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Article(id=1243253927202898532, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.07.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737388800000, receivedDateStr=2025-01-21, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774344434785, onlineDateStr=2026-03-24, pubDate=1752940800000, pubDateStr=2025-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774344434785, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774344434785, creator=13701087609, updateTime=1774344434785, updator=13701087609, issue=Issue{id=1243253924128469739, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='7', pageStart='1013', pageEnd='1180', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774344434053, creator=13701087609, updateTime=1774501521460, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243912796535107926, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243912796535107927, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1147, endPage=1158, ext={EN=ArticleExt(id=1243253927479722598, articleId=1243253927202898532, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Research on model test of global vibration of a large cruise ship, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

Vibration comfort is one of the key technical indicators to evaluate the passenger experience of large cruise ships. Due to the high superstructure and the large difference from ordinary ship types, there is no mature approximate calculation method for global vibration of cruise ships. According to the stiffness and mass distribution of a large cruise ship, this paper proposes a design method for the steel global vibration test model, and designs two schemes: the equiscale model and the non-equiscale abnormal model. Then the abnormal model is used to complete the modal test in the air and the pool, and the test results of the dry/wet modes under the loading and unloading condition are given. The results show that the ratio of the natural frequencies of the wet mode to the corresponding dry mode is basically unchanged under the loading or unloading condition. For the same order mode, the ratio of the natural frequencies under the loading condition to the corresponding unloading condition also remains basically unchanged. The steel-hull global vibration test model can better consider the influence of added water mass, which can provide a valuable reference for the design of the global vibration model and the natural frequency prediction of special ship types.

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振动舒适性是评价大型邮轮乘客体验的关键技术指标之一。由于邮轮上层建筑高，与普通船型差异大，目前还没有成熟的总振动近似计算方法。本文根据某大型邮轮的刚度和质量分布，提出了一种钢制总振动试验模型的设计方法，设计了等比例模型和非等比例变态模型两种方案，并采用变态模型在空气中和水池中完成了模态试验，给出了有压载和无压载工况的干/湿模态的试验结果。结果表明，无论有、无压载，湿模态与对应干模态的固有频率的比值基本不变；对于同一阶模态，有压载工况与对应无压载工况的固有频率的比值也基本保持不变。钢制船体总振动试验模型能够更好地考虑附连水质量的影响，可为特殊船型的总振动模型设计和固有频率预报提供有价值的参考。

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通讯作者，E-mail：
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刘哲（1989-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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刘哲（1989-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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刘哲（1989-），男，博士研究生，高级工程师，通讯作者，E-mail：。

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articleId=1243253927202898532, language=CN, label=图12, caption=干模态振型计算结果, figureFileSmall=MtgHvoTNmVxQ4CQeOLGT8A==, figureFileBig=+9/cOJXYXB2Hw94fLLoHpg==, tableContent=null), ArticleFig(id=1243253937856430106, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Fig.13, caption=Test results of torsion modes, figureFileSmall=9UXGJfZ/LqaqcPnXHj80lw==, figureFileBig=oxoM0d7p67ROsTkmkgz9pA==, tableContent=null), ArticleFig(id=1243253938024202270, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=图13, caption=扭转振型测试结果, figureFileSmall=9UXGJfZ/LqaqcPnXHj80lw==, figureFileBig=oxoM0d7p67ROsTkmkgz9pA==, tableContent=null), ArticleFig(id=1243253938124865571, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.1, caption=

Calculation results of natural frequency of beams with rectangular cross-section

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次固有频率/Hz振型
原型梁缩比梁1缩比梁2
121.342.684.8一阶弯曲 (x-z)
242.484.884.8一阶弯曲 (x-y)
358.6116.9231二阶弯曲 (x-z)
4114.4228.2445.9三阶弯曲 (x-z)
5115.7231.0231.0二阶弯曲 (x-y)
6188375.0722.7四阶弯曲 (x-z)
), ArticleFig(id=1243253938263277606, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表1, caption=

矩形截面梁固有频率计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次固有频率/Hz振型
原型梁缩比梁1缩比梁2
121.342.684.8一阶弯曲 (x-z)
242.484.884.8一阶弯曲 (x-y)
358.6116.9231二阶弯曲 (x-z)
4114.4228.2445.9三阶弯曲 (x-z)
5115.7231.0231.0二阶弯曲 (x-y)
6188375.0722.7四阶弯曲 (x-z)
), ArticleFig(id=1243253938351357996, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.2, caption=

Calculation results of natural frequency of beams with circular cross-section

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次固有频率/Hz振型
原型梁（梁单元）原型梁（实体单元）缩比梁（梁单元）缩比梁（实体单元）
134.633.469.366.6一阶弯曲
234.633.969.367.4一阶弯曲
394.891.6189.6182.5二阶弯曲
494.892.8189.6184.5二阶弯曲
), ArticleFig(id=1243253938422661169, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表2, caption=

圆形截面梁固有频率计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次固有频率/Hz振型
原型梁（梁单元）原型梁（实体单元）缩比梁（梁单元）缩比梁（实体单元）
134.633.469.366.6一阶弯曲
234.633.969.367.4一阶弯曲
394.891.6189.6182.5二阶弯曲
494.892.8189.6184.5二阶弯曲
), ArticleFig(id=1243253938527518773, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.3, caption=

Main parameters of the large cruise ship

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值/单位参数名称数值/单位
总吨135 500 t载重吨（设计吃水）9745 t
总长323.6 m设计航速18.0 kn
垂线间长287.1 m最大航速22.6 kn
型宽37.2 m最大载员6538
最大船宽49.5 m最大高度72.2 m
设计吃水8.26 m最大甲板高度55.2 m
最大吃水8.55 m
), ArticleFig(id=1243253938686902333, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表3, caption=

某大型邮轮主要设计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值/单位参数名称数值/单位
总吨135 500 t载重吨（设计吃水）9745 t
总长323.6 m设计航速18.0 kn
垂线间长287.1 m最大航速22.6 kn
型宽37.2 m最大载员6538
最大船宽49.5 m最大高度72.2 m
设计吃水8.26 m最大甲板高度55.2 m
最大吃水8.55 m
), ArticleFig(id=1243253938754011203, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.4, caption=

Main parameters of the proportional scaling mode

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号实船模型惯性矩比质量比频率比
截面惯性矩/m4分段质量/t截面惯性矩/mm4结构质量/kg附加质量/kg
-32350268.41.3E+073.202.8E+078.3E+0454.6
-818502609.27.2E+078.41.72.6E+072.6E+05100.4
1625162802.08.7E+077.81.92.9E+072.9E+0599.9
4030192802.01.0E+087.91.63.0E+073.0E+0599.6
6431383024.31.1E+086.83.82.9E+072.9E+05100.1
8846483565.11.6E+089.43.02.9E+072.9E+0599.9
11247994891.11.7E+089.67.72.8E+072.8E+0599.9
13635514778.71.3E+088.88.12.8E+072.8E+05100.1
16047233702.01.7E+089.73.42.8E+072.8E+0599.7
18433393307.31.2E+087.44.22.9E+072.8E+0599.7
20833993241.71.1E+087.33.13.1E+073.1E+0599.8
23237993458.31.3E+089.03.42.8E+072.8E+0599.5
25662883576.82.1E+0813.103.0E+072.7E+0594.9
28063693518.41.9E+0813.003.3E+072.7E+0590.1
30442833077.01.5E+0810.20.52.9E+072.9E+0599.8
32838502704.41.3E+089.902.9E+072.7E+0598.0
35224092559.98.3E+078.60.32.9E+072.9E+0599.6
3769501894.73.5E+075.01.92.7E+072.7E+0599.9
400233821.98.1E+066.902.9E+071.2E+0564.1
41211610.2-0.40-2.4E+04-
总重量-56613.4-162.444.6---
), ArticleFig(id=1243253938854674505, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表4, caption=

等比例模型主要设计参数

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号实船模型惯性矩比质量比频率比
截面惯性矩/m4分段质量/t截面惯性矩/mm4结构质量/kg附加质量/kg
-32350268.41.3E+073.202.8E+078.3E+0454.6
-818502609.27.2E+078.41.72.6E+072.6E+05100.4
1625162802.08.7E+077.81.92.9E+072.9E+0599.9
4030192802.01.0E+087.91.63.0E+073.0E+0599.6
6431383024.31.1E+086.83.82.9E+072.9E+05100.1
8846483565.11.6E+089.43.02.9E+072.9E+0599.9
11247994891.11.7E+089.67.72.8E+072.8E+0599.9
13635514778.71.3E+088.88.12.8E+072.8E+05100.1
16047233702.01.7E+089.73.42.8E+072.8E+0599.7
18433393307.31.2E+087.44.22.9E+072.8E+0599.7
20833993241.71.1E+087.33.13.1E+073.1E+0599.8
23237993458.31.3E+089.03.42.8E+072.8E+0599.5
25662883576.82.1E+0813.103.0E+072.7E+0594.9
28063693518.41.9E+0813.003.3E+072.7E+0590.1
30442833077.01.5E+0810.20.52.9E+072.9E+0599.8
32838502704.41.3E+089.902.9E+072.7E+0598.0
35224092559.98.3E+078.60.32.9E+072.9E+0599.6
3769501894.73.5E+075.01.92.7E+072.7E+0599.9
400233821.98.1E+066.902.9E+071.2E+0564.1
41211610.2-0.40-2.4E+04-
总重量-56613.4-162.444.6---
), ArticleFig(id=1243253938930171982, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.5, caption=

Main parameters of the non-proportional scaling model model (Full-load condition)

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号实船模型惯性矩比质量比频率比
截面惯性矩/m4分段质量/t截面惯性矩/mm4结构质量/kg附加质量/kg
-32350268.42.2E+062.00.01.6E+081.3E+0528.7
-818502609.21.2E+076.41.01.6E+083.5E+0547.1
16251628021.5E+075.82.21.7E+083.5E+0545.0
40301928021.8E+076.02.01.7E+083.5E+0545.2
6431383024.31.9E+074.73.91.7E+083.5E+0545.8
8846483565.12.8E+076.83.41.6E+083.5E+0546.3
11247994891.12.9E+076.97.11.6E+083.5E+0546.2
13635514778.72.1E+076.27.41.7E+083.5E+0545.8
160472337022.9E+075.65.01.6E+083.5E+0546.6
18433393307.32.0E+076.23.21.7E+083.5E+0545.9
20833993241.72.1E+076.13.21.6E+083.5E+0546.8
23237993458.32.4E+075.04.91.6E+083.5E+0546.5
25662883576.83.9E+079.21.01.6E+083.5E+0546.7
28063693518.44.2E+079.90.21.5E+083.5E+0547.8
304428330772.8E+077.21.61.5E+083.5E+0548.2
32838502704.42.6E+077.20.51.5E+083.5E+0549.0
35224092559.91.5E+074.52.81.6E+083.5E+0546.3
3769501894.75.4E+064.50.91.8E+083.5E+0544.6
400233821.91.5E+062.70.01.6E+083.1E+0544.0
41211610.2——
总重量—56 613.4—112.850.5———
), ArticleFig(id=1243253939030835287, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表5, caption=

变态模型主要设计参数（满载工况）

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号实船模型惯性矩比质量比频率比
截面惯性矩/m4分段质量/t截面惯性矩/mm4结构质量/kg附加质量/kg
-32350268.42.2E+062.00.01.6E+081.3E+0528.7
-818502609.21.2E+076.41.01.6E+083.5E+0547.1
16251628021.5E+075.82.21.7E+083.5E+0545.0
40301928021.8E+076.02.01.7E+083.5E+0545.2
6431383024.31.9E+074.73.91.7E+083.5E+0545.8
8846483565.12.8E+076.83.41.6E+083.5E+0546.3
11247994891.12.9E+076.97.11.6E+083.5E+0546.2
13635514778.72.1E+076.27.41.7E+083.5E+0545.8
160472337022.9E+075.65.01.6E+083.5E+0546.6
18433393307.32.0E+076.23.21.7E+083.5E+0545.9
20833993241.72.1E+076.13.21.6E+083.5E+0546.8
23237993458.32.4E+075.04.91.6E+083.5E+0546.5
25662883576.83.9E+079.21.01.6E+083.5E+0546.7
28063693518.44.2E+079.90.21.5E+083.5E+0547.8
304428330772.8E+077.21.61.5E+083.5E+0548.2
32838502704.42.6E+077.20.51.5E+083.5E+0549.0
35224092559.91.5E+074.52.81.6E+083.5E+0546.3
3769501894.75.4E+064.50.91.8E+083.5E+0544.6
400233821.91.5E+062.70.01.6E+083.1E+0544.0
41211610.2——
总重量—56 613.4—112.850.5———
), ArticleFig(id=1243253939127304284, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.6, caption=

Added mass under no-load and full-load conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号空载工况/kg满载工况/kg肋位号空载工况/kg满载工况/kg
FR00.00.0FR115.14.9
FR10.01.0FR120.21.0
FR22.92.2FR130.70.2
FR32.42.0FR142.81.6
FR44.93.9FR151.10.5
FR53.13.4FR163.22.8
FR64.37.1FR170.70.9
FR75.37.4FR180.00.0
FR84.25.0FR190.20.1
FR93.73.2总质量47.750.6
FR103.13.2
), ArticleFig(id=1243253939236356194, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表6, caption=

空载工况和满载工况的附加质量

, figureFileSmall=null, figureFileBig=null, tableContent=
肋位号空载工况/kg满载工况/kg肋位号空载工况/kg满载工况/kg
FR00.00.0FR115.14.9
FR10.01.0FR120.21.0
FR22.92.2FR130.70.2
FR32.42.0FR142.81.6
FR44.93.9FR151.10.5
FR53.13.4FR163.22.8
FR64.37.1FR170.70.9
FR75.37.4FR180.00.0
FR84.25.0FR190.20.1
FR93.73.2总质量47.750.6
FR103.13.2
), ArticleFig(id=1243253939341213802, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.7, caption=

Modal test conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
工况1234
压载情况无压载无压载有压载有压载
干/湿模态干模态湿模态干模态湿模态
), ArticleFig(id=1243253939450265714, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表7, caption=

模态试验工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况1234
压载情况无压载无压载有压载有压载
干/湿模态干模态湿模态干模态湿模态
), ArticleFig(id=1243253939521568886, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.8, caption=

Modal test results of the cruise ship model

, figureFileSmall=null, figureFileBig=null, tableContent=
工况压载情况干/湿模态一阶弯曲振动固有频率/Hz二阶弯曲振动固有频率/Hz
1无压载干模态126.0283.8
2湿模态86.5196.0
3有压载干模态114.8267.4
4湿模态79.3184.5
), ArticleFig(id=1243253939609649276, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表8, caption=

邮轮模型的模态试验结果

, figureFileSmall=null, figureFileBig=null, tableContent=
工况压载情况干/湿模态一阶弯曲振动固有频率/Hz二阶弯曲振动固有频率/Hz
1无压载干模态126.0283.8
2湿模态86.5196.0
3有压载干模态114.8267.4
4湿模态79.3184.5
), ArticleFig(id=1243253939714506883, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=EN, label=Tab.9, caption=

Calculation results and test results of dry modes

, figureFileSmall=null, figureFileBig=null, tableContent=
振型计算值/Hz测试值/Hz偏差
一阶垂向弯曲131.0126.03.8%
二阶垂向弯曲300.7283.85.6%
一阶扭转165.1162.51.6%
二阶扭转191.8193.4-0.8%
), ArticleFig(id=1243253939810975882, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243253927202898532, language=CN, label=表9, caption=

干模态计算值与测试值

, figureFileSmall=null, figureFileBig=null, tableContent=
振型计算值/Hz测试值/Hz偏差
一阶垂向弯曲131.0126.03.8%
二阶垂向弯曲300.7283.85.6%
一阶扭转165.1162.51.6%
二阶扭转191.8193.4-0.8%
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大型邮轮总振动模型试验研究
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刘哲 1, 2 , 王纬波 1, 2 , 胡志宽 1, 2 , 杨智雄 1, 2
船舶力学 | 流体与结构声学 2025,29(7): 1147-1158
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船舶力学 | 流体与结构声学 2025, 29(7): 1147-1158
大型邮轮总振动模型试验研究
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刘哲1, 2 , 王纬波1, 2, 胡志宽1, 2, 杨智雄1, 2
作者信息
  • 1.中国船舶科学研究中心，江苏　无锡　214082
  • 2.船舶振动噪声重点实验室，江苏　无锡　214082

    • 刘哲（1989-），男，博士研究生，高级工程师，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Research on model test of global vibration of a large cruise ship
Zhe LIU1, 2 , Wei-bo WANG1, 2, Zhi-kuan HU1, 2, Zhi-xiong YANG1, 2
Affiliations
  • 1.China Ship Scientific Research Center, Wuxi 214082, China
  • 2.National Key Laboratory on Ship Vibration & Noise, Wuxi 214082, China
出版时间: 2025-07-20 doi: 10.3969/j.issn.1007-7294.2025.07.013
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摘要
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振动舒适性是评价大型邮轮乘客体验的关键技术指标之一。由于邮轮上层建筑高，与普通船型差异大，目前还没有成熟的总振动近似计算方法。本文根据某大型邮轮的刚度和质量分布，提出了一种钢制总振动试验模型的设计方法，设计了等比例模型和非等比例变态模型两种方案，并采用变态模型在空气中和水池中完成了模态试验，给出了有压载和无压载工况的干/湿模态的试验结果。结果表明，无论有、无压载，湿模态与对应干模态的固有频率的比值基本不变；对于同一阶模态，有压载工况与对应无压载工况的固有频率的比值也基本保持不变。钢制船体总振动试验模型能够更好地考虑附连水质量的影响，可为特殊船型的总振动模型设计和固有频率预报提供有价值的参考。

大型邮轮  /  总振动  /  固有频率  /  试验模型

Vibration comfort is one of the key technical indicators to evaluate the passenger experience of large cruise ships. Due to the high superstructure and the large difference from ordinary ship types, there is no mature approximate calculation method for global vibration of cruise ships. According to the stiffness and mass distribution of a large cruise ship, this paper proposes a design method for the steel global vibration test model, and designs two schemes: the equiscale model and the non-equiscale abnormal model. Then the abnormal model is used to complete the modal test in the air and the pool, and the test results of the dry/wet modes under the loading and unloading condition are given. The results show that the ratio of the natural frequencies of the wet mode to the corresponding dry mode is basically unchanged under the loading or unloading condition. For the same order mode, the ratio of the natural frequencies under the loading condition to the corresponding unloading condition also remains basically unchanged. The steel-hull global vibration test model can better consider the influence of added water mass, which can provide a valuable reference for the design of the global vibration model and the natural frequency prediction of special ship types.

large cruise ship  /  global vibration  /  natural frequency  /  test model
刘哲, 王纬波, 胡志宽, 杨智雄. 大型邮轮总振动模型试验研究. 船舶力学, 2025 , 29 (7) : 1147 -1158 . DOI: 10.3969/j.issn.1007-7294.2025.07.013
Zhe LIU, Wei-bo WANG, Zhi-kuan HU, Zhi-xiong YANG. Research on model test of global vibration of a large cruise ship[J]. Journal of Ship Mechanics, 2025 , 29 (7) : 1147 -1158 . DOI: 10.3969/j.issn.1007-7294.2025.07.013
正文
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0　引言
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大型豪华邮轮被誉为造船工业“皇冠上的明珠”，不仅建造难度大，对乘坐舒适性也提出了极高的要求，其中振动舒适性是最为关键的评价指标之一[1]，对邮轮的声学设计提出了巨大的挑战。船体结构的总振动预报是船舶结构声学设计中的基础性问题，总振动的固有频率要与主要的激励频率之间保持足够的频率储备，以避免产生结构的共振。船体共振不仅会造成结构的疲劳破坏，还会对振动舒适性产生严重的不良影响。由于总振动频率低，与全船结构和质量分布有关，一旦出现共振问题，治理难度非常大，因此必须在设计阶段尽可能给出准确的预报结果。
对于常规船型而言，船体总振动固有频率的预报方法非常成熟，主要有近似方法和有限元法等。对于不同的船型，不同国家的船级社和标准化组织都给出了总振动固有频率的近似计算公式，可以在方案设计阶段和技术设计阶段使用[2]，有些估算公式仅需要知道几个总体设计参数，就可以给出令人满意的结果。有限元方法则主要应用于详细设计阶段，可采用一维梁模型或三维空间模型进行计算。一维梁模型是将船体梁视为具有剪切和转动惯量的铁木辛柯梁，并将船体梁划分为若干段，每段按等截面梁来处理，需要事先准备剖面惯性矩、剖面剪切面积以及各段分布质量等输入数据，其中，最为关键的步骤是要根据外部型线估算各阶振型对应的附连水质量[3]。三维空间模型则需要根据图纸建立详细的船体结构有限元模型，附连水效应一般通过虚拟质量法模拟，或直接采用声学有限元等流-固耦合方法进行分析。大型邮轮总振动预报的困难在于，邮轮与普通船型差异大（上层建筑高，甲板层数多，总吨位大），各类标准规范的近似计算公式无法直接使用；此外，一维梁模型需要估算准确的附连水质量，而三维空间模型需要大量的输入数据，这些在早期设计阶段均难以实施。
模型试验是一种重要的结构动力学研究方法，在大型建筑、桥梁、水坝、海洋平台等重大装备和结构分析中得到了广泛的应用[4]。在船舶与海洋工程领域，模型试验最常应用于各类水池试验以获得船舶的水动力性能。在结构动力学分析方面，王均刚等[5]基于量纲分析法推导了海洋平台的相似模型设计条件，设计了满足固有频率相似的海洋平台试验模型。安延涛等[6-7]通过分析固有频率比相对误差的影响参数，提出了海洋平台动力学模型设计的实用方法，他们还研究了材料阻尼的影响，设计并建造了相似模型，开展了模态试验对理论分析结果进行验证。俞孟萨等[8]分析了弹性矩形板的结构振动和声辐射的相似条件。盛美萍等[9]分析了水下航行器实航振动级与全功率台架试验振动级之间的关系，给出了二者的振动相似律。但是，相似模型在船体总振动性能预报方面应用相对较少，主要是因为船体结构的几何相似性难以精确满足，特别是在厚度方向。何韫如等[10]推导了总振动固有频率的相似性判据，并采用钢制模型设计了一艘27 000 TEU集装箱船的总振动试验模型，但仅给出了截面惯性矩的设计计算结果，没有提供最终的试验结果。
在进行水动力船模设计时，船体结构的刚度特性通常是采用钢梁模拟，船体外形则采用分段的木质模型制作以准确考虑其水动力性能，一般不关心船体结构的振动响应，且无法考虑附连水质量的影响。本文首先对梁的干/湿模态的相似性关系进行了理论验证，然后提出了一种采用钢制船模进行总振动模型试验的方法，通过设计可基本保证船体梁的刚度和质量分布相似。由于船模外形与实船相似，因此可以更好地研究附连水质量的影响。同时设计了等比例模型和非等比例变态模型两种方案，并采用变态模型进行了模态试验，给出了有压载工况和无压载工况的干/湿模态的试验结果和误差分析。该方法同样适用于其他船型，可为特殊船型的总振动试验模型设计和固有频率预报提供有价值的参考。
1　船体梁总振动相似理论及验证
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1.1　船体梁总振动的相似关系
船体总振动相似关系的实现，是将船体结构看作是一条变截面梁，从而通过计算其振动特性来满足。对于大多数船型而言，弯曲振动是其最主要的振动形式。因此，对于总振动试验而言，模型设计的目标就是要保证缩比模型与原型两者的弯曲振动具有相似的固有频率和振型。
船体梁通常简化为变截面的铁木辛柯梁模型。当船体较为细长时，可以忽略剪切变形和转动惯量的影响，使用欧拉-伯努利梁模型。此时，梁振动的固有频率判据方程为[10]：
式中，λ表示梁弯曲振动的固有频率，L、A和I分别表示梁的长度、截面面积和截面惯性矩，ρ和E表示材料的密度和杨氏模量，下标m和s分别表示模型和实船。该方程只是模型与实船相似的必要条件。根据相似定理，要保证系统相似，还需要满足其他相似条件，即
（1）几何相似
要使试验模型严格满足几何相似关系十分困难（特别是厚度尺寸），根据固有频率判据方程（1）可知，如果能够保证梁的质量和刚度分布相似，振动模态就能够保持相似性。因此，几何相似条件可以适当放宽。
（2）材料相似
如果采用同一种材料（如钢材），则材料相似性便容易满足。此时，固有频率判据方程（1）可写为如下形式：
（3）边界条件相似
船体梁的总振动一般采用两端自由的边界条件，相似性容易满足。
（4）初始条件相似
船体梁的总振动一般不考虑初始条件，即初始位移为零，相似性容易满足。
船体梁的振动不仅包含船体结构自身的质量，还要考虑船舶装载质量和附连水质量的影响。由于截面尺寸通常无法保持几何相似，截面面积的相似性也无法满足，因此可将固有频率判据方程（2）写成如下形式：
式中，M表示包含了船体梁结构、船舶载重和附连水的总质量，即保证截面惯性矩和质量分布相似。在模型设计时，可优先保证截面惯性矩相似，再通过附加质量来调整质量分布，从而实现固有频率的相似。
1.2　总振动相似关系的数值验证
本节采用有限元方法对船体梁总振动固有频率的相似关系进行理论验证。首先，采用矩形截面梁对其干模态的频率相似律进行计算验证。原型梁和缩比梁长度和截面尺寸如下：
（1）原型梁：长5 m，矩形截面尺寸为0.1 m×0.2 m；
（2）缩比梁1：长2.5 m，矩形截面尺寸为0.05 m×0.1 m，x、y、z三向的几何缩尺比均为1:2；
（3）缩比梁2：长2.5 m，矩形截面尺寸为0.1 m×0.1 m，x、y、z三向的几何缩尺比分别为1:2、1:1和1:2。
这里，梁轴向为x方向，其中缩比梁1在x-z和x-y平面内的理论频率比均为2，缩比梁2在x-z平面内理论频率比为4，在x-y平面内理论频率比为2。上述各矩形梁固有频率计算结果如表1所示。可以看出，矩形截面梁在两个方向上的弯曲振动固有频率均满足式（2）的相似律。
其次，采用圆形截面梁对其湿模态的频率相似律进行计算验证。原型梁长5 m，截面为圆形，半径为0.1 m；模型缩比梁长2.5 m，截面为圆形，半径为0.05 m，梁完全浸没在水中，几何缩尺比为2，固有频率相似比理论值为2。梁单元采用两种方式进行建模，一是采用一维梁单元，二是采用三维实体单元。一维梁单元的流体负载在截面属性中直接定义，三维实体单元的梁则采用声学单元模拟外部流体的相互作用，在结构与流体的接触部位设置声-固耦合约束条件，流体的外表面通过声学无限单元模拟无穷远处的无反射边界条件，如图1所示（外部水域为球形，图中为便于显示进行了剖切）。
圆形截面梁的湿模态计算结果如表2所示。可以看出，三维实体单元和一维梁单元结果两者略有差异，但均满足振动固有频率的相似律，一维梁单元基本无偏差，三维实体单元的偏差不大于2%，主要来自于声-固耦合的计算误差。
2　大型邮轮总振动试验模型设计
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2.1　总振动试验模型设计流程
某大型邮轮总长323.6 m，总吨位约13.55×104 t，主要设计参数如表3所示，船体结构主要采用AH36高强度钢和铝合金材料。
为准确考虑附连水效应的影响，本文采用整体钢制模型方案，使船体外形与实船尽可能保持相似。为了满足刚度分布的要求，内部结构需要根据截面参数进行重新设计。最后根据刚度分布调整质量分布，从而满足模态相似的单值条件。由于水平弯曲和垂向弯曲振动相似条件无法同时满足，而且一般垂向振动更为重要，因此本文主要考虑垂向振动。
邮轮总振动试验模型设计的主要步骤如下：
（1）确定缩尺比
从模型试验的角度来说，模型总长度以2~4 m为宜[10]。为了便于计算，一般可取1:2、1:5、1:10、1:20、1:50或1:100等比例。邮轮总长度为322.7 m，本文选择1:100的缩尺比进行模型制作，船模长度约3.2 m，钢板厚度取3 mm。
（2）选择材料
常用的模型材料主要有钢、铝、有机玻璃以及玻璃钢等材料，邮轮的主要船体材料为船用钢，本文选择相同的钢材作为模型材质。
（3）简化型线
船体表面是一个复杂曲面，因为与外部水介质接触，对船体总振动有着重要影响。但对于总振动试验来说，由于模型大幅缩小，在保持型线基本相似的情况下，可对首尾线型进行适当简化，以方便模型加工。邮轮总振动试验模型简化的线型如图2所示。
（4）简化结构
实船内部的船体结构十分复杂，仅关心垂向振动时，横向构件可不予考虑，同时对纵向构件进行合并以减少构件数量。横向构件的设置主要考虑整体结构的刚度和强度，以保证模型能够表现出理想的振型。该邮轮共有19层甲板，且大部分甲板长度超过一半船长，试验模型共设计了两层甲板，主甲板大致与实船DECK 3对应，上甲板大致与实船DECK 12对应，外部的型线也进行了适当的简化，主要是去除了艏部的球鼻艏，并对艉部推进器附近的线型做了适当调整，如图3所示。
（5）核算惯性矩
这是总振动试验模型设计中最关键的一个步骤，主要由以下三个子步骤构成：
a）计算截面形心高度：
式中，Ami和Zmi分别表示模型中各构件的截面积和到基线的距离。
b）计算截面惯性矩（相对于形心主轴）：
式中，J表示模型中各构件自身的惯性矩。
c）计算截面惯性矩相似比：
这一过程通常较为繁琐，需要通过试凑的方法不断调整构件的布置和尺寸，使截面惯性矩满足设计要求。
（6）计算附加质量
根据实船的质量分布（包括结构质量和装载质量）和质量相似比，计算模型每个分段所需的附加质量。
式中，Msi表示实船各分段的总重量，CM表示质量相似比，Mmi、ΔMmi分别表示模型各分段的结构质量和附加质量。
2.2　总振动试验模型设计方案
根据上述总振动试验模型设计方法和流程，本文设计了两种船模方案：等比例模型方案和变态模型方案（非等比例）。
2.2.1　等比例模型方案
等比例模型方案的长、宽、高缩尺比均为1:100，模型长3272 mm，宽372 mm，高470 mm，结构总重约163 kg，附加质量为44.6 kg。模型由19个站位（FR0~FR18）加上首尾段共分成20段，其中FR0~FR16肋间距为174 mm，每个肋位均设有横向框架，框架高度为30 mm，理论频率比为100，如图4所示。
船体梁的截面参数和试验模型的设计参数如表4所示。可以看出，由于首尾刚度和质量分布悬殊，未进行折减，因此首尾两段设计误差较大，其他中间分段基本接近理论值。其中，模型的附加质量是为了保证其分段质量与实船保持相似。
根据本方案建立船模的声-固耦合有限元模型（如图5所示），通过模态计算可知，船模一阶垂向振动固有频率为248.4 Hz，二阶垂向振动固有频率为590.2 Hz。由于二阶固有频率过高，且与局部模态存在严重耦合（如图6所示），不利于试验模态的识别，因此本文又提出了一种非等比例的变态模型设计方案。
2.2.2　变态模型方案
为使试验模型能够表现出理想的前两阶弯曲振动模态，需要减小频率比。通过多种变态模型方案计算对比，最终长、宽、高的缩尺比分别取为1:100、1:100和1:200，此时前两阶垂向振动固有频率计算值分别为131.0 Hz和300.7 Hz，模态试验较容易识别。按照上述缩尺比对截面进行重新设计，变态模型总长度为3272 mm，宽372 mm，高235 mm，结构重量为112.8 kg，如图7所示。
空船和压载工况可通过调整附加质量来实现相似要求，模型试验通过铁砂来调整，以保证质量分布相似。满载工况下，截面参数和压载质量设计值如表5所示，惯性矩之比约为1.6×108，质量比约为3.5×105，理论频率比约为46.8。除首尾两个分段差别较大外，其他分段基本满足设计要求。两种压载工况的附加质量如表6所示。
3　大型邮轮总振动模型模态试验
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3.1　总振动模型模态试验概述
大型邮轮总振动模型试验采用上述变态船模开展，试验地点为中国船舶科学研究中心的小型室内水池。根据GB/T 11 349.2-2006《振动与冲击机械导纳的试验确定第3部分：冲击激励法》的试验程序，分别在空气中和水池中测量了模型的前两阶垂向弯曲振动的干模态和湿模态。
（1）测点布置
振动加速度响应测点分别布置在模型的FR0、FR2、FR4、FR6、FR8、FR10、FR12、FR14和FR16肋位处，左右对称布置2个，激励测点位于首部，共计19个测点，测量方向均为垂向，如图8所示（注：图中数字为测点编号，非肋位号）。
（2）试验工况
试验分为有压载和无压载两种工况，每种压载工况分别在空气中和水池中进行干模态和湿模态测试。因此共有四种试验工况（如表7），其中有压载工况吃水为40 mm，对应实船设计吃水状态。
（3）边界条件
模型采用粗制弹性橡皮绳进行自由悬吊，两个吊点接近1阶弯曲模态节点位置，如图9所示。通过敲击模型并测量结构振动的自由衰减信号，可知系统安装频率均小于1 Hz，远低于试验模型的一阶弯曲振动固有频率，满足自由约束条件。
3.2　总振动试验模型测试结果
大型邮轮总振动试验模型的模态测试结果如表8所示，对应的干模态和湿模态的前两阶弯曲振型分别如图10和图11所示，将试验结果除以频率比就能够得到实船的弯曲振动固有频率。因此，大型邮轮一阶弯曲振动固有频率约为1.7 Hz，二阶弯曲振动固有频率约为3.9 Hz。
分析试验结果可以发现：1）在有压载和无压载工况下，湿模态弯曲振动的固有频率均为对应干模态的69%左右；2）无论是干模态还是湿模态，对于一阶弯曲振动而言，有压载工况的固有频率均为对应无压载工况的91.5%左右；对于二阶弯曲振动而言，有压载工况的固有频率均为对应无压载工况的94%左右。
3.3　试验结果误差分析
船体总振动试验模型的预报结果主要有两个误差来源。第一，缩比模型的截面参数与设计值存在一定的误差，可以称作设计误差，会导致理论预测的频率相似比存在一定的偏差。第二，实际加工出来的试验模型与理论设计的模型存在一定的偏差，可以称作加工误差，会导致实际模型测量的固有频率与理论计算结果存在一定的偏差。
加工误差可以通过对比缩比模型的计算结果与实际模型的测试结果得到。在本次试验中，无压载工况下，试验模型前两阶垂向弯曲模态频率计算值和测试值对比情况如表9所示，计算得到模态振型如图12所示，测试得到的扭转模态振型如图13所示。
可以看出，前两阶垂向弯曲模态频率的相对偏差分别为3.8%和5.6%。由于有/无压载以及干/湿模态基本成比例变化，可以认为压载状态下湿模态的加工误差也与此相同，因此在进行实船固有频率预报时，可以将这部分偏差予以扣除。
4　结论
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本文对梁振动的干/湿模态的相似关系进行了理论验证，提出了一种船体总振动的钢制试验模型的设计方法，可以较好地考虑附连水质量的影响。根据某大型邮轮的质量和刚度分布，完成了总振动试验模型的设计和试验，并分析了主要的误差来源和修正方法。该方法同样适用于其他船型，可为特殊船型的总振动试验模型设计和固有频率预报提供参考。本文主要结论有：
（1）简单截面梁的干/湿模态在理论上均满足固有频率的相似关系；
（2）无论有无压载，大型邮轮湿模态与对应干模态的固有频率的比值基本不变（约为69%）；
（3）无论是干模态还是湿模态，对于同一阶模态，大型邮轮有压载工况与对应无压载工况的固有频率的比值基本不变，一阶弯曲振动的比值约为91.5%，二阶弯曲振动的比值约为94%。
基金
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  • 高技术远洋客船项目(MC-202011-C06)
文献
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2025年第29卷第7期
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文章信息
doi: 10.3969/j.issn.1007-7294.2025.07.013
  • 接收时间：2025-01-21
  • 首发时间：2026-03-24
  • 出版时间：2025-07-20
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  • 收稿日期：2025-01-21
基金
高技术远洋客船项目(MC-202011-C06)
作者信息
    1.中国船舶科学研究中心，江苏　无锡　214082
    2.船舶振动噪声重点实验室，江苏　无锡　214082

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2种不同金属材料的力学参数
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小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
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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
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