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Article(id=1243306312294056680, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243306309064442584, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.05.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1732032000000, receivedDateStr=2024-11-20, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774356924364, onlineDateStr=2026-03-24, pubDate=1747670400000, pubDateStr=2025-05-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774356924364, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774356924364, creator=13701087609, updateTime=1774356924364, 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=722, endPage=731, ext={EN=ArticleExt(id=1243306312566686446, articleId=1243306312294056680, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Numerical simulation of waves generated due to vertical motion of underwater shaking table, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

The motion of an underwater shaking table will make waves in water. In this paper, a numerical tank including wave maker, wave absorber and underwater shaking table was established and validated. Waves made by the vertical harmonic motion of the underwater shaking table were investigated. The velocity, dynamic water pressure and wave factors were discussed. This study aims to provide reference testing in coupled earthquake-wave-current environment and eliminating tank wave disturbance. The results show that (1) the water velocity of the center of the underwater shaking table in vertical direction increases with the increase of the vertical moving amplitude and the length of the shaking table while the velocity decreases with the increase of the period of the shaking table; (2) the distribution of dynamic water pressure above the center of the underwater shaking table depicts a trend of “decrease-first, increase-second” in the water depth direction; (3) the dynamic water pressure increases with the increase of the vertical moving amplitude of the shaking table; (4) the wave height increases with the increase of the vertical moving amplitude of the shaking table, and decreases with the increase of water depth; (5) and the wave period increases with the increase of the period of the shaking table while the wave length increases with the increase of the period of the shaking table and the water depth.

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水下振动台在运动过程中会引起兴波效应。本文建立并验证具有造波、消波功能并包含水下振动台的数值水槽，基于数值水槽探索水下振动台竖向简谐运动过程中的兴波过程，分析水体速度、动水压强及扰动波各要素的影响，旨在为地震-波流联合试验及水池扰动波消除提供参考。结果表明：振动台中心上方的竖向速度随振动台振幅、台长增大而增大，随振动台周期增大而减小；振动台中心上方的动水压强沿水深呈先减小、再增大的分布规律，其幅值随振动台振幅增大而增大；兴波波高随振动台振幅增大而增大，随水深增大而减小；兴波周期随振动台周期增大而增大；兴波波长随振动台周期、水深增大而增大。

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通讯作者，E-mail：
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燕翔（1988-），男，博士，副研究员

白志刚（1966-），男，博士，副教授，通讯作者，E-mail：。

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燕翔（1988-），男，博士，副研究员

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燕翔（1988-），男，博士，副研究员

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白志刚（1966-），男，博士，副教授，通讯作者，E-mail：。

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白志刚（1966-），男，博士，副教授，通讯作者，E-mail：。

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caption=自由水面的兴波波高变化规律, figureFileSmall=D7ukFBH5/eZNHw7xiLMcpQ==, figureFileBig=nYsHuV9rxPQ/gqoG7CnkRA==, tableContent=null), ArticleFig(id=1243306329708806258, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Fig.9, caption=Variation of wave period and wave length on free water surface, figureFileSmall=DVeJ4fkh6PtLLQl6T1bC5w==, figureFileBig=0WX8PxRo7E/yTwe4pic8hg==, tableContent=null), ArticleFig(id=1243306329775915130, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=图9, caption=自由水面的兴波周期与兴波波长变化规律, figureFileSmall=DVeJ4fkh6PtLLQl6T1bC5w==, figureFileBig=0WX8PxRo7E/yTwe4pic8hg==, tableContent=null), ArticleFig(id=1243306329855606910, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Tab.1, caption=

Working conditions of wavemaking

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工况造波板推幅/m造波板周期/s造波板加速度幅值/（m·s-2）水深/m数值波高/m理论波高/m波高误差/%
W-10.052.00.4920.1720.1710.585
W-20.102.00.9920.3280.3434.373
W-30.1222.01.2020.3810.4188.852
W-40.1752.41.2020.4710.4965.040
), ArticleFig(id=1243306329947881601, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=表1, caption=

造波工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况造波板推幅/m造波板周期/s造波板加速度幅值/（m·s-2）水深/m数值波高/m理论波高/m波高误差/%
W-10.052.00.4920.1720.1710.585
W-20.102.00.9920.3280.3434.373
W-30.1222.01.2020.3810.4188.852
W-40.1752.41.2020.4710.4965.040
), ArticleFig(id=1243306330073710725, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Tab.2, caption=

Cases with different motion amplitudes

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
D-10.052.03.02.0
D-20.102.03.02.0
D-30.152.03.02.0
D-40.202.03.02.0
D-50.252.03.02.0
), ArticleFig(id=1243306330178568329, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=表2, caption=

变振幅工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
D-10.052.03.02.0
D-20.102.03.02.0
D-30.152.03.02.0
D-40.202.03.02.0
D-50.252.03.02.0
), ArticleFig(id=1243306330270843021, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Tab.3, caption=

Cases with different motion periods

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
T-10.151.53.02.0
T-20.152.03.02.0
T-30.152.53.02.0
T-40.153.03.02.0
T-50.153.53.02.0
), ArticleFig(id=1243306330354729105, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=表3, caption=

变周期工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
T-10.151.53.02.0
T-20.152.03.02.0
T-30.152.53.02.0
T-40.153.03.02.0
T-50.153.53.02.0
), ArticleFig(id=1243306330430226581, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Tab.4, caption=

Cases with different table lengths

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
A-10.152.01.02.0
A-20.152.02.02.0
A-30.152.03.02.0
A-40.152.04.02.0
A-50.152.05.02.0
), ArticleFig(id=1243306330593804442, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=表4, caption=

变台长工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
A-10.152.01.02.0
A-20.152.02.02.0
A-30.152.03.02.0
A-40.152.04.02.0
A-50.152.05.02.0
), ArticleFig(id=1243306330728022175, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=EN, label=Tab.5, caption=

Cases with different water depths

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
H-10.152.03.01.0
H-20.152.03.01.5
H-30.152.03.02.0
H-40.152.03.02.5
H-50.152.03.03.0
), ArticleFig(id=1243306330820296868, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243306312294056680, language=CN, label=表5, caption=

变水深工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
H-10.152.03.01.0
H-20.152.03.01.5
H-30.152.03.02.0
H-40.152.03.02.5
H-50.152.03.03.0
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Cases with different table lengths and water depths while AXH unchanged

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工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
P-10.152.02.03.0
P-20.152.03.02.0
P-30.152.04.01.5
P-40.152.05.01.2
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变台长及水深工况（AXH保持不变）

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工况运动振幅D/m运动周期T/s台面长度A/m水深H/m
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P-30.152.04.01.5
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水下振动台竖向运动下的兴波数值模拟
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燕翔 1, 2 , 李棂繁 1 , 吴晓生 3 , 白志刚 1, 2 , 臧志鹏 1, 2 , 杨涵 1, 2
船舶力学 | 流体力学 2025,29(5): 722-731
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船舶力学 | 流体力学 2025, 29(5): 722-731
水下振动台竖向运动下的兴波数值模拟
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燕翔1, 2, 李棂繁1, 吴晓生3, 白志刚1, 2 , 臧志鹏1, 2, 杨涵1, 2
作者信息
  • 1.天津大学　水利工程智能建设与维护国家重点实验室，天津　300072
  • 2.中国地震局　地震工程综合模拟与城乡抗震韧性重点实验室，天津　300072
  • 3.中国船舶科学研究中心，江苏　无锡　214082

    • 燕翔（1988-），男，博士，副研究员

    白志刚（1966-），男，博士，副教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Numerical simulation of waves generated due to vertical motion of underwater shaking table
Xiang YAN1, 2, Ling-fan LI1, Xiao-sheng WU3, Zhi-gang BAI1, 2 , Zhi-peng ZANG1, 2, Han YANG1, 2
Affiliations
  • 1.State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin 300072, China
  • 2.Key Laboratory of Comprehensive Simulation of Earthquake Engineering and Urban Rural Seismic Resilience, China Earthquake Administration, Tianjin 300072, China
  • 3.China Ship Scientific Research Center, Wuxi 214082, China
出版时间: 2025-05-20 doi: 10.3969/j.issn.1007-7294.2025.05.005
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摘要
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水下振动台在运动过程中会引起兴波效应。本文建立并验证具有造波、消波功能并包含水下振动台的数值水槽，基于数值水槽探索水下振动台竖向简谐运动过程中的兴波过程，分析水体速度、动水压强及扰动波各要素的影响，旨在为地震-波流联合试验及水池扰动波消除提供参考。结果表明：振动台中心上方的竖向速度随振动台振幅、台长增大而增大，随振动台周期增大而减小；振动台中心上方的动水压强沿水深呈先减小、再增大的分布规律，其幅值随振动台振幅增大而增大；兴波波高随振动台振幅增大而增大，随水深增大而减小；兴波周期随振动台周期增大而增大；兴波波长随振动台周期、水深增大而增大。

水下振动台  /  竖向运动  /  兴波

The motion of an underwater shaking table will make waves in water. In this paper, a numerical tank including wave maker, wave absorber and underwater shaking table was established and validated. Waves made by the vertical harmonic motion of the underwater shaking table were investigated. The velocity, dynamic water pressure and wave factors were discussed. This study aims to provide reference testing in coupled earthquake-wave-current environment and eliminating tank wave disturbance. The results show that (1) the water velocity of the center of the underwater shaking table in vertical direction increases with the increase of the vertical moving amplitude and the length of the shaking table while the velocity decreases with the increase of the period of the shaking table; (2) the distribution of dynamic water pressure above the center of the underwater shaking table depicts a trend of “decrease-first, increase-second” in the water depth direction; (3) the dynamic water pressure increases with the increase of the vertical moving amplitude of the shaking table; (4) the wave height increases with the increase of the vertical moving amplitude of the shaking table, and decreases with the increase of water depth; (5) and the wave period increases with the increase of the period of the shaking table while the wave length increases with the increase of the period of the shaking table and the water depth.

underwater shaking table  /  vertical motion  /  wave making
燕翔, 李棂繁, 吴晓生, 白志刚, 臧志鹏, 杨涵. 水下振动台竖向运动下的兴波数值模拟. 船舶力学, 2025 , 29 (5) : 722 -731 . DOI: 10.3969/j.issn.1007-7294.2025.05.005
Xiang YAN, Ling-fan LI, Xiao-sheng WU, Zhi-gang BAI, Zhi-peng ZANG, Han YANG. Numerical simulation of waves generated due to vertical motion of underwater shaking table[J]. Journal of Ship Mechanics, 2025 , 29 (5) : 722 -731 . DOI: 10.3969/j.issn.1007-7294.2025.05.005
正文
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0　引言
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地震是对人类生活与生产危害最大且最频繁的自然灾害之一[1]。受欧亚地震带与环太平洋地震带影响，近年来我国东部沿海建设的海上风电、跨海大桥、海底隧道、近海平台等大型近海结构地处地震高危区，受海洋地震威胁严重。为了更加真实地模拟海洋地震环境，需开展地震-波流联合作用模拟。水下振动台是进行地震-波流联合作用模拟的重要试验设备，与无水振动台相比，水下振动台可以很好地实现水下地震的模拟，满足了涉水建筑物水下地震试验的环境需求，拓展了振动台的应用场景。然而，水下振动台的运动势必会造成兴波现象，影响地震-波流联合作用模拟精度，因此对水下振动台运动下的兴波特性进行探索十分必要。
现阶段，国内外学者对水下振动台的研究主要集中在水体-振动台相互作用、水体-模型耦合抗震研究等方面。吴昌聚等[2]计算了振动台台面在空气中及水下振动的谐响应，分析了振动台在无限流体域中的台面附加质量；沈润杰等[3]开展了大型宽频带水下振动台中运动部件的流固耦合动力学特性研究；牛志伟等[4]探究了台上水体对水下振动台反力基础动力响应的影响；李忠献等[5]依靠试验方法，探究了动水附加质量随振动台激励频率、激励幅值、水深的变化规律；郑人逢等[6-7]利用试验方法，对台面范围与台面中心至水池边界的水体振动特性、水下振动台竖向运动时水附加质量特征进行了研究；何晓宇等[8]分析了不同工况下流体附加质量效应及流固耦合效应对桩柱结构响应的影响，以及该影响随工作水深和波浪参数的变化规律；柳春光等[9]利用水下振动台模型试验，对深水斜拉桥主塔结构在地震作用下的动力响应进行了探究；Liu等[10]通过对斜拉桥桥塔群桩基础开展水下振动台试验，分析了地震、波浪和流共同作用下试验破坏过程中的水动力压力分布；Ding等[11]为研究地震-波流联合作用下桥墩的动力响应，开展了相应的水下振动台试验；张士博[12]开展了斜拉桥单塔结构在地震、波浪和海流单独/联合作用下的动力模型试验；吴堃[13]将深水桥墩作为研究对象，探究了地震作用下水与桥墩的相互作用机理及水下振动台试验的协调相似律；Yun等[14]为研究深水高桥墩整座桥梁的动力响应，开展了地震、波浪和流联合作用下的水下振动台试验。目前，关于水下振动台的研究，很少涉及水下振动台竖向运动下的兴波特性。
随着计算机性能的不断提高与计算数学理论的持续发展，数值方法现已成为研究问题与解决问题的重要手段之一[15]。与物理试验相比，数值水槽具有经济性高、比尺效应小等优点[16]。本文利用数值方法，建立并验证数值水槽，对水下振动台竖向运动过程中的兴波过程进行模拟，归纳总结水下振动台的运动振幅、运动周期、台面长度以及水池水深对水体速度、压强、波高、波长及波浪周期的影响，探究水下振动台竖向运动下的兴波特性。研究旨在为地震-波流联合试验及水池扰动波消除提供参考，技术路线如图1所示。
1　数值水槽
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1.1　控制方程与湍流模型
利用FLOW-3D构建数值水槽，采用k-ω湍流模型，基于独特的FAVOR网格技术，在连续性方程与动量方程中引入体积与面积分数参数。
连续性方程为
动量方程为
式中，Ax、Ay、Az分别为x、y、z方向的可流动面积分数，u、v、w分别为x、y、z方向的速度分量，ρ为流体密度，VF为可流动体积分数，p为压力，Gx、Gy、Gz分别为x、y、z方向的重力加速度，fx、fy、fz分别为x、y、z方向的粘滞力加速度。
1.2　数值水槽建立
构建兼具造波机与水下振动台的数值水槽，如图2所示，数值水槽净尺寸为61 m×0.1 m，槽深4 m。在数值水槽左端设造波机，右端设消波区，消波区长度大于1.4倍波长。水下振动台设于数值水槽槽底，水下振动台中心距右端消波区30.5 m，距造波机30.5 m。为实现二维模拟效果，造波机、水下振动台、消波区以及水槽内部尺寸在y方向长度均为0.1 m。
文中仿照造波机与水下振动台的实际工作原理，可分别控制水下振动台在z方向做运动形式为N(t)=-Dsinω1t的简谐运动，造波机在x方向做运动形式为X(t)=Asinω2t的简谐运动。其中：D、A分别为水下振动台、造波机的运动位移振幅；ω1、ω2分别为水下振动台、造波机的运动角频率。数值水槽的边界条件设置如下：数值水槽的Ymin端、Ymax端均设为对称边界条件，自由表面设为压力边界条件，其余各面均设为出流边界条件。初始时刻数值水槽内的水流速度为0，压强为静水压强，采用静水面作为初始化流场。
1.3　数值水槽验证
为保证数值模型的有效性，文中利用数值水槽分别对工况W-1至W-4进行模拟计算。通过选取距造波机20 m位置处稳定时段的波浪数据计算数值波高可知：工况W-1、工况W-2、工况W-3、工况W-4的数值波高分别为0.172 m、0.328 m、0.381 m、0.471 m，与利用波高方程[17]计算出的理论波高相比，误差小于10%，如表1所示。同时由图3可知：数值波面升高时程曲线与理论波面升高时程曲线拟合较好，消波区可有效吸收波浪能量，末端水面波动很小，数值水槽较为可靠。其中：波高误差=|（数值波高-理论波高）/理论波高|×100%。
1.4　网格敏感性分析
数值模拟精度主要取决于网格数量，一般网格数量越多，模拟精度越高，但是过多的网格数量通常会导致计算时间过长，浪费计算资源。本文主要研究x、z方向的水下振动台竖向运动兴波特性，综合考虑计算时长、计算精度、计算机性能等多方面因素，将y方向网格尺寸定为0.02 m。在此基础上，利用工况W-1、工况W-2、工况W-3及W-4对不同x、z方向网格尺寸下的计算精度进行探究，并绘制波高误差变化曲线，如图4所示。其中，x方向网格尺寸和z方向网格尺寸为1:1；波高误差为|（数值波高-理论波高）/理论波高|×100%。
依据图4可知：当x、z方向网格尺寸为0.02 m左右时，数值波浪高度与理论波浪高度之间的误差较小，在误差允许范围内。在尽可能减小误差的同时，为提高计算效率，本文x、y、z网格尺寸均选用0.02 m，因受计算机能力限制，且该尺寸下模拟精度较好，故本文不再对自由表面z方向网格进一步加密。
2　工况与测点
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水下振动台小幅运动过程中，振动台上方水体视为刚体（忽略水体粘性作用），水体动能与振幅、频率、台长、水深有关，若振幅、频率固定，水体能量跟台长与水深的乘积相关。
延长水下振动台左侧水槽，在造波机右侧增设消波区，消波区长度大于1.4倍波长，水下振动台中心至两侧消波区距离均为30.5 m，以水下振动台中心为坐标原点，水槽长度方向为x轴，水深方向为z轴构建坐标系，如图5所示。本文通过模拟表2~6中的水下振动台竖向运动过程，分析稳定时段位置X1、X2、X3的波浪数据及Z1、Z2、Z3的速度、动水压强数据，归纳总结各影响因素对速度、动水压强、波浪高度、波浪长度、波浪周期的影响。
3　结果与讨论
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3.1　 z方向速度
由于水下振动台中心上方水体的x方向速度远小于z方向（竖直方向）速度，故在此仅选取z方向速度进行分析。将测点Z1（x=0 m，z=0.5 m）、Z2（x=0 m，z=1.0 m）、Z3（x=0 m，z=1.5 m）作为研究对象，选取工况D-3（该工况下振动台运动规律与工况T-2、A-3、H-3、P-2相同）稳定时段（90~100 s）的数值计算结果，绘制速度时程变化曲线，如图6（b）所示，探究不同位置处z方向速度的变化规律。同时依据各工况的数值计算结果，绘制z方向速度幅值随水下振动台运动振幅、运动周期、台面长度变化曲线，归纳总结各变量对z方向速度的影响。
由图6可知，当水下振动台运动至平衡位置时，水下振动台上方水体的z方向速度明显大于水下振动台外侧水体的z方向速度，且自由水面的z方向速度沿水下振动台中心轴（x=0 m）呈对称分布，z方向速度大小相近，方向相同；z方向速度随时间呈周期性波动变化；当振幅、频率、水深固定时，随着台长增大，振动台中心上方水体的z方向速度幅值具有逐渐增大的变化趋势；水下振动台中心上方水体的z方向速度幅值随水下振动台运动振幅增大而增大，随水下振动台运动周期增大而减小。上述现象原因分析如下：考虑水体的不可压缩性，振动台中心上方（x=0）水体的速度等于振动台的运动速度，振动台运动速度随振幅增大而增大，随周期增大而减小，因此水体z方向速度也随振幅增大而增大，随周期增大而减小。
3.2　动水压强
选取测点Z1、Z2、Z3的水体作为研究对象，探究水下振动台的运动振幅、运动周期、台面长度对动水压强的影响，依据动水压强时程变化曲线，归纳总结动水压强的变化规律。
依据图7可知，水下振动台中心上方的动水压强随时间呈周期性波动变化；当振幅、频率、水深固定时，随着台长增大，水下振动台中心上方的动水压强幅值先增大后减小；水下振动台中心上方的动水压强幅值随水下振动台运动振幅增大而增大，随水下振动台运动周期增大无统一变化趋势。此外，从图中可发现动水压强幅值具有“中间位置（Z2）小、两头位置（Z1、Z3）大”的特点。振动台的兴波原理与造波机存在差异，前者是因为底部运动造成的水体涌出，当水下振动台在池底作竖向简谐运动时，台面会对水体产生一定的冲击力及吸力，且距振动台面越近的水体受到的影响越大。因此，随着距自由水面距离的增大，动水压强出现了中间小、两头大的特征现象。
3.3　兴波波高
将测点X1（x=0 m，自由水面）、X2（x=10 m，自由水面）、X3（x=20 m，自由水面）的波高作为研究对象，在工况D-3的条件下，选取稳定时段的数值结果，绘制波面升高随时间变化曲线，如图8（a）所示，探究不同位置处的波高变化规律。依据各工况的数值计算结果，绘制波高随水下振动台运动振幅、运动周期、台面长度、水深的变化曲线，归纳总结各变量对兴波波高的影响。
依据图8可知，与水下振动台外侧水体相比，水下振动台中心上方水体的波面升高更大；兴波波高随水下振动台运动振幅增大而增大；随振动台运动周期增大，振动台上方波高与振动台外侧波高变化趋势存在差异；水下振动台中心上方自由水面的兴波波高随水下振动台台面长度增大具有先逐渐增大、后趋于平稳的变化特点；随着水池水深增大，兴波波高总体呈现出逐渐减小的变化趋势。上述现象主要原因分析如下：当水深与台长之比较大时，振动台上方水体无法再被视为简单刚体，台面运动带动的水体范围有限，故兴波波高随水深与台长之比减小而增大，当水深与台长之比减小至振动台可带动上方全部水体运动时，振动台中心上方兴波波高不会继续随水深与台长之比减小而改变。
3.4　兴波周期与兴波波长
由图9可知，兴波周期仅与水下振动台运动周期有关，兴波周期与水下振动台运动周期成正比，与水下振动台运动振幅、台面长度、水深无关；兴波波长随水下振动台运动振幅改变无明显变化，随水下振动台运动周期增大而增大，随水深增大而增大；当振幅、频率、水深固定，台长增大时，兴波波长不随台长变化而改变；当振幅、频率固定，台长与水深乘积为定值时，兴波波长随台长增大而减小。由色散方程可知，波数与水深、周期均为负相关，故波长随水深、周期增大而增大。
4　结论
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本文构建了兼具造波、消波功能并包含水下振动台的数值水槽，利用造波模拟与理论结果对比，验证了数值水槽的可靠性，基于数值水槽开展了水下振动台竖向运动下的兴波特性研究，探讨了水体速度、动水压强及扰动波各要素的变化规律，旨在为地震-波流联合试验及水池扰动波消除提供参考。主要结论如下：
（1）振动台中心上方的竖向速度随时间呈周期性波动变化，竖向速度幅值随振动台振幅增大而增大，随振动台周期增大而减小。
（2）振动台中心上方的动水压强沿水深呈先减小、后增大的变化趋势，动水压强幅值随振动台振幅增大而增大。
（3）兴波波高随振动台振幅增大而增大，随水深增大而减小。随着台长增大，水下振动台中心上方的兴波波高具有先增大、后趋于平稳的变化特点。
（4）兴波周期与振动台周期成正比；兴波波长与振动台周期、水深呈正相关。
基金
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  • 天津市科技计划项目(23ZYYYJC00010)
  • 河北省自然科学基金资助项目(E2022402074)
  • 中国地震局地震工程综合模拟与城乡抗震韧性重点实验室开放课题(EESSR24-05)
文献
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2025年第29卷第5期
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doi: 10.3969/j.issn.1007-7294.2025.05.005
  • 接收时间：2024-11-20
  • 首发时间：2026-03-24
  • 出版时间：2025-05-20
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  • 收稿日期：2024-11-20
基金
天津市科技计划项目(23ZYYYJC00010)
河北省自然科学基金资助项目(E2022402074)
中国地震局地震工程综合模拟与城乡抗震韧性重点实验室开放课题(EESSR24-05)
作者信息
    1.天津大学　水利工程智能建设与维护国家重点实验室，天津　300072
    2.中国地震局　地震工程综合模拟与城乡抗震韧性重点实验室，天津　300072
    3.中国船舶科学研究中心，江苏　无锡　214082

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