船舶声弹性力学理论及其应用

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doi:10.6052/1000-0992-16-031

邹明松^{1, 2, 3,,},
吴有生^{1, 2, 3}

1.
中国船舶科学研究中心, 江苏无锡 214082
2.
深海载人装备国家重点实验室, 江苏无锡 214082
3.
船舶振动噪声重点实验室, 江苏无锡 214082

详细信息

作者简介:
吴有生, 中国首批工程院院士, 船舶力学国际知名专家, 创造性地建立了广义三维线性船舶水弹性力学理论.长期投身于船舶水动力学与结构力学交叉领域的研究.在舰艇抗爆抗冲击技术领域、船舶水弹性力学/声弹性力学理论与工程应用领域、新型高性能船舶及深海装备的研究与设计方面都取得丰硕成果.现任国际水动力学学术会议执行委员会主席, 总装备部科技委兼职委员、国防科工局科技委委员与船舶分委员会副主任、中国船级社技术咨询与评议委员会主席、中国船舶重工集团军工专家咨询委员会副主任, 上海交通大学、武汉理工大学、哈尔滨工程大学等高校的兼职教授, 无锡市发展决策咨询顾问.现致力于我国海洋运载工程与科技发展战略及产业发展战略的研究, 促成了“蛟龙”号7 000 m载人深潜器的立项并进一步提出了发展深海装备技术的建议和设想

通讯作者:
邹明松, 浙江海宁人, 师从吴有生院士、司马灿研究员, 2014年获中国舰船研究院船舶与海洋结构物设计制造专业博士学位, 2016年获江苏省优秀博士学位论文.将船舶三维水弹性理论与水声信道理论相结合, 建立了船舶三维声弹性理论. 2015年应邀在圣彼德堡召开的第八届“当代海军与造船”国际会议上就相关研究作大会报告.现任中国船舶科学研究中心高级工程师, 硕士生导师, 主要从事船舶三维水弹性/声弹性理论、舰船减振降噪研究与设计以及结构设计的工作, 主持完成总装预研重大项目1项(被评为优秀) 以及其余各类科研项目多项.在国内外学术刊物和会议上发表论文30余篇, 担任国际SCI期刊Journal of Hydrodynamics和Ocean Engineering审稿人.曾获中船重工集团科学技术一等、二等奖、无锡市自然科学优秀学术论文特等奖等奖项.E-mail:zoumings@126.com

中图分类号:O427.5, U661.44
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- 被引次数:0
出版历程
- 收稿日期:2016-09-22
- 网络出版日期:2017-01-18
- 刊出日期:2017-02-24

Sono-elasticity of ships and the related applications

ZOU Mingsong^{1, 2, 3,,},
WU Yousheng^{1, 2, 3}

1.
China Ship Scientific Research Center, Wuxi 214082, Jiangsu, China
2.
State Key Laboratory of Deep-sea Manned Vehicles, Wuxi 214082, Jiangsu, China
3.
National Key Laboratory on Ship Vibration and Noise, Wuxi 214082, Jiangsu, China

More Information

Corresponding author:ZOU Mingsong

摘要

摘要:船舶结构与水介质耦合动力学在改善船舶运动性能与结构安全性, 控制船舶振动噪声与提高水下声隐身性能, 进行船舶综合性能的优化设计等一系列工程问题中有广泛的应用需求与发展前景.本文综述了船舶水弹性力学、声弹性力学的理论方法、试验技术与应用技术的国内外研究进展; 介绍了在带航速三维水弹性力学理论(Wu 1984) 基础上, 作者所在课题组近年来发展的船舶三维声弹性理论、计算技术及工程应用的概况.简述了船舶三维声弹性理论的部分应用情况及发展方向.
- 船舶/
- 流固耦合/
- 水弹性力学/
- 声弹性理论/
- 计算技术/
- 试验技术
Abstract:Dynamics of coupled fluid-structure interaction of ships has great demand for applications, and vast vistas in improving motion behavior and structural safety, controlling vibration and noise, and enhancing stealth capability of ships. In this paper, we summarize the status-of-the-art of theoretical and experimental developments of ship hydroelasticity and ship sono-elasticity, as well as applied techniques. We briefly describe the results obtained by the authors' research group in the three-dimensional sono-elasticity theory based on a three-dimensional hydroelasticity theory (Wu 1984), the improvements of computational techniques, and the extensions in engineering applications. Some future directions are also discussed.
- ships/
- fluid-structure interaction/
- hydroelasticity/
- sono-elasticity/
- computational techniques/
- experimental techniques

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图 1整体弹性材料船模的水池试验照片(CSSRC). (a) S175船型的船模试验, (b) 一艘驱逐舰的船模试验

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图 2(a) 典型超大型浮动平台三维效果图, (b) 3个300m长半潜式模块柔性连接的超大型浮动平台示意图, (c) 等深海底与变深海底环境中0度浪向规则波作用下平台垂向动变形幅值沿全长分布的比较(Yang et al. 2015)

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图 3船舶以12节航速迎浪航行, 不规则波海况为H_1/3=3.25 m,T₀₁=7.53 s (田超2007). (a) 1 500 t SWATH海洋调查船, (b) 横舱壁上von Mises应力分布的线性解, (c) 横舱壁上von Mises应力分布的考虑瞬时湿表面变化的非线性解

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图 4环形实肋板连接的无限长双层加肋圆柱壳声辐射计算模型(吴文伟等2002)

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图 5某实船9.8节航速下, 艏部声呐自噪声计算与实测比对(俞孟萨2007). (a) 艏部声呐罩外形, (b) 艏部声呐罩自噪声测量示意图, (c) 艏部声呐自噪声谱级计算与实测结果比对

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图 6半径为0.5 m的单层弹性球壳水下声辐射考核算例(Zou et al. 2010). (a) 计算模型及坐标系示意图, (b) 无界流场环境中位于(r,θ) 处场点的声压级数值结果与解析解的比对

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图 7Pekeris波导模型及其Green函数的近似级数表达式的验证(Zou et al. 2012). (a) 海水和海底为参数不同的理想声介质的Pekeris波导模型, (b) 源点和场点相对位置满足要求时, 近似Green函数计算精度考核

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图 8外壳半径为0.65 m内壳半径为0.5 m的双层弹性球壳水下声辐射考核算例(邹明松和吴有生2012). (a) 计算模型及坐标系示意图, (b) 无界流场中(r=100,θ=π) 处场点的声压换算的声源级数值结果与解析结果的比对

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图 9用MANS方法预报总长为22 m的圆柱壳模型水下声辐射的比较结果(邹明松2014). (a) 计算模型, (b) 1号点施加垂向单位力激励时无界流场中辐射噪声声源级的比对结果

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图 10加筋圆柱壳模型水下声辐射全频域计算结果的比较(Zou & Wu 2015). (a) 半径为2.5m的加筋圆柱壳及激励点, (b) 用声弹性理论数值方法、MANS方法和SEA方法预报辐射噪声声源级的比对结果

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图 11消除不规则频率的虚拟阻抗封闭曲面法. (a) 虚拟阻抗曲面及内外流场示意图, (b) 半径为0.5m的球体刚体平动对应的无量纲声抗(采用边长为b的立方体虚拟阻抗曲面, 其阻抗值取为流体特征阻抗)

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图 12THAFTS-Acoustic 1.0软件后处理功能的示例. (a) 包络船体的圆柱面上的声压级云图, (b) 包络船体的圆柱面上的声强云图

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图 13电磁激振机激励的半径为0.36 m的加筋圆柱壳的水下声辐射考核试验(邹明松2014). (a) 新安江水库开阔水域中试验模型吊放及水听器布置示意图, (b) 模型吊放现场照片, (c) 水听器场点1/3Oct声压谱级比对结果

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图 14由两个舱室组成总长约19 m的实尺度船体水下声辐射考核试验(邹明松2014). (a) 船体在水池中的试验位置, (b) 移动扫描测量船体辐射声功率的由48对双水听器构成的环形声强传感器阵, (c) 在舱内机械设备激励下由船体辐射声功率换算的声源级比对结果(因水池环境限制, 有效测试频段在100 Hz以上)

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图 15有限水深环境中一艘LNG船的低频声波驻波现象. (a) 计算对象, (b) 计算取不同水深h时, 船体一阶垂向弯曲振动对应的无量纲化附连水质量(Zou et al. 2013)

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图 16一艘小水线面双体船在机械激励下的水下辐射噪声. (a) 典型模态(下潜体内外摆动) 振型示例, (b) 推进电机和主辅发电机激励下场点声压换算的声源级比对结果(Zou et al. 2014)

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图 17不同水深潜深环境下船体水平剖面内的声场分布云图(邹明松2014). (a) 水深65m, 潜深30m; (b) 水深500m, 潜深250m

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图 18潜水器尾部结构减振优化(Sun & Zou 2015). (a) 潜水器尾部结构横向摇摆的典型模态振型, (b) 尾部框架结构改进前后振动速度响应比对, (c) 潜水器试验照片

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参考文献 (211)

[1]	布列霍夫斯基. 1983.海洋声学.北京:科学出版社 Brekhovskikh L M. 1983. Ocean Acoustics. Beijing:Science Press
[2]	陈美霞, 骆东平, 陈小宁, 蔡敏波, 周锋. 2003.有限长双层壳体声辐射理论及数值分析.中国造船, 44:59-67http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC200304010.htm Chen M X, Luo D P, Chen X N, Cai M B, Zhou F. 2003. Theoretical and numerical analysis on sound radiation of a finite double shell. Shipbuilding of China, 44: 59-67http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC200304010.htm
[3]	陈清坤, 陈美霞, 和卫平, 高菊. 2010.舱壁与压载对流场中有限长圆柱壳声辐射影响.舰船科学技术, 32: 21-25http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201011005.htm Chen Q K, Chen M X, He W P, Gao J. 2010. Impact of bulkhead and ballast on acoustic radiation of submerged finite cylindrical shell. Ship Science and Technology, 32: 21-25http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201011005.htm
[4]	陈书明, 王登峰, 曹晓琳, 昝建明. 2010.车内噪声FE-SEA混合建模及分析方法.振动工程学报, 23: 140-144http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201002003.htm Chen S M, Wang D F, Cao X L, Zan J M. 2010. Hybrid FE-SEA modeling and analysis method of car interior noise. Journal of Vibration Engineering, 23: 140-144http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201002003.htm
[5]	陈徐均. 2001.浮体二阶非线性水弹性力学分析方法.[博士论文].无锡:中国船舶科学研究中心 Chen X J. 2001. Second order hydroelasticity analyses for marine structure.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[6]	陈燕, 汤渭霖, 范军. 2010.浅海波导中目标回声计算的射线声学方法.声学学报, 35: 335-342http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA201003009.htm Chen Y, Tang W L, Fan J. 2010. The geometrical acoustic method for calculating the echo targets submerged in a shallow water waveguide. Acta Acustica, 35: 335-342http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA201003009.htm
[7]	陈越澎. 1999.加筋柱壳的声学设计方法研究.[博士论文].武汉:华中理工大学 Chen Y P. 1999. Research on acoustic design method of stiffened cylindricalshell.[PhD Thesis]. Wuhan: Huazhong University of Science and Technology
[8]	崔宏武, 赵德有, 罗志雍, 宗智. 1990.结构振动的水中声辐射计算.中国造船, 31: 49-54http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199004006.htm Cui H W, Zhao D Y, Luo J Y, Zong Z. 1990. Numerical calculation of underwater acoustic radiation by structure vibration. Shipbuilding of China, 3: 49-54http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199004006.htm
[9]	丁宏, 陈美霞. 2011.基于统计能量法的双层圆柱壳振动与声性能分析//第十三届船舶水下噪声学术讨论会论文集, 鹰潭, 138-146 Ding H, Chen M X. 2011. Analysis of vibro-acoustic characteristics of double cylindrical shells by using statistical energy method//Proceedings of the 13th Conference on Underwater Noise of Ships, Yingtan, 138-146
[10]	丁渭平. 2002.车身乘坐室声振耦合的动态子结构修改方法.噪声与振动控制, 2: 17-19http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK200202006.htm Ding W P. 2002. A new dynamic substructure modification method for structure-acoustic coupling analysis of an automobile's passenger compartment. Noise and Vibration Control, 2: 17-19http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK200202006.htm
[11]	董艳秋, 林维学, 朱建国. 1989.浅吃水肥大船波激振动研究.中国造船, 1: 76-83http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC198901008.htm Dong Y Q, Lin W X, Zhu J G. 1989. A study on wave-excited vibration of shallow draft fullform ship. Shipbuilding of China, 1: 76-83http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC198901008.htm
[12]	杜双兴. 1990.海洋浮体结构的直接分析方法-三维线性水弹性随机分析理论及应用.[硕士论文].无锡:中国船舶科学研究中心 Du S X. 1990. Direct analysis method of the ocean floating bodies-the random analysis theory and application of linear three-dimensional hydroelasticity.[Master Thesis]. Wuxi: China Ship Scientific Research Center
[13]	杜双兴. 1996.完善的三维航行船体线性水弹性力学频域分析方法.[博士论文].无锡:中国船舶科学研究中心 Du S X. 1996. Perfect frequency domain analysis method of linear three-dimensional hydroelasticity of ships with forward speed.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[14]	杜双兴, 林吉如. 1993. 25000G/T浮动船坞拖航中运动和结构动应力的水弹性分析.舰船性能研究, 4: 43-58 Du S X, Lin J R. 1993. Hydroelastic analysis of the movement and structure dynamic stress of a 25000G/T floating dock during towage. Research on Ship Performance, 4: 43-58
[15]	杜双兴, 吴有生. 1998. Bessho型移动脉动源格林函数快速数值积分法.中国造船, 2: 40-48http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199802006.htm Du S X, Wu Y S. 1998. A fast evaluation method for the Bessho form translating-pulsating source Green's function. Shipbuilding of China, 2: 40-48http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199802006.htm
[16]	范军. 2001.水中复杂目标回声特性研究.[博士论文].上海:上海交通大学 Fan J. 2001. Study on echo characteristics of underwater complex targets.[PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[17]	范军, 刘涛, 汤渭霖. 2003.水中双层无限长圆柱壳体声散射.声学学报, 28: 345-350http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200304009.htm Fan J, Liu T, Tang W L. 2003. Acoustic scatter from double infinite concentric cylindrical shells in water. Acta Acustica, 28: 345-350http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200304009.htm
[18]	范威, 范军, 陈燕. 2012.浅海波导中目标散射的边界元方法.声学学报, 37: 132-142http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA201202004.htm Fan W, Fan J, Chen Y. 2012. Boundary element method for target scattering in shallow water waveguide. Acta Acustica, 37: 132-142http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA201202004.htm
[19]	顾懋祥, 吴有生, 夏锦祝. 1987.波浪中弹性船舶对称响应的时域分析.舰船性能研究, 4: 31-44 Gu M X, Wu Y S, Xia J Z. 1987. Time domain analysis of symmetric response of elastic ships in waves. Research on ship performance, 4: 31-44
[20]	何祚镛. 2001.结构振动与声辐射.哈尔滨:哈尔滨工程大学出版社 He Z Y. 2001. Vibration and Acoustic Radiation of Structures. Harbin: Harbin Engineering University Press
[21]	胡宗军, 牛忠荣, 程长征, 周焕林. 2010.三维Helmholtz积分方程外问题几乎奇异积分的半解析算法.应用力学学报, 27: 532-537http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201003021.htm Hu Z J, Niu Z R, Cheng C Z, Zhou H L. 2010. A semi-analytical algorithm for nearly singular integral of three dimensional exterior Helmholtz integral equation problem. Chinese Journal of Applied Mechanics, 27: 532-537http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201003021.htm
[22]	嵇醒, 臧跃龙, 程玉民. 1997.边界元法进展及通用程序.上海:同济大学出版社 Ji X, Zhang Y L, Cheng Y M. 1997. Progress of Boundary Element Method and General Program. Shanghai: Tongji University Press
[23]	姜琳, 赵德有. 2008.浅海波导中椭球体声散射特性研究.大连理工大学学报, 48: 528-532http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200804013.htm Jiang L, Zhao D Y. 2008. Study of acoustic scattering from ellipsoids in shallow water wave-guide. Journal of Dalian University of Technology, 48: 528-532http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200804013.htm
[24]	李善德, 黄其柏, 张潜. 2011.快速多极边界元方法在大规模声学问题中的应用.机械工程学报, 47: 82-89http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201107013.htm Li S D, Huang Q B, Zhang Q. Application of fast multipole boundary element method for large-scale acoustic problems. Journal of Mechanical Engineering, 47: 82-89http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201107013.htm
[25]	黎胜. 2001.水下结构声辐射和声传输的数值分析及主动控制模拟研究.[博士论文].大连:大连理工大学 Li S. 2001. Numerical analysis and active control simulation of underwater structural acoustic radiation and transmission.[PhD Thesis]. Dalian: Dalian University of Technology
[26]	黎胜, 赵德有. 2000.用边界元法计算结构振动辐射声场.大连理工大学学报, 40: 391-394http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200004003.htm Li S, Zhao D Y. 2000. Calculation of acoustic field radiated by vibrating structures using BEM. Journal of Dalian University of Technology, 40: 391-394http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200004003.htm
[27]	李小瑜, 傅志方. 1989.结构振动辐射声场的预估--边界积分方程中奇异积分的间接处理.振动工程学报, 2: 59-65http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC198901007.htm Li X Y, Fu Z F. 1989. Pre-estimation of sound field radiated by a vibrating structure-singular integral processing method in boundary integral equation. Journal of Vibration Engineering, 2: 59-65http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC198901007.htm
[28]	林吉如, 郑苏龙, 孙勇, 章一军, 王雅洁. 1992.整体弹性船模试验技术.中国造船, 2: 63-71http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202006.htm Lin J R, Zheng S L, Sun Y, Zhang Y J, Wang Y J. 1992. Experimental techniques of the continued elastic model. Shipbuilding of China, 2: 63-71http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202006.htm
[29]	刘国利, 汤渭霖. 1996.平面声波斜入射到水中无限圆柱的纯弹性共振散射.声学学报, 21: 506-516http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA6S1.013.htm Liu G L, Tang W L. 1996. Pure elastic resonance scattering of an obliquely incident plane acoustic wave by a submerged infinite cylinder. Acta Acustica, 21: 506-516http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA6S1.013.htm
[30]	刘涛. 2002.水中复杂壳体的声-振特性研究.[博士论文].上海:上海交通大学 Liu T. Research on sound and vibration characteristics of complex cylindrical shell submerged in water.[PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[31]	刘涛, 汤渭霖, 何世平. 2003.数值/解析混合方法计算含复杂结构的有限长圆柱壳体声辐射.船舶力学, 7: 99-104http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200304013.htm Liu T, Tang W L, He S P. 2003. Computation of sound radiation from complicated cylindrical shell by using numerical analytical matching method. Journal of Ship Mechanics, 7: 99-104http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200304013.htm
[32]	刘兴章. 2011.美国潜艇水声试验场现状及启示.舰船科学技术, 33: 140-143http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201102036.htm Liu X Z. 2011. Development prospect and revelation of submarine underwater noise test ground of US navy. Ship Science and Technology, 33: 140-143http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201102036.htm
[33]	刘兴章, 陈涛. 2011.挪威海格纳斯潜艇水声试验场测量设施分析.噪声与振动控制, 5: 161-164http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK201105039.htm Liu X Z, Chen T. 2011. Analysis of facilities of Norwegian acoustic testing field in Heggernes. Noise and Vibration Control, 5: 161-164http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK201105039.htm
[34]	骆东平, 肖邵予, 曹钢, 郭华林. 2004.甲板刚度和垂向位置对环肋圆柱壳声辐射性能的影响.哈尔滨工程大学学报, 25: 605-609http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200405013.htm Luo D P, Xiao S Y, Cao G, Guo H L. 2004. Vibroacoustic influence of the stiffness and location of the floating deck to cylindrical shell. Journal of Harbin Engineering University, 25: 605-609http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200405013.htm
[35]	彭旭. 2004.敷设阻尼层潜艇舱段结构声辐射性能分析.[硕士论文].武汉:华中科技大学 Peng X. Analysis of structure-borne noise of submarine compartment coated with viscoelastic layer.[Master Thesis]. Wuhan: Huazhong University of Science and Technology
[36]	祁立波. 2015.桨-轴-艇体耦合振动声辐射的三维声弹性分析方法.[博士论文].无锡:中国船舶科学研究中心 Qi L B. 2015. Three-dimensional sono-elastical analysis method of propeller-shaft-hull coupled vibration and acoustic radiation of a ship.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[37]	祁立波, 邹明松. 2015.加肋圆柱体水下低频辐射声特性研究.船舶力学, 19: 874-883http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201507014.htm Qi L B, Zou M S. 2015. Research on acoustic radiation of stiffened cylinder in low-frequency. Journal of Ship Mechanics, 19: 874-883http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201507014.htm
[38]	商德江. 2000.复杂弹性壳体水下结构振动和声场特性研究.[博士论文].哈尔滨:哈尔滨工程大学 Shang D J. 2000. Research on sound and vibration characteristics of complex elastic shell submerged in water.[PhD Thesis]. Harbin: Harbin Engineering University
[39]	沈顺根, 李琪华, 王大云, 程贯一. 1992.加肋旋转壳结构噪声声辐射水弹性研究.中国造船, 117: 53-62http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202005.htm Shen S G, Li Q H, Wang D Y, Cheng G Y. 1992. Hydroelastic analysis of sound radiation from a stiffened shell of revolution. Shipbuilding of China, 117: 53-62http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202005.htm
[40]	宋竞正, 任慧龙, 戴仰山. 1995.船体非线性波浪载荷的水弹性分析.中国造船, 2: 22-31http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199502002.htm Song J Z, Ren H L, Dai Y S. 1995. Hydroelastic analysis of nonlinear wave-induced loads of ship hull. Shipbuilding of China, 2: 22-31http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199502002.htm
[41]	孙丽萍. 2004.能量有限元法研究及其应用.[博士论文].哈尔滨:哈尔滨工程大学 Sun L P. 2004. Investigation and application of energy finite element method.[PhD Thesis]. Harbin: Harbin Engineering University
[42]	谭林森, 骆东平, 吴崇健, 伏同先. 1999.潜水器动力舱振动与声辐射.华中理工大学学报, 27: 7-9http://www.cnki.com.cn/Article/CJFDTOTAL-HZLG199911002.htm Tan L S, Luo D P, Wu C J, Fu T X. 1999. The vibration and sound radiation of submarine dynamic cabin. J. Huazhong Univ. of Sci. & Tech., 27: 7-9http://www.cnki.com.cn/Article/CJFDTOTAL-HZLG199911002.htm
[43]	汤渭霖. 1999.用物理声学方法计算界面附近目标的回波.声学学报, 24: 1-5http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA199901000.htm
[44]	Tang W L. 2001. Calculation of acoustic scattering from object near an interface using physical acoustic method. Acta Acustica, 24: 1-5https://www.researchgate.net/publication/294216724_Calculation_of_acoustic_scattering_from_object_near_an_interface_using_physical_acoustic_method
[45]	汤渭霖, 范军. 1999.水中双层弹性球壳的回声特性.声学学报, 24: 174-182http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA199902008.htm Tang W L, Fan J. 1999. Echoes from double elastic spherical shell in water. Acta Acustica, 24: 174-182http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA199902008.htm
[46]	汤渭霖, 何兵蓉. 2001.水中有限长加肋圆柱壳体振动和声辐射近似解析解.声学学报, 26: 1-5http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200101000.htm Tang W L, He B R. 2001. Approximate analytic solution of vibration and sound radiation from stiffened finite cylindrical shells in water. Acta Acustica, 26: 1-5http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200101000.htm
[47]	田宝晶. 2006.敷设阻尼层的加肋圆柱壳辐射性能及噪声特性分析.[博士论文].哈尔滨:哈尔滨工程大学http://cdmd.cnki.com.cn/Article/CDMD-10217-2006133439.htm Tian B J. 2006. Cylindrical shells with viscoelastic layer and noise characteristics analysis.[PhD Thesis]. Harbin: Harbin Engineering Universityhttp://cdmd.cnki.com.cn/Article/CDMD-10217-2006133439.htm
[48]	田超. 2007.航行船舶的非线性水弹性理论与应用研究.[博士论文].上海:上海交通大学 Tian C. 2007. Study on the theory and applications of nonlinear hydroelasticity of ships with forward speed. [PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[49]	王大云. 1996.三维船舶水弹性力学的时域分析方法.[博士论文].无锡:中国船舶科学研究中心http://d.wanfangdata.com.cn/Thesis_Y204979.aspx Wang D Y. 1996. Time domain analysis method of three-dimensional hydroelasticity of ships.[PhD Thesis]. Wuxi: China Ship Scientific Research Centerhttp://d.wanfangdata.com.cn/Thesis_Y204979.aspx
[50]	王桂波, 彭临慧. 2005.浅海波导中刚性球声散射特性研究.中国海洋大学学报, 35: 515-520http://www.cnki.com.cn/Article/CJFDTOTAL-QDHY200503036.htm Wang G B, Peng L H. 2005. Studies on scattering from a rigid sphere in a shallow water wave-guide. Periodical of Ocean University of China, 35: 515-520http://www.cnki.com.cn/Article/CJFDTOTAL-QDHY200503036.htm
[51]	王旌生. 2007.黏弹性复合材料结构水中振动和声辐射特性研究.[博士论文].上海:上海交通大学 Wang J S. 2007. Study on the vibration and acoustic properties of submerged composite material and composite structures.[PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[52]	王振鸿, 吴文伟, 徐敏, 席亦农. 1999.船舶在波浪中的水平弯曲-扭转耦合响应水弹性分析.中国造船, 40: 42-47http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199902006.htm Wang Z H, Wu W W, Xu M, Xi Y N. 1999. Hydroelasticity analysis of horizontal bend-torsion coupled responses of ships in waves. Shipbuilding of China, 40: 42-47http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199902006.htm
[53]	王志军. 2001.箱式超大型浮体结构的水弹性响应研究.[博士论文].上海:上海交通大学 Wang Z J. 2001. Study on hydroelastic response of box-type very large floating structure.[PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[54]	吴文伟, 沈荣瀛, 沈顺根. 2004.设备基座输入机械阻抗工程估算方法.振动工程学报, 17: 694-697 Wu W W, Shen R Y, Shen S G. 2004. An engineering approach to evaluate the input impedance of the machine foundation. Journal of Vibration Engineering, 17: 694-697
[55]	吴文伟, 吴崇健, 沈顺根. 2002.双层加肋圆柱壳振动和声辐射研究.船舶力学, 6: 44-51http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200201005.htm Wu W W, Wu C J, Shen S G. 2002. Study of the vibroacoustic radiation from the reinforced double cylindrical shells. Journal of Ship Mechanics, 6: 44-51http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200201005.htm
[56]	吴轶钢. 2008.零阶能量有限元方法及其在船舶结构声辐射中的应用研究.[博士论文].武汉:武汉理工大学 Wu Y G. 2008. The research on zero-order energy flow analysis and its application in structural acoustic problems of ship structure.[PhD Thesis]. Wuhan: Wuhan University of Technology
[57]	吴有生. 1999.世纪之交的船舶力学.上海:上海交通大学出版社, 353-399 Wu Y S. 1999. Ship Mechanics at the Beginning of the 21st Century. Shanghai: Shanghai Jiao Tong University Press, 353-399
[58]	吴有生, 司马灿, 刘建湖. 2007.船舶结构耦合动力学问题//第九届全国振动理论及应用学术会议论文集, 杭州, 25-31 Wu Y S, Sima C, Liu J H. 2007. Fluid-structure interaction problems of ships//Proceedings of the 9th National Conference on Vibration Theory and Application, Hangzhou, 25-31
[59]	吴有生, 夏锦祝, 王朝晖, 刘应中. 1994.船舶波浪砰击的二维非线性水弹性力学分析.中国船舶科学研究中心技术报告 Wu Y S, Xia J Z, Wang C H, Liu Y Z. Two-dimensional nonlinear hydroelastic analysis of wave slamming of ships. China Ship Scientific Research Center Reports
[60]	夏锦祝. 1994.细长浮体的水弹性力学理论.[博士论文].无锡:中国船舶科学研究中心 Xia J Z. 1994. Hydroelasticity theories of slenser floating structures.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[61]	夏锦祝, 吴有生. 1993.流固耦合问题的一个一般交界面条件.舰船性能研究, 3: 15-22 Xia J Z, Wu Y S. 1993. A general interface condition of the fluid-structure interaction problems. Research on Ship Performance, 3: 15-22
[62]	向树红, 邱吉宝, 王大钧. 2004.模态分析与动态子结构方法新进展.力学进展, 34: 289-303http://lxjz.m.koryoan.com/CN/abstract/abstract132720.shtml Xiang S H, Qiu J B, Wang D J. 2004. The resent progresses on modal analysis and dynamic sub-structure method. Advances in Mechanics, 34: 289-303http://lxjz.m.koryoan.com/CN/abstract/abstract132720.shtml
[63]	谢基榕. 2011.推进器激励下的艇体声辐射及其控制技术研究.[博士论文].无锡:中国船舶科学研究中心 Xie J R. 2011. Propeller excitated noise radiation of ship hull structure.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[64]	谢永和, 李润培, 杨建民. 2006.水深对超大型FPSO水弹性响应的影响.上海交通大学学报, 40: 993-996http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT200606025.htm Xie Y H, Li R P, Yang J M. 2006. The effects of water depth on hydroelastic response of a very large FPSO. Journal of Shanghai Jiaotong University, 40: 993-996http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT200606025.htm
[65]	徐向东. 1996.舰船结构冲击屈曲破损机理.[硕士论文].无锡:中国船舶科学研究中心 Xu X D. Damage mechanism of impact buckling of ship structures.[Master Thesis]. Wuxi: China Ship Scientific Research Center
[66]	杨士莪. 1994.水声传播原理.哈尔滨:哈尔滨工程大学出版社 Yang S E. 1994. Principle of Underwater Acoustic Propagation. Harbin: Harbin Engineering University Press
[67]	姚熊亮, 计方, 钱德进, 明磊. 2009.壳间连接介质对双层壳声辐射性能的影响.声学技术, 28: 312-317http://www.cnki.com.cn/Article/CJFDTOTAL-SXJS200903027.htm Yao X L, Ji F, Qian D J, Ming L. 2009. The effect of linked materials on the sound radiation from double cylindrical shell. Technical Acoustics, 28: 312-317http://www.cnki.com.cn/Article/CJFDTOTAL-SXJS200903027.htm
[68]	姚熊亮, 钱德进, 张爱国, 张阿漫. 2008.内部含基座的加筋双层壳振动与声辐射计算.中国舰船研究, 3: 31-36http://www.cnki.com.cn/Article/CJFDTOTAL-JCZG200801009.htm Yao X L, Qian D J, Zhang A G, Zhang A M. 2008. Computation of vibration and sound radiation from double cylindrical shell coupled with frame. Chinese Journal of Ship Research, 3: 31-36http://www.cnki.com.cn/Article/CJFDTOTAL-JCZG200801009.htm
[69]	姚熊亮, 王献忠, 孙龙泉, 庞福振. 2011.复杂结构中频声振问题的方法研究.振动工程学报, 24: 444-449http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201104018.htm Yao X L, Wang X Z, Sun L Q, Pang F Z. 2011. The hybrid method for vibro-acoustic problem of the complex structure. Journal of Vibration Engineering, 24: 444-449http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201104018.htm
[70]	叶永林. 2012.波浪中航行船体结构振动与噪声的水弹性分析.[博士论文].无锡:中国船舶科学研究中心 Ye Y L. 2012. Hydroelastic analysis of the structural vibration and noise radiation of a ship traveling in wave.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[71]	叶永林, 吴有生, 尤国红. 2010.小水线面双体船波浪外载荷分析//北京造船工程学会学术交流论文集, 53-60 Ye Y L, Wu Y S, You G H. 2010. Analysis of SWATH ship wave loads//Proceeding of the Beijing Society of Naval Architects and Marine Engineers Conference, 53-60
[72]	叶永林, 邹明松, 周金华, 吴有生, 尤国红. 2011.基于三维水弹性力学的浮体结构机械阻抗分析.中国造船, 52: 53-60http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC201101008.htm Ye Y L, Zou M S, Zhou J H, Wu Y S, You G H. 2011. Mechanical impedance analysis by 3D hydroelasticity method. Shipbuilding of China, 52: 53-60http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC201101008.htm
[73]	殷学纲, 陈淮, 蹇开林. 1991.结构振动分析的子结构方法.北京:中国铁道出版社 Yin X G, Chen H, Jian K L. 1991. Substructure Method for Structure Vibration Analysis. Beijing: China Railway Publishing House
[74]	殷学文. 2001.敷设消声瓦的双层加筋圆柱壳结构的振动和声辐射研究.[硕士论文].无锡:中国船舶科学研究中心 Yin X W. 2001. Research on vibration and acoustic radiation of stiffened double cylindrical shells coated with anechoic tile.[Master Thesis]. Wuxi: China Ship Scientific Research Center
[75]	尤云祥, 潘文峰, 缪国平. 2007.三维海洋波导中Helmholtz方程外问题的数值解.上海交通大学学报, 41: 830-834http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT200705034.htm You Y X, Pan W F, Miao G P. 2007. The numerical solution for the exterior problem of the Helmholtz equation in 3D ocean waveguide. Journal of Shanghai Jiaotong University, 41: 830-834http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT200705034.htm
[76]	俞孟萨. 2007.舰船随机声弹性理论及声纳罩声学设计研究.[博士论文].无锡:中国船舶科学研究中心 Yu M S. 2007. Theory of random acoustoelasticity for ships and its application in acoustic design of sonar domes.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[77]	曾革委. 2004.无限长双层加肋圆柱壳水下声辐射解析计算.振动工程学报, 17: 1010-1013 Zeng G W. 2004. Acoustic radiation from fluid-loaded infinite circular cylindrical double-shell. Journal of Vibration Engineering, 17: 1010-1013
[78]	张健飞, 姜弘道. 2003.大型边界元方程组的并行直接分块求解算法.应用力学学报, 20: 129-133http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200304029.htm Zhang J F, Jiang H D. A parallel direct block algorithm for large-scale BEM equation system. Chinese Journal of Applied Mechanics, 20: 129-133http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200304029.htm
[79]	张敬东, 何祚镛. 1990.有限元+边界元--修正的模态分解法预报水下旋转薄壳的振动和声辐射.声学学报, 15: 12-19http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA199001002.htm Zhang J D, He Z Y. 1990. A finite element+boundary element-modified modal decomposition method for vibration and sound radiation from submerged revolutional shells. Acta Acustica, 15: 12-19http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA199001002.htm
[80]	张瑾, 马兴瑞, 韩增尧, 邹元杰. 2012.中频力学环境预示的FE-SEA混合方法研究.振动工程学报, 25: 206-214http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201202017.htm Zhang J, Ma X R, Han Z Y, Zou Y J. FE-SEA hybrid method for the mid-frequency dynamic prediction. Journal of Vibration Engineering, 25: 206-214http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201202017.htm
[81]	赵键, 汪鸿振, 朱物华. 1989.边界元法计算已知振速封闭面的声辐射.声学学报, 14: 250-257http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA198904001.htm Zhao J, Wang H Z, Zhu W H. Boundary element method for calculating acoustic radiation from closed surfaces with prescribed velocity distribution. Acta Acustica, 14: 250-257http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA198904001.htm
[82]	郑国垠, 范军, 汤渭霖. 2009.充水有限长圆柱薄壳声散射: I.理论.声学学报, 34: 490-497 Zheng G Y, Fan J, Tang W L. Acoustic scattering from fluid-filled finite cylindrical shell in water: I. theory. Acta Acustica, 34: 490-497
[83]	郑国垠, 范军, 汤渭霖. 2010.充水有限长圆柱薄壳声散射: Ⅱ.实验.声学学报, 35: 31-37 Zheng G Y, Fan J, Tang W L. Acoustic scattering from fluid-filled finite cylindrical shell in water: Ⅱ.experiment. Acta Acustica, 35: 31-37
[84]	朱克强, 郑道昌, 周江华, 刘桂云, 包雄关. 2005.典型高速船的非线性水弹性响应.宁波大学学报(理工版), 18: 458-462http://www.cnki.com.cn/Article/CJFDTOTAL-NBDZ200504011.htm Zhu K Q, Zheng D C, Zhou J H, Liu G Y, Bao X G. 2005. Nonlinear hydroelasticity response of representative high speed ship. Journal of Ningbo University (NSEE), 18: 458-462http://www.cnki.com.cn/Article/CJFDTOTAL-NBDZ200504011.htm
[85]	周海安, 王晓明, 梅玉林. 2012.流固耦合的周期加强板的振动及声辐射研究.力学学报, 44: 287-296http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201202014.htm Zhou H A, Wang X M, Mei Y L. 2012. Theoretical analysis of the vibration and sound radiation from an infinite fluid-structure coupled plate stiffened by two-dimensional periodic structures. Chinese Journal of Theoretical and Applied Mechanics, 44: 287-296http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201202014.htm
[86]	邹春平, 陈端石, 华宏星. 2004.船舶水下辐射噪声特性研究.船舶力学, 8: 113-124http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200401014.htm Zou C P, Chen D S, Hua H X. Study on characteristics of ship underwater radiation noise. Journal of Ship Mechanics, 8: 113-124http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200401014.htm
[87]	邹明松. 2012.敷设声学覆盖层的双层加筋圆柱壳结构声辐射建模及声特性研究.中国船舶科学研究中心技术报告 Zou M S. 2012. Research on acoustic radiation of stiffened double cylindrical shells covered with acoustic layers. China Ship Scientific Research Center Reports
[88]	邹明松. 2014.船舶三维声弹性理论.[博士论文].无锡:中国船舶科学研究中心 Zou M S. 2014. Three-dimensional sono-elasticity of ships.[PhD Thesis]. Wuxi: China Ship Scientific Research Center
[89]	邹明松, 刘艳敏, 祁立波. 2013.舷间充水双层弹性薄球壳结构声辐射研究.船舶力学, 17: 155-163http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX2013Z1021.htm Zou M S, Liu Y M, Qi L B. 2013. Structural-acoustic radiation of elastic thin spheric double-shell with contained water. Journal of Ship Mechanics, 17: 155-163http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX2013Z1021.htm
[90]	邹明松, 吴文伟, 余晓丽, 廖彬彬. 2013.静水压下声学覆盖层声阻抗研究.舰船科学技术, 35: 57-60http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201303014.htm Zou M S, Wu W W, Yu X L, Liao B B. 2013. Calculation of acoustic coating's impedance under hydrostatic pressure. Ship Science and Technology, 35: 57-60http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201303014.htm
[91]	邹明松, 吴有生. 2012.多不连通流域耦合的声介质中三维结构水弹性力学研究.中国造船, 53: 85-94http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC201203011.htm Zou M S, Wu Y S. 2012. Three dimensional hydroelasticity analysis of acoustic responses of structures coupled with multiply-disconnected fluid regions. Shipbuilding of China, 53: 85-94http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC201203011.htm
[92]	邹明松, 吴有生. 2014.水弹性子结构分离及集成方法.船舶力学, 18: 574-580http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201405012.htm Zou M S, Wu Y S. 2014. A method used for separating and coupling substructure based on hydroelasticity theory and dynamic substructural theory. Journal of Ship Mechanics, 18: 574-580http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201405012.htm
[93]	邹明松, 吴有生, 祁立波, 周金华. 2013.声介质中水弹性力学消除不规则频率的方法.船舶力学, 17: 1202-1208http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201310014.htm Zou M S, Wu Y S, Qi L B, Zhou J H. 2013. Method to eliminate irregular frequencies in three-dimensional hydroelasticity in acoustic medium. Journal of Ship Mechanics, 17: 1202-1208http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201310014.htm
[94]	邹明松, 吴有生, 沈顺根, 吴文伟. 2010.考虑航速及自由液面影响的声介质中三维结构水弹性力学研究.船舶力学, 14: 1304-1311http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201011015.htm Zou M S, Wu Y S, Shen S G, Wu W W. 2010. Three-dimensional hydroelasticity with forward speed and free surface in acoustic medium. Journal of Ship Mechanics, 14: 1304-1311http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX201011015.htm
[95]	邹元杰. 2004.水中阻尼复合壳体结构声振特性的数值分析.[博士论文].大连:大连理工大学 Zou Y J. 2004. Numerical analysis of vibro-acoustic characteristics of underwater damped composite shells. [PhD Thesis]. Dalian: Dalian University of Technology
[96]	邹元杰, 赵德有. 2004.结构在浅水中的振动和声辐射特性研究.振动工程学报, 17: 269-274http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200403003.htm Zou Y J, ZhaoD Y. 2004. A vibro-acoustic study on structures in shallow water. Journal of Vibration Engineering, 17: 269-274http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200403003.htm
[97]	Abawi A T. 2011. The use of the virtual source technique in computing scattering from periodic ocean surface.J. Acoust. Soc. Am., 130: 683-688.doi:10.1121/1.3613707
[98]	Abawi A T, Porter M B. 2007. Propagation in an elastic wedge using the virtual source technique. J. Acoust. Soc. Am., 121: 1374-1382.doi:10.1121/1.2431336
[99]	Achenbach J D, Kechter J D, Xu Y L. 1988. Off boundary approach to the boundary element method. Comput. Mech. Appl. Mech. Engng., 70: 191-201.doi:10.1016/0045-7825(88)90157-0
[100]	Astley R J, Macaulay G J. 1994. Mapped wave envelope element for acoustic radiation and scattering. J. of Sound and Vibration, 170: 97-117.doi:10.1006/jsvi.1994.1048
[101]	Belik O, Bishop R E D, Price W D. 1980. On the slamming response of ships to regular head waves. Trans. RINA, 122: 325-337.
[102]	Bessho M. 1977. On the fundamental singularity in the theory of ship motions in a seaway. Memoirs of the Defense Academy of Japan, 17: 95-105.
[103]	Bishop R E D, Price W G. 1979. Hydroelasticity of Ships. Cambridge University Press.
[104]	Bishop R E D, Price W G, Temarel P. 1980. A unified dynamic analysis of antisymmetric ship response to waves, Suppl. Papers RINA, 122: 349-365.
[105]	Bishop R E D, Price W G, Temarel P. 1991. A theory on the loss of the MV Derbyshire. Trans. RINA, 133: 389-453.
[106]	Bishop R E D, Price W G, Wu Y S. 1986. A general linear hydroelasticity theory of floating structures moving in a seaway. Phil. Trans. Royal Soc. London., 316: 375-426.doi:10.1098/rsta.1986.0016
[107]	Bjarnason J, Igusa T, Choi S H, Achenbach J D. 1994. The effect of substructures on the acoustic radiation from axisymmetric shells of finite length.J. Acoust. Soc. Am., 96: 246-255.doi:10.1121/1.410477
[108]	Borlase G A, Vlahopoulos N. 2000. An energy finite element optimization process for reducing high-frequency vibration in large-scale structures. Finite Element in Analysis and Design, 36: 51-67.doi:10.1016/S0168-874X(00)00007-X
[109]	Bouthier O M, Bernhard R J. 1995. Simple models of the energetics of transversely vibrating plates. Journal of Sound and Vibration, 182: 149-1666.doi:10.1006/jsvi.1995.0187
[110]	Burnett D S, Holford R L. 1998. Prolate and oblate spheroidal acoustic infinite element. Comput. Methods Appl. Mech. Eng., 158: 117-141.doi:10.1016/S0045-7825(97)00251-X
[111]	Burroughs C B. 1984. Acoustics radiation from fluid loaded infinite circular cylinders with doubly periodic ring supports. J. Acoust. Soc. Am.. 75: 715-722.doi:10.1121/1.390582
[112]	Burton A J, Miller G F. 1971. The application of the integral equation method to the numerical solution of some exterior boundary value problems. Proc. R. Soc. Lond. A., 323: 201-210.doi:10.1098/rspa.1971.0097
[113]	Cabos C, Jokat J. 1998. Computation of structure-borne noise propagation in ship structures using noiseFEM. In: Proceedings PRADS98, Osterveld and Tan eds. Elsevier, 927-934.
[114]	Cao X T, Hua H X, Ma C. 2012. Acoustic radiation from shear deformable stiffened laminated cylindrical shells. Journal of Sound and Vibration, 331: 651-670.doi:10.1016/j.jsv.2011.10.006
[115]	Che X L, Riggs H R, Ertekin R C, Wu Y S, Wang M L. 1992. Two-dimensional analysis of prying response of twin-hull floating structures//Proceeding of Second International Offshore & Polar Engineering Conference, ISOPE'92.
[116]	Chen J T, Chang M H, Chen K H, Lin S R. 2002. The Boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function. Journal of Sound and Vibration, 257: 667-711.doi:10.1006/jsvi.2002.5038
[117]	Chen L H, Schweikert D G. 1963. Sound radiation from an arbitary body. J. Acoust. Soc. Am., 35: 1626-1632.doi:10.1121/1.1918770
[118]	Chen X J, Wu Y S, Cui W C, Tang X F. 2003. Nonlinear hydroelastic analysis of a moored floating body. Ocean Engineering, 30: 965-1003.doi:10.1016/S0029-8018(02)00078-1
[119]	Choi S B, Pierre C, Castanier M P. 1997. Statistical energy methods for mid-frequency vibration analysis//Proceeding 1997 SAE noise and Vibration Conference and Exposition, Traverse City, MI, USA.
[120]	Choi S H, Igusa T, Achenbach J D. 1995. Nonaxisymmetric vibration and acoustic radiation of submerged cylindrical shell of finite length containing internal substructures. J. Acoust. Soc. Am., 98: 353-362.doi:10.1121/1.413689
[121]	Dowell E H, Kubota Y. 1985. Asymptotic modal and statistical energy analysis of dynamical systems. J. Applied Mech., 52: 949-957.doi:10.1115/1.3169174
[122]	Du S X, Ertekin R C. 1991. Dynamic response analysis of a flexibly joined Multimodule very large floating structure//OCEANS'91, USA.
[123]	Epton M, Dembart B. 1995. Multipole translation theory for the three dimensional Laplace and Helmholtz equations. SIAM Journal scientific Computing, 16: 865-897.doi:10.1137/0916051
[124]	Everstine G C, Henderson F M. 1990. Coupled finite element/boundary element approach for fluid-structure interaction. J. Acoust. Soc. Am., 87: 1938-1947.doi:10.1121/1.399320
[125]	Fahy F, Gardonio P. 2007. Sound and Structural Vibration-Radiation, Transmission and Response, Second Edition. Oxford: Academic Press in an imprint of Elsevier.
[126]	Fredo C R. 1997. A SEA-like approach for the derivation of energy flow coefficients with a finite element model. Journal of Sound and Vibration, 199: 645-666.doi:10.1006/jsvi.1996.0634
[127]	Giordano J A, Koopmann G H. 1995. State space boundary element-finite element coupling for fluidstructure interaction analysis. J. Acoust. Soc. Am., 98: 363-372.doi:10.1121/1.413691
[128]	Gladwell G M L. 1964. Branch mode analysis of vibrating systems. Journal of Sound and Vibration, 1: 41-59.doi:10.1016/0022-460X(64)90006-9
[129]	Gu M X, Wu Y S, Xia J Z. 1989. Time domain analysis of non-linear hydroelastic response of ships//Fourth PRADS, Varna, Bulgaria.
[130]	Gumerov N A, Duraiswami R. 2009. A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation. 125: 191-205.
[131]	Guo Y P. 1996. Acoustic radiation from cylindrical shells due to internal forcing. J. Acoust. Soc. Am., 99: 1495-1505.doi:10.1121/1.414728
[132]	Heller S R, Abramson H N. 1959. Hydroelasticity: A new naval science.J. Am. Soc. Naval Engns., 71: 205-209.https://www.researchgate.net/publication/249372377_HYDROELASTICITY_A_NEW_NAVAL_SCIENCE
[133]	Hu J J, Wu Y S, Tian C, Wang X L, Zhang F. 2012. Hydroelastic analysis and model test of structural responses and fatigue behaviors of an ultra large ore carrier in waves. J. of Eng. for the Maritime Environment, 226: 135-155.
[134]	Hui C Y, Shia D. 1999. Evaluations of hypersingular integrals using Gaussian quadrature. Int. J. Num. Meth. Eng., 44: 205-214.doi:10.1002/(ISSN)1097-0207
[135]	Hunt J T, Knittel M R, Barach D. 1974. Finite element approach to acoustic radiation from elastic structures. J. Acoust. Soc. Am., 55: 269-280.doi:10.1121/1.1914498
[136]	Hunt J T, Knittel M R, Nichols C S, Barach D. 1975. Finite element approach to acoustic scattering from elastic structures. J. Acoust. Soc. Am., 57: 287-299.doi:10.1121/1.380459
[137]	Hurty W C. 1960. Vibration of structure systems by component mode synthesis. Jour. Engr. Mech. Div., ASCE, 86: 51-59.
[138]	Hynna P, Klinge P, Vuoksinen J. 1995. Prediction of structure-borne sound transmission in large welded ship structures using statistical energy analysis. Journal of Sound and Vibration, 180: 583-607.doi:10.1006/jsvi.1995.0101
[139]	James J, Faran J R. 1951. Sound scattering by solid cylinders and spheres. J. Acoust. Soc. Am., 23: 405-418.doi:10.1121/1.1906780
[140]	Jang H W, Ih J G. 2013. Stabilization of time domain acoustic boundary element method for the exterior problem avoiding the nonuniqueness. J. Acoust. Soc. Am., 133: 1237-1244.doi:10.1121/1.4774377
[141]	Jensen F B, Kuperman W A, Porter M B, Schmidt H. 2011. Computational Ocean Acoustics, Second Edition. Springer.
[142]	Jiang L, Hong M. 2009. Studies on scattering from ellipsoids in a shallow water with sea bottom impedance. Journal of Ship Mechanics, 13: 1013-1021.https://www.researchgate.net/publication/287054868_Studies_on_Scattering_from_Ellipsoids_in_a_Shallow_Water_with_sea_bottom_impedance?_sg=eNsWU3Sbv-cvJpagdGGhYjLme-CSah_oWK89dIsGoHokuNfPLlWw9eTIDGF8msIIgBLBccVcfJ_77HSn6Ds84Q
[143]	Junger M C. 1952. Sound scattering by thin elastic shells. J. Acoust. Soc. Am., 24: 366-373.doi:10.1121/1.1906905
[144]	Junger M C, Feit D. 1986. Sound, Structures, and Their Interaction, Second Edition. Cambridge, Massachusetts: The MIT Press.
[145]	Kallivokas L F, Bielak J. 1993. Time-domain analysis of transient structural acoustics problems based on the finite element method and a novel absorbing boundary element. J. Acoust. Soc. Am., 94: 3480-3492.doi:10.1121/1.407202
[146]	Kassem M, Soize C, Gagliardini L. 2009. Energy-density field approach for low-and medium-frequency vibroacoustic analysis of complex structure using a statistical computational model. Journal of Sound and Vibration, 323: 849-863.doi:10.1016/j.jsv.2009.01.014
[147]	Kean A J, Temarel P, Wu X J, Wu Y S. 1991. Hydroelasticity of non-beamlike ships in waves. The Dynamics of Ships, The Royal Soc. London, 153.https://www.researchgate.net/publication/239038084_Hydroelasticity_of_Non-Beamlike_Ships_in_Waves_Discussion
[148]	Kim K H, Kim Y. 2012. Numerical analysis on ship hydroelasticity by using 3D rankine panel method and 3D finite element method//Proc. 6th International Conference on Hydroelasticity in Marine Technology, Tokyo, Japan, 63-74.
[149]	Koopmann G H, Song L, Fahnline J B. 1989. A method for computing acoustic fields based on the principle of wave superposition. J. Acoust. Soc. Am., 86: 2433-2438.doi:10.1121/1.398450
[150]	Langley R S, Bremner P. 1999. A hybrid method for the vibration analysis of complex structural-acoustic systems. J. Acoust. Soc. Am., 105: 1657-1671.doi:10.1121/1.426705
[151]	Laulagnet B, Guyader J L. 1991. Sound radiation from a finite cylindrical shell covered with a compliant layer. J. Vibration and Acoustics, 113: 267-272.doi:10.1115/1.2930180
[152]	Laulagnet B, Guyader J L. 1994. Sound radiation from finite cylindrical coated shells by means of asymptotic expansion of three-dimension equation for coating. J. Acoust. Soc. Am., 96: 277-286.doi:10.1121/1.410480
[153]	Lase Y, Ichchou M N, Jezequel L. 1996. Energy flow analysis of bars and beams: theoretical formulations. Journal of Sound and Vibration, 192: 281-308.doi:10.1006/jsvi.1996.0188
[154]	Li W L, Wu T W, Seybert A F. 1994. A half-space boundary element method for acoustic problems with a reflecting plane of arbitrary impedance. Journal of Sound and Vibration, 171: 173-184.doi:10.1006/jsvi.1994.1112
[155]	Lin J, Chen W, Chen C S. 2014. Numerical treatment of acoustic problems with boundary singularities by the singular boundary method. Journal of Sound and Vibration, 333: 3177-3188.doi:10.1016/j.jsv.2014.02.032
[156]	Lucifredi I, Schmidt H. 2006. Subcritical scattering from buried elastic shells. J. Acoust. Soc. Am., 120: 3566-3583.doi:10.1121/1.2357711
[157]	Lundgren J, Price W G, Wu Y S. 1988. A hydroelastic investigation into the behaviour of a floating 'dry' dock in waves//Spring Meeting, RINA, London.
[158]	Maidanik G, Biancardi R. 1982. Use decoupling to reduce the radiated noise generated by panels. J. Sound and Vibration, 81: 165-185.doi:10.1016/0022-460X(82)90202-4
[159]	Maxit L, Ege K, Totaro N, Guyader J L. 2014. Non resonant transmission modeling with statistical modal energy distribution analysis. Journal of Sound and Vibration, 333: 499-519.doi:10.1016/j.jsv.2013.09.007
[160]	Maxit L, Guyader J L. 2003. Extension of SEA model to subsystems with non-uniform modal energy distribution. Journal of Sound and Vibration, 265: 337-358.doi:10.1016/S0022-460X(02)01459-1
[161]	Mocormick J M, Baron M L. 1965. Sound radiation from submerged cylindrical shells of finite length. ASME Trns., Ser.B., 87: 393-405.
[162]	Newman J N. 1978. The theory of ship motions. Advances in Applied Mechanics, 18: 221-285.
[163]	Peters H, Kinns R, Kessissoglou N. 2014. Effects of internal mass distribution and its isolation on the acoustic characteristics of a submerged hull. Journal of Sound and Vibration, 333: 1684-1697.doi:10.1016/j.jsv.2013.10.017
[164]	Porter M B. 2001. The KRAKEN normal mode program. SACLANT Undersea Research Center.
[165]	Price W G, Wu Y S. 1984. Hydroelasticity of marine structure//Sectional Lecture S-10, the 16th In. Congress of Theoretical and Applied Mechanics (IUTAM), Lyngby, Denmark.
[166]	Price W G, Wu Y S. 1985. Structural responses of a SWATH of multi-hulled vessel travelling in waves//Int. Conf. On SWATH ships and Advanced Multi-hulled Vessels, RINA, London.
[167]	Price W G, Wu Y S. 1989. The influence of non-linear fluid forces in the time domain responses of flexible SWATH ships excited by a seaway//OMAE'89, 2: 125-135.
[168]	Qi L B, Zou M S. 2013. Acoustic radiation of stiffened cylinder with different shells. Journal of Ship Mechanics, 17: 697-701.https://www.researchgate.net/publication/290731442_Acoustic_radiation_of_stiffened_cylinder_with_different_shells
[169]	Riggs H R, Ertekin R C. 1991. Approximate methods for dynamic response of multi-module floating structures//Proceedings of 1st International Workshop on Very Large Floating Structures, VLFS'91.
[170]	Salvesen N, Tuck E O, Faltinsen O. 1970. Ship motions and sealoads. Transaction of the Society of Naval Architecture and Marine Engineers, 78: 250-287.
[171]	Schenck H A. 1968. Improved integral formulation for acoustic radiation problems. J. Acoust. Soc. Am., 44: 41-58.doi:10.1121/1.1911085
[172]	Schmidt H. 2004. Virtual source approach to scattering from partially buried elastic targets. In Porter M B, Siderius M and Kuperman W A, editors, American Institute of Physics Conference Series, 728: 456-463.https://www.researchgate.net/publication/251935637_Virtual_Source_Approach_to_Scattering_from_Partially_Buried_Elastic_Targets
[173]	Seybert A F, Soenarko B. 1988. Radiation and scattering of acoustic waves from bodies of arbitrary shape in a three-dimensional half space. ASME Transactions, J. Vib. Acoust. Stress Rel. Dsgn., 110: 112-117.doi:10.1115/1.3269465
[174]	Seybert A F, Soenarko B, Rizzo F J, Shippy D J. 1984. Application of the BIE method to sound radiation problems using an isoparametric element. ASME Transactions, J. Vib. Acoust. Stress Rel. Dsgn., 106: 414-420.doi:10.1115/1.3269211
[175]	Skelton E A, James J H. 1997. Theoretical Acoustics of Underwater Structures. London: Imperial College Press.
[176]	Shorter P J, Langley R S. 2005. Vibro-acoustic analysis of complex systems. Journal of Sound and Vibration, 288: 669-699.doi:10.1016/j.jsv.2005.07.010
[177]	Soize C. 1993. A model and numerical method in the medium frequency range for vibroacoustic predicitions using the theory of structural fuzzy. J. Acoust. Soc. Am., 94: 849-965.doi:10.1121/1.408186
[178]	Strasberg M, Feit D. 1996. Vibration damping of large structures induced by attached small resonant structures. J. Acoust. Soc. Am., 99: 335-344.doi:10.1121/1.414545
[179]	Sun J G, Zou M S. 2015. Vibration response analysis of an underwater submersible. Journal of Ship Mechanics, 19: 303-310.https://www.researchgate.net/publication/283843470_Vibration_Response_Analysis_of_an_Underwater_Submersible?_sg=8zaYN4j2zDR76MaTj2hn7NRX22EJ1YFTDQW28QsUWenQ0o72HJ64S7t8oXTOR0rIZu4aDie17rO7CBhZ8fs4Zg
[180]	Takahashi T, Hamada T. 2009. GPU-accelerated boundary element method for Helmholtz equation in three dimensions. Int. J. Numer. Meth. Engng., 80: 1295-1321.doi:10.1002/nme.v80:10
[181]	Temarel P. 1980. Unified dynamic analysis of antisymmetric response of ships to waves.[PhD Thesis]. London: University of London.
[182]	Tian C, Wu Y S. 2006. The second-order hydroelastic analysis of a SWATH ship moving in large-amplitude waves. Journal of Hydrodynamics, Ser. B., 18: 631-639.doi:10.1016/S1001-6058(07)60001-8
[183]	Tian C, Wu Y S, Chen Y Q. 2009. Numerical predictions on the hydroelastic responses of a large bulker in waves//Proceedings of the 5th International Conference on Hydroelasticity in Marine Technology, Southampton, UK.
[184]	Wang D Y, Wu Y S. 1998. Three dimensional hydroelastic analysis in time domain with application to an elastic ship model. Journal of Hydrodynamics, 10: 54-61.https://www.researchgate.net/publication/264944058_Three-dimensional_hydroelastic_analysis_in_time_domain_with_application_to_an_elastic_ship_model
[185]	Wang M L, Du S X, Ertekin R C. 1991. Hydroelastic reponse and fatigue analysis of a multi-module very large floating structure//International Symposium on Fatigue and Fracture in Steel and Concrete Structures, Madras, India.
[186]	Wang X R, Ji Z L. 2008. Application of FMBEM to predict silencer acoustic performance. Journal of University of Science and Technology of China, 38: 207-217.
[187]	Wohlever J C, Bernhard R J. 1990. Mechanical energy flow models of rods and beams. Journal of Sound and Vibration, 153: 1-19.https://www.researchgate.net/publication/222897937_Mechanical_energy_flow_models_of_rods_and_beams
[188]	Wu M K, Moan T. 1996. Linear and nonlinear hydroelastic analysis of high speed vessels. Journal of Ship Research, 40: 149-163.https://www.researchgate.net/publication/283159321_Linear_and_nonlinear_hydroelastic_analysis_of_high-speed_vessels
[189]	Wu T W. and Seybert A F. 1991. A weighted residual formulation for the CHIEF method in acoustics. J. Acoust. Soc. Am., 90: 1608-1614.doi:10.1121/1.401901
[190]	Wu Y S. 1984. Hydroelasticity of floating bodies.[PhD Thesis]. London: Brunel University.
[191]	Wu Y S. 1991. A modified hydroelasticity theory and its application to long multi-body structures. China Ship Scientific Research Center Reports.
[192]	Wu Y S, Chen R Z, Lin J R. 2003. Experimental technique of hydroelastic ship model//Proceedings of the Third International Conference on Hydroelasticity in Marine Technology, Oxford, UK.
[193]	Wu Y S, Du S X, Riggs H R, Ertekin R C. 1993. Fluid-structure interaction analysis of very large floating structures// Aero-Hydroelasticity Developments and Applications. Beijing: Seismological Press.
[194]	Wu Y S, Maeda H, Kinoshita T. 1997. The second order hydrodynamic actions on a flexible body.SEISANKENKYU, Institute of Industrial Science of Univ. of Tokyo, 49: 8-19.
[195]	Wu Y S, Ni Q J, Xie W, Zhou S Y, Tian C, Zhang Y, Wu Q. 2007. Hydrodynamic performance and structural design of a SWATH ship//Proceedings of International Conference on Practical Design of Ships and Other Floating Structures, Huston, USA.
[196]	Wu Y S, Wang D Y, Riggs H R, Ertekin R C. 1991. Composite singularity distribution method with application to hydroelasticity//Proceedings of the First International Workshop on Very Large Floating Structures, Honolulu, Hawaii, USA. Marine Structure, 6: 143-163.
[197]	Wu Y S, Xia J Z, Du S X. 1991. Two engineering approaches to hydroelastic analysis of slender ships//Dynamics of Marine Vehicles and Structures in Waves. Elsevier Science Publishers, 157-165.
[198]	Xia J Z, Wang Z H, Jensen J J. 1998. Non-linear wave loads and ship responses by a time-domain strip theory. Marine Structures, 11: 101-123.doi:10.1016/S0951-8339(98)00008-2
[199]	Xie Y H, Li R P. 2006. The effects of water depth on wave-induced loads of a very large FPSO by 3D hydroelastic theory//Proc. 4th International Conference on Hydroelasticity in Marine Technology, Wuxi, 35-40.
[200]	Yamamoto Y, Fujino M, Fukasawa T, Ohtsubo H. 1978. Slamming and whipping of ship among rough seas//Symp. Numerical Analysis of the Dynamics of Ship Structures, Association Technique Maritime at Aeronautique.
[201]	Yang P, Liu X L, Ding J, et al.. 2015. Hydroelastic responses of a VLFS in the waves influenced by complicated geographic environment//Proceedings of the 7th International Conference on Hydroelasticity in Marine Technology, Split, Croatia, 541-559.
[202]	Yin X W, Gu X J, Cui H F, Shen R Y. 2007. Acoustic radiation a laminated composite plate reinforced by doubly periodic parallel stiffeners. Journal of Sound and Vibration, 306: 877-889.doi:10.1016/j.jsv.2007.06.047
[203]	Young D L, Chen K H, Lee C W. 2006. Singular meshless method using double layer potentials for exterior acoustics. J. Acoust. Soc. Am., 119: 96-107.doi:10.1121/1.2141130
[204]	Zhang J T, He Z Y. 1987. Study of sound radiation of arbitrary revolution elastic shells dense medium excited by force//4th Int. cong. of Int. Maritime Association of East in Mediterrenean, Varna, Bulgarian.
[205]	Zhu X Q. 1986. Sound generation from a moving shell//Proc. and Int. Symp. on Shipboard Acoustic, Holland.
[206]	Zou M S, Wu Y S. 2015. A mixed analytical-numerical sono-elastic substructure method of submerged structures//Proceedings of the 8th International Conference on Navy and Shipbuilding Nowadays, St. Petersburg, Russia, 24-32.
[207]	Zou M S, Wu Y S, Liu Y M, Lin C G. 2013. A three-dimensional hydroelasticity theory for ship structures in acoustic field of shallow sea. Journal of Hydrodynamics, 25: 929-937.doi:10.1016/S1001-6058(13)60442-4
[208]	Zou M S, Wu Y S, Liu Y M. 2014. The application of three-dimensional hydroelastic analysis of ship structures in Pekeris hydro-acoustic waveguide environment. Acta Mechanica Sinica, 30: 59-66.doi:10.1007/s10409-013-0096-0
[209]	Zou M S, Wu Y S, Sima C. 2015. Time domain three-dimensional hydroelastic analysis of acoustic responses of a floating structure//Proceedings of the 7th International Conference on Hydroelasticity in Marine Technology, Split, Croatia, 729-738.
[210]	Zou M S, Wu Y S, Wu W W, Ye Y L, Tian C. 2012. The three-dimensional hydroelasticity theory of ship structures in acoustic fluid of shallow sea//Proceedings of the 6th International Conference on Hydroelasticity in Marine Technology, Tokyo, Japan, 125-134.
[211]	Zou M S, Wu Y S, Ye Y L. 2010. Three-dimensional hydroelasticity analysis of acoustic responses of ship structures//9th International Conference on Hydrodynamics, Shanghai, China, 844-851.