真中设置的结构阻尼比进行不确定度分析，其他参数保持不变，以的放大比例均匀改变龙骨梁模型的结构阻尼比，ξ1、ξ2、ξ、3分别取0.025、0.035、0.05，借以分析结构阻尼对砰击颤振响应的影响。计算得到的不同结构阻尼比下垂向弯矩的时域和频域计算结果如图13所示。
根据图13和表8可以看出，Mv1中的1阶和2阶波浪弯矩的不确定度URCUR分别为SR2的1.68%和4.76%，二节点弯矩的不确定度UR为SR2的6.04%；计算的校正不确定度UGC值相对较小。表中的三个校核值均在阻尼的变化下单调收敛，结果表明反映砰击颤振特性的船模二节点垂向弯矩对阻尼的敏感性更高；阻尼对于船体梁结构的二节点高频振动存在相对更大的影响。
3.5　砰击压力不确定度分析
船舶在波浪中航行时，船艏易受到瞬态高幅值的砰击载荷作用，而砰击载荷会诱发舰船高频颤振响应。通过CFD-FEM双向流固耦合仿真方法来计算船艏部测点的砰击压力，砰击压力的不确定度分析通常需要考虑多个外部因素，此处综合前述几类影响因素即水域大小、网格大小、时间步长，来对砰击压力的不确定度进行单独分析，船模的运动与弯矩的分析已于前文介绍。
选择水线上方遭受外飘砰击的压力测点P3进行上述各个因素的砰击压力的不确定度分析，测点位置如图14所示。不同影响因素下船艏砰击压力时域曲线如图15所示，表9中记录了不确定度计算过程及结果。
对比得到的不同影响因素下的船艏测点砰击压力不确定度，可以看出网格对于砰击压力幅值影响较大，网格方案因素下的不确定度UJ为SJ2的8.26%，校正不确定度UJC为SJ2的4.00%。时间步长方案因素下的砰击压力不确定度量级较小，UJ为SJ2的0.38%。可以得出以下结论，船艏的砰击压力对网格大小的敏感度更高。
4　船模砰击颤振响应结果对比分析
收起
在先前常规开展的分段水弹性船模模型CFD-FEM双向流固耦合仿真研究的基础上，对影响船模砰击颤振响应结果的多个因素进行不确定度分析。得到收敛性较好、计算精度和效率更高的仿真模型，将船模运动、弯矩响应的仿真计算结果与试验数据进行对比，完成不确定度分析中的“确认”过程。CFD计算中水域大小为：−2.0L<x<1.5L，0<y<1.5L，−2L<z<1.2L，重叠区域网格大小为0.018 m，时间步长为0.001 s；结构模型中龙骨梁结构阻尼比ξ为0.035。
在与试验相同的工况条件参数下，采用CFD-FEM双向流固耦合仿真模型计算所得的船模遭遇入射波幅ζa，与试验测量结果的比较如图16所示。由图可见，仿真模型计算与试验中测量的波浪高度和周期均具有良好的一致性，其中，平均波高之间的偏差为1.97%。
船舶在波浪中大幅运动时会发生砰击现象，基于砰击现象所产生的船体结构砰击颤振响应问题值得重点关注。船模底部在遭受剧烈的瞬态砰击载荷后会产生高频的砰击颤振。在危险遭遇频率ωe=5.713 rad/s、波高H=0.083 m的规则波条件下，同时采用仿真与试验方法得到船模首部截面1处的弯矩Mv1与船中截面4处的弯矩Mv4，经傅里叶变换后的频域曲线对比如图17所示。
可以看出，采用仿真方法计算的结果与试验测量数据吻合较好，Mv1和Mv4仿真计算的一阶弯矩幅值比试验值约高5.5%和4.2%，垂向弯矩幅频响应中均存在明显的二阶倍频弯矩分量（ωe=11.505 rad/s处）。由于此时为小波高工况，且未发生明显砰击颤振现象，故在幅频响应的频域分析中没有出现二节点垂向弯矩高频分量。
随着波高的增大，在遭遇波浪频率ωe=5.713 rad/s、波高H=0.167 m规则波条件下，采用CFD-FEM双向流固耦合方法与试验方法得到的船模首部两个载荷测量截面1和2处的垂向弯矩（Mv1和Mv2）时域曲线，以及傅里叶变换后的频域曲线，一起绘制在图18中。Mv1和Mv2的波峰处都出现了高频非线性简谐特性，且相较于更靠近船舯位置的截面2（#7.5），船艏部截面1（#3）处的高频成分更加明显。
在危险遭遇频率和波高的工况下，采用CFD-FEM双向流固耦合仿真方法的计算结果和试验结果，均出现了明显的垂向弯矩高频振动现象，可以观察到清晰的2 ~ 7阶倍频成分。仿真与试验的垂向弯矩时域和频域的结果趋于一致，波峰处都存在高频非线性简谐特性，且相较于船舯附近的非线性特性，船艏附近的高频成分更明显，Mv1和Mv2的各阶倍频弯矩分量数值占比如表10所示。在上述多阶倍频谐振的叠加耦合作用下，船体结构存在砰击颤振的非线性振动现象，垂向弯矩中存在二节点高频分量，其中Mv1二节点垂向弯矩高频分量是其低频分量的4.56%。
将船模截面1和2处的各阶弯矩通过带宽滤波进行分离，得到低频波浪弯矩和高频倍频弯矩的时域曲线图，如图19所示。其中给出了垂向弯矩的低频（WF）和高频（HF，包括垂向二节点弯矩响应）时域曲线，其中WF和HF共同叠加作用下为弯矩总和（Total）。
由图19可知，截面1处的高频垂向弯矩在波浪弯矩总量中占比与截面2相比较大，截面2更靠近船模中部，砰击颤振对其截面弯矩的影响逐渐减小。截面2处的高频垂向弯矩分量占比相对较小，但仍占一阶波浪弯矩的49.95%。
5　结论
收起
本文通过分段龙骨梁水弹性模型试验以及CFD-FEM双向流固耦合仿真方法，开展了波浪下船体的砰击颤振高频响应特性及其不确定度分析，系统地揭示了流体域尺寸、时间步长、网格尺寸及结构阻尼比对砰击颤振响应的影响及不确定度。基于本文的研究分析总结出以下结论：
（1）对比数值仿真与试验测试可知，CFD-FEM双向流固耦合仿真可精确捕捉全船结构砰击颤振响应。在巡航工况（波高5 m，航速15 kn，波长船长比λ/L=1）下，高频弯矩成分高达低频波浪弯矩的49.95%以上，砰击载荷诱发的舰船高频颤振的动态响应不容忽视，在此类舰船的结构设计及安全评估中须考虑其影响。
（2）本文可为船舶砰击颤振此类高频结构动态响应的不确定度分析提供参考，通过不确定度分析能够给出上述影响因素的结果在一定水平条件下的可靠性，一定程度上减少船舶水弹性仿真过程的不确定度。数值不确定度的计算结果能够提供不同影响因素下结果是否收敛的判别依据和不确定度水平。船艏砰击压力和船舶运动对于网格大小的敏感度更高，引起的不确定度高达到13.12%，流体域尺寸不确定度最小，仅为1.05~3.02%。分析船体高低频波浪弯矩不确定度时，低频波浪弯矩不确定度小于5%，高频弯矩成分不确定度较大。文中额外考虑了结构阻尼的不确定度影响分析，结构阻尼对于高低阶弯矩的影响均处在相对较低水平，Mv1的1阶和2阶波浪弯矩不确定度UR分别为SR2的1.68%和4.76%，Mv1二节点弯矩不确定度UR为SR2的6.04%。这可能是由于二节点砰击颤振响应不仅与结构阻尼有关，还与刚度、质量分布、分段数、模态和外部因素有关。
基金
收起
  • 装备预先研究教育部联合基金青年人才项目(8091B03012406)
  • 武汉市知识创新专项曙光计划项目(2023010201020318)
文献
收起
参考文献 引证文献
排序方式：
[1]
Lakshmynarayanana P A, Temarel P. Application of a two-way partitioned method for predicting the wave-induced loads of a flexible containership[J]. Applied Ocean Research, 2020, 96:102052.
[2]
Lakshmynarayanana P A, Temarel P. Application of CFD and FEA coupling to predict dynamic behaviour of a flexible barge in regular head waves[J]. Marine Structures, 2019, 65(1): 308-325.
[3]
Lakshmynarayanana P A, Hirdaris S. Comparison of nonlinear one- and two-way FFSI methods for the prediction of the symmetric response of a containership in waves[J]. Ocean Engineering, 2020, 203:107179.
[4]
Jiao J L, Huang S X, Wang S, et al. A CFD-FEA two-way coupling method for predicting ship wave loads and hydroelastic responses[J]. Applied Ocean Research, 2021, 117(102919): 117-139.
[5]
Roache P J. Verification and validation in computational science and engineering[M]. Hermvsa, 1998.
[6]
邓小刚，宗文刚，张来平，等. 计算流体力学中的验证与确认[J]. 力学进展，2007, 37(2):279-288.
Deng X G, Zong W G, Zhang L P, et al. Verification and validation in computational fluid dynamics[J]. Advance in Mechanics, 2007, 37(2): 279-288. (in Chinese)
[7]
马向能，孙张群，冯骏. 测量不确定度分析在操纵性试验中的应用[J]. 船舶力学，2004, 8(5):52-61.
Ma X N, Sun Z Q, Feng J. Uncertainty analysis in captive model test[J]. Journal of Ship Mechanics, 2004, 8(5): 52-61. (in Chinese)
[8]
Zhu S J, Wu M K, Moan T. Experimental and numerical study of wave-induced load effects of open ships in oblique seas[J]. Journal of Ship Research, 2011, 55(2): 100-123.
[9]
Zhu S J, Moan T. Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large container ship model in severe head and oblique seas[J]. Marine Structures, 2014, 35:1-25.
[10]
司海龙，顾学康，胡嘉骏，等. 船模波浪载荷试验不确定度分析方法研究[J]. 船舶力学，2022, 26(2):202-214.
Si H L, Gu X K, Hu J J, et al. Uncertainty analysis of ship model wave-induced load experiment[J]. Journal of Ship Mechanics, 2022, 26(2): 202-214. (in Chinese)
[11]
Guedes Soares C. Effect of transfer function uncertainty on short-term ship responses[J]. Ocean Engineering, 1991, 18(4): 329-362.
[12]
朱德祥，张志荣，吴乘胜，等. 船舶CFD不确定度分析及ITTC临时规程的初步应用[J]. 水动力学研究与进展A辑，2007, 22(3):363-370.
Zhu D X, Zhang Z R, Wu C S, et al. Uncertainty analysis in ship CFD and the primary application of ITTC procedures[J]. Journal of Hydrodynamics, 2007, 22(3): 363-370. (in Chinese)
[13]
Drummen I, Holtmann M. Benchmark study of slamming and whipping[J]. Ocean Engineering, 2014, 86:3-10.
[14]
Huang S X, Jiao J L, Guedes S C. Uncertainty analyses on the CFD-FEA co-simulations of ship wave loads and whipping responses[J]. Marine Structures, 2022, 82:103129.
[15]
ITTC. 7.5-03-01-01, Uncertainty analysis in CFD verification and validation methodology and procedures[S]. 2021.
[16]
Wilson R, Shao J, Stern F. Discussion: Criticism of the “correction factor verification” method[J]. ASME J. Fluids Eng, 2004, 126(4): 704-706.
[17]
Xing T, Stern F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Engineering, 2010, 132(6): 061403.
[18]
Lakshmynarayanana P A, Temarel P. Application of a two-way partitioned method for predicting the wave-induced loads of a flexible container ship[J]. Applied Ocean Research, 2020, 96:102052.
2025年第29卷第5期
PDF下载
82
36
引用本文
BibTeX
文章信息
doi: 10.3969/j.issn.1007-7294.2025.05.011
  • 接收时间：2024-11-22
  • 首发时间：2026-03-24
  • 出版时间：2025-05-20
补充材料
相关文章
文章信息
作者
出版历史
  • 收稿日期：2024-11-22
基金
装备预先研究教育部联合基金青年人才项目(8091B03012406)
武汉市知识创新专项曙光计划项目(2023010201020318)
作者信息
    a.武汉理工大学　绿色智能江海直达船舶与邮轮游艇研究中心，武汉　430063
    b.武汉理工大学　船海与能源动力工程学院，武汉　430063

通讯作者:

通讯作者；E-mail：
参考文献
分享链接
https://castjournals.cast.org.cn/joweb/cblx/CN/10.3969/j.issn.1007-7294.2025.05.011
分享至
全文二维码

扫描看全文

引用本文
BibTeX
本文的引用情况
2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
关闭全屏
相关链接
论文
最新文章
热读文章
热点专题
内参
蓝皮书
产业发展报告
传播力报告
期刊分级目录
资讯
学术新闻
行业新闻
学术会议
行业会议
关于
关于我们
联系我们
北京市海淀区学院南路86号
100081
010-62199257
qkjq@cast.org.cn

中国科学技术协会版权所有 京ICP 备10216604号-4 海淀分局备案 1101084647
科技导报社主办 中国科协信息中心技术支持