VLCC液舱晃荡仿真及结构强度评估方法研究
|
摘要
随着大型原油货轮(VLCC)、液化石油气船(LPG)及液化天然气船(LNG)等载液货船相继被开发应用，液舱晃荡问题成为载液货船结构设计过程中面临的一个共性问题。液货船在航行过程中，不可避免地会有液货舱部分装载的可能。当船体在波浪中运动的频率与液舱内液体振动的固有频率相近时，舱内液体将会发生剧烈的运动，晃荡发生了。晃动的液体将对液舱结构产生严重的冲击。因此，在载液货船的研发设计中，液舱晃荡分析及结构强度评估是一项非常重要的研究课题。本文的主要目的是研究具有工程实用性的用于大型油轮液舱晃荡仿真及结构强度评估的方法。为此，文中着重在下列几个方面进行了探讨。
首先，本文阐述了船体六个自由度时历预报所采用的方法。在对现有的船体运动预报理论进行了简要评述后，选定更适合本文作为船体运动预报方法的二维线性切片理论；推导出了从整船船体运动时间历程到目标舱运动时历的相关公式；针对船体各自由度运动初始相位不同带来的问题，提出了初始位置归零的运动时历曲线修正方法。
其次，分析了DNV基于压力的液舱晃荡分析方法，指出该方法存在的问题，提出了以短期搜索、长期分析和流体结构耦合响应分析为流程的液舱晃荡仿真及结构强度评估方法。并在本文方法中引入时间和空间放大技术和体积模量减缩技术，缩短了仿真时间又能够得到关键部位的应力分布的细节，避免了对整舱结构进行流固耦合分析的困难。同时给出了三个短期搜索和长期分析的模型方案。根据舱内流体流动的特点和目前大型油轮液舱布置的特点，采用二维模型对大型油轮进行晃荡的短期搜索和长期分析，进一步提高仿真效率，可以在技术设计阶段充分考虑晃荡对结构的影响，而且可以进行结构设计的不断改进，得到最优化的结构设计。
在此基础上，对一条大型油轮进行了液舱晃荡仿真和结构强度评估，按本文的方法，工程实践了VLCC液舱晃荡数值分析的全过程。通过对结果的分析，得出了一些供设计参考的有益结论。
With the R&D and application of liquid carries, such as VLCC, LPG and LNG, sloshing in tanks is becoming main interest in tank structure design. Liquid carries sometimes unavoidably sail with partially filled tanks. Fluid in these tanks moves duo to ship motion in waves. Violent fluid motion (sloshing) is found in such partially filled tanks when ship motion period is close to fluid natural oscillation period in these tanks. Sloshing causes violent fluid impacts on tank boundary structure with high pressure. Therefore, to investigate tank structure response and any possible damage induced by sloshing impact pressure is a big problem in ship design. The major purpose of this thesis is to present a practical method for VLCC sloshing simulation and structural response and assessment in tanks. For this reason, the following problems are emphatically investigated.
Firstly, the method for ship's 6-DOF time history motion is presented. By comparison of all sea-keeping theories available for ship motion prediction, 2D slice theory is thought as the suitable one and selected for its simpleness and efficiency in this calculation. Basing on ship time history motion, formulas for tank time history motion is derived. In order to have the ship be motionless at the beginning of simulation, a method is given for modifying ship time history curve of 6-DOF with different initial phases.
Secondly, the approach (pressure-based method for sloshing in tanks) presented by DNV is discussed, and also its uncertain problems. Then a coupled sloshing simulation and structural strength assessment method is presented by the procedure of short term scanning, long term analysis and structural response where fluid and structure interactions are considered. In this method, time and space zooming technique and reduce of bulk modulus are introduced. By this, time expense for simulation is decreased dramatically, and we could not only obtain stress distribution in details but also avoid the difficulties of coupled simulation for the whole tank. Also, three tank model strategies are given for shot term scanning and long term analysis. Taking advantage of feature of fluid flowing in tanks and general distribution of tank in VLCC, 2D model is a good selection among the three strategies. By this, we could not only improve simulation efficiency, but also could consider sloshing effects on tank structures sufficiently during technique design. And structure optimization could be possible.
On the basis of above studying work, taking a VLCC as an example, the sloshing simulation and structure assessment is carried out. Some conclusions are made for its structure design.
首先，本文阐述了船体六个自由度时历预报所采用的方法。在对现有的船体运动预报理论进行了简要评述后，选定更适合本文作为船体运动预报方法的二维线性切片理论；推导出了从整船船体运动时间历程到目标舱运动时历的相关公式；针对船体各自由度运动初始相位不同带来的问题，提出了初始位置归零的运动时历曲线修正方法。
其次，分析了DNV基于压力的液舱晃荡分析方法，指出该方法存在的问题，提出了以短期搜索、长期分析和流体结构耦合响应分析为流程的液舱晃荡仿真及结构强度评估方法。并在本文方法中引入时间和空间放大技术和体积模量减缩技术，缩短了仿真时间又能够得到关键部位的应力分布的细节，避免了对整舱结构进行流固耦合分析的困难。同时给出了三个短期搜索和长期分析的模型方案。根据舱内流体流动的特点和目前大型油轮液舱布置的特点，采用二维模型对大型油轮进行晃荡的短期搜索和长期分析，进一步提高仿真效率，可以在技术设计阶段充分考虑晃荡对结构的影响，而且可以进行结构设计的不断改进，得到最优化的结构设计。
在此基础上，对一条大型油轮进行了液舱晃荡仿真和结构强度评估，按本文的方法，工程实践了VLCC液舱晃荡数值分析的全过程。通过对结果的分析，得出了一些供设计参考的有益结论。
With the R&D and application of liquid carries, such as VLCC, LPG and LNG, sloshing in tanks is becoming main interest in tank structure design. Liquid carries sometimes unavoidably sail with partially filled tanks. Fluid in these tanks moves duo to ship motion in waves. Violent fluid motion (sloshing) is found in such partially filled tanks when ship motion period is close to fluid natural oscillation period in these tanks. Sloshing causes violent fluid impacts on tank boundary structure with high pressure. Therefore, to investigate tank structure response and any possible damage induced by sloshing impact pressure is a big problem in ship design. The major purpose of this thesis is to present a practical method for VLCC sloshing simulation and structural response and assessment in tanks. For this reason, the following problems are emphatically investigated.
Firstly, the method for ship's 6-DOF time history motion is presented. By comparison of all sea-keeping theories available for ship motion prediction, 2D slice theory is thought as the suitable one and selected for its simpleness and efficiency in this calculation. Basing on ship time history motion, formulas for tank time history motion is derived. In order to have the ship be motionless at the beginning of simulation, a method is given for modifying ship time history curve of 6-DOF with different initial phases.
Secondly, the approach (pressure-based method for sloshing in tanks) presented by DNV is discussed, and also its uncertain problems. Then a coupled sloshing simulation and structural strength assessment method is presented by the procedure of short term scanning, long term analysis and structural response where fluid and structure interactions are considered. In this method, time and space zooming technique and reduce of bulk modulus are introduced. By this, time expense for simulation is decreased dramatically, and we could not only obtain stress distribution in details but also avoid the difficulties of coupled simulation for the whole tank. Also, three tank model strategies are given for shot term scanning and long term analysis. Taking advantage of feature of fluid flowing in tanks and general distribution of tank in VLCC, 2D model is a good selection among the three strategies. By this, we could not only improve simulation efficiency, but also could consider sloshing effects on tank structures sufficiently during technique design. And structure optimization could be possible.
On the basis of above studying work, taking a VLCC as an example, the sloshing simulation and structure assessment is carried out. Some conclusions are made for its structure design.
引文
[1] Abramson H.N. (1966). The dynamic behavior of liquids in moving containers. NASA SP-106.
[2] ABS. ABS presentation for large LNG designs to MARIC. 2005.
[3] Alain Cariou, Guido Casella. Liquid sloshing in ship tanks: a comparative study of numerical simulation. Marine Structures. 12 183-198P.
[4] A.A. Fediw, N. Isyumov, B.J. Vickery.(1995). Performance of a tuned sloshing water damper. Journal of wind engineering and industrial aerodynamics 57, 237-247P.
[5] Antonio Huerta and Wing Kam Liu. (1988). Viscous flow with large free surface motion. Computer methods in applie mechanics and engineering. 69: 277-324P.
[6] Bang-Fuh Chen, Hsuen-Weng Chiang. (2000). Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank. Ocean Engineering. 953-977P.
[7] Bass R.L.,Bowles E.B. and Cox P.A. (1980) Liquid dynamic loads in LNG cargo tanks. SNAME Transactions. 88: 103-126P.
[8] Belytschko T and Kennedy J M.(1978). Computer models for subassembly simulation. Nucl. Engrg. Design. 49: 17-38P.
[9] Belytschko T and Kennedy J M. et al. (1980). Quasi-eulerian finite element formulation for fluid-structure interaction. J. Pressure Vessel Technol. ASME. 102: 62-69P.
[10] Chen S., Merriman B. and Osher S.A.(1997). A simple level set method for solving Stefan problems. J. Comput. Phys. 135: 8-29P.
[11] Chen, B.F. and Chiang, H.W.(2000). Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank. Journal of Ocean Engineering 27:9, 953-977P.
[12] Cho, J.R., Lee, J.K., Song, J.M., Park, S.H. and Lee, J.N.(2000). Free vibration analysis of above ground LNG-storage tanks by the finite element method. KSME International Journal 14: 6,633-644P.
[13] Cho, J. R. and Song, J. M. (2001). Assessment of classical numerical models for the separate fluid-structure modal analysis. Journal of Sound and Vibration 239:5. 995-1012P.
[14] Cleary W. A. Jr. (1982) Subdivision, stability, liability. Marine Technology. 18: 38-50P.
[15] C. W. Hirt, A.A.Amsden, and J.L. Cook.(1974). An arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds. Journal of computational physics 135, 203-216P.
[16] C. Z. Wang, B. C. Khoo.(2005). Finite element analysis of two-dimensional nonlinear sloshing problems in random excitations. Ocean Engineering. 32 107-133P.
[17] Faltinsen, O. M. and Timokha, A. N.(2001). An adaptive multimodal approach to nonlinear sloshing in a rectangular tank. Journal of Fluid Mechanics 432, 167-200P.
[18] Faltinsen, O. M.(2000). Hydroelastic slamming. Journal of Marine Science and Technology 5, 49-65P.
[19] Faltinsen, O. M.(1974). A nonlinear theory of sloshing in rectangular tanks. Journal of ship research. 18(4): 224-241P.
[20] Faltinsen, O. M.(1978). A numerical nonlinear method of sloshing in tanks with two-dimensional flow. Journal of ship research. 22(3): 193-202P.
[21] ED. Fischer, F. G.. Rammerstorfer.(1999). A refined analysis of sloshing effects in seismically excited tanks. Pressure Vessels and Piping. 76 69.3-709P.
[22] Gao Huanqiu, Xie nan, Shen Wanan Qian Yaoxin.(1998). Experimental Study on Effect of Sloshing on Ship Roll Motion. Journal of Ship Mechanics. Vol. 2 No.6.
[23] Gavin. So, S. Eren Semerciail.(2004). A note on a natural sloshing absorber for vibration control. Journal of Sound and Vibration. 269, 1119-1127P.
[24] G. X. Wu, Q. W. Ma, R.Eatock Taylor(1998). Numerical simulation of sloshing waves in a 3D tank based on a finite element method. Applied Ocean Research 20, 337-355E
[25] Hakan Akyildiz, Eredm Unal. (2005). Experimental investigation of pressure distribution on a rectangular tank due to the liquid sloshing. Ocean Engineering 32, 1503-1516P.
[26] H Lee, JW Kim, C Whang. (2004). Dynamic strength analysis of membrane type LNG Containment system. The international conference on design and operation of gas carriers. Sept 22-25, 2004, London, UK.
[27] Hamlin, N. A. et al. (1986). Liquid sloshing in slack ship tanks-theory. Observations and experiments. 94: 159-195P.
[28] Hayama, S. et al. (1983). Nonlinear sloshing in tectangular container(in Japanese). Trans. JSME. Part C. 54(501):1102-1107P.
[29] Hirt C. W., Nichols B. D. (1981). Volume of fluid (VOF) method for the dynamics of free surface fluidflow. J. Compute Physics. 39: 201-225P.
[30] Huerta A., Liu W. K.(1988). Viscous flow structure interaction. J. of pressure Vessel tchnolog. 110: 15-21P
[31] Hughes TJR, Liu WK, Zimmerman TK. (1981). Lagrangian-eulerian finite element formulation for incompressible viscous flows. Comput. Meths. Appl. Mech. Engrg. 29: 329-349P.
[32] Jannette B. Frandsen.(2004). Sloshing motion in excited tanks. Journal of Computational Physics. 196, 53-87P.
[33] Jean Donea.(1983). Arbitrary Lagrangian-Eulerian Finite Element Methods. Computational Methods for Transient Analysis. Chapter 10, 473-516P.
[34] J. Donea, E Fasoli Stella, et al.(1977). Lagrangian and eulerian finite element techniques for transient dynamic fluid-structure interaction problems. Paper B1/2, Trans SMIRT-4P.
[35] J. Donea, E Fasoli Stella, S. Giuliani, J.E Halleux, A.V. Jones.(1979). An arbitrary lagrangian-eulerian finite element procedure for transient dynamic fluid-structure interaction problems. Paper B1/3, Trans SMIRT-5, Germany.
[36] J. Donea, S.Giuliani and J. P. Halleux.(1982). An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interaction. Computer methods in applied mechanics and engineering. 33: 689-723P.
[37] J. G. Anderson, S. E. Semercigil and O. E Turan.(2000). A standing-wave-type sloshing absorber to control transient osciliations. Journal of sound and vibtation. 232 839-856P.
[38] J. G. Anderson, S. E. Semercigil and O. F. Turan.(2000). An improved stand-wave-type sloshing absorber. Journal of sound and vibration. 235(4) 702-710P.
[39] J. R. Cho, H. W. Lee.(2004). Numerical study on liquid sloshing in baffled tank by nonlinear finite element method. Comput. Methods Applied Mech. Engrg. 193 2581-2598P.
[40] K. Kimura, K. Ogura, T. Mieda, K. Yamamoto, Y. Eguchi. S. Moriya, et al. (1995). Experimental and analytical studies on the multi-surface sloshing characteristics of a top entry loop type FBR. Nuclear Engineering and Design 157, 49-63P.
[41] Katsuya Umemoto, Takao, Hodaka Shimizu, Akio Murakami.(1996). An experimental study on sloshing loads of double hull tankers and a consideration on structural response. Proceedings of SNAJ.
[42] Li, Y. L., Liu, Y. Z. and Miao, G. P.(2000a). Numerical analysis of the sloshing effects on ship roll motion. Journal of Shanghai Jiaotong University. 34:1, 6-9P.
[43] Liu W. K.,(1981). Finite element procedures for fluid-structure interactions with application to liquid storage tanks. Nucl. Engrg. Design. , 65:221-238P.
[44] Liu W. K. and Belytschko T. (1983). Fluid structure interaction with sloshing. In: Trans SMIRT-7, Vol. B, Chicago, L,11-18P.
[45] Liu Z., Huang Y.(1994). A new method for large amplitude sloshing problems. J. sound vibration. 175(2):185-195P.
[46] Liu WK., Belytschko T, et al. (1986). An arbitrary lagrangian-eulerian finite element method for path-dependent materials. Comput. Meths. Appl. Mech. Engrg., 58: 227-245P.
[47] Lou YK, Choi H.(1987). Spatial pressure vibrations and Three-dimensional effects on liquid sloshing loads. US Mar Admin Rep Ma-RD-760-87036.
[48] LR. Sloshing loads and scatling assessment. 2002.
[49] LR. Structural design assessment.
[50] M. Serdar Celebi, Hakan Akyildiz.(2002). Nonlinear modeling of liquid sloshing in a moving rectangular tank. Ocean Engineering. 29 1527-1553P.
[51] Mansour and R. C. Ertekin, Proceedings of the 15th international Ship and offshore structures congress Vol.1.
[52] Marco Anghileri, Luigi-M. L. Castelletti, Maurizio Tirelli.(2005). Fluid-structure interaction of water filled tanks during the impact with the ground. International Journal of Impact Engineering. 31,235-254P.
[53] Matauura Y., Matsumoto K.(1986). On a mean to reduce excite-vibration with the sloshing in a tank. SNAJ160.
[54] Michele La Rocca, Giampiero Sciortino, Maria Antonietta Boniforti.(2000). A fully nonlinear model for sloshing in a rotation container. Fluid Dynamics Research. 27 23-52P.
[55] Mikelis N.E., Miller J. K., et al. (1984). Sloshing in partially filled liquid tanks and its effects on ship motions: numerical simulations and experimental verification. Transactions of the Roral institute of Naval Architect. 126: 267-281P.
[56] Mikelis N. E. and J. M. J. Journee.(1984). Experimental and Numerical simulation of sloshing behaviour in liquid cargo tanks and its effect on ship motions. Delft University of Technology, Ship Hydromenchanics Laboratory, Report 0661-P.
[57] MSC. MSC. Dytran user's manual.
[58] N. C. Pal, S. K. Bhatacharry, P. K. Sinha.(2003). Non-linear coupled slosh dynamics of liquid-filled laminated composite containers: a two dimensional finite element approach. Journal of sound and vibration 261 729-749P.
[59] Noh W. F. (1964). CEL: A time-dependent weo-space-dimensional coupled Eulerian-lagrangian code, in B. Alder, S. Fernbach and M. Rotenberg, eds. Methods in Computaional Physics 3, (Academic press, New York, 1964)
[60] Osher S. and Sethian J. A. (1988). Fronts propagation with curvature-dependent speed: algorithms based on Hamilton-Jacobin formulations. J. Comput. Phys. 79:2
[61] P. K. Ojak, L. Konieczny, H. Michniewicz.(2001). Comparison of the ship tank structure response to sloshing determined experimentally and using MSC/Dytran computer code. Fourth ICMT 23-25 may 2001, Poland.
[62] R. K. Gupta.(1995). Sloshing in shallow cylindrical tanks. Journal of sound and vibration. 180(3), 397-415P.
[63] S. H. Lee, J. Y. Kim, K. J. Lee, J. M. Kang, D.J. Yum, Y.S. Seol, S. Rashed, A. Kawahara.(1995) Simulation of 3-D sloshing and structural response in ship's tanks taking account of fluid-structure interaction. SNAME.
[64] Sethian J.A. Level set methods. Cambrige Univ. Press. Cambridge UK. 1996.
[65] Shahrouz Aliabadi, Andrew Johnson, Jalal Abedi.(2003). Comparison of finite element and pendulum models for simulation of sloshing. Computers & Fluids. 32, 535-545P.
[66] Sudo S. and Hashimoo H. (1988). Unsteady pressure response of a liquid in a cylindrical container subject to horizontal vibration. Trans. JSME. Part B. 31(2): 227-233P.
[67] S. Subhash Babu and S.K. Bhattaharyya. (1996). Finite element analysis of fluid-structure interaction effect on liquid retaining structures due to sloshing. Computers & Structures Vol.59, No.6, 1165-1171P.
[68] S. Valsgard, Trym Tveitnes, Wouter Pastoor. Gas Carriers Developments and sloshing load determination for new operations and trades. DNV AS Paper Series No. 2003-P014.
[69] T. Ikeda and N. Nakagawa.(1997). Non-linear vibration of a structure caused by water sloshing in a rectangular tank. Journal of sound and vibration. 201(1), 23-41P.
[70] Takashi. Nomura, Thomas J. R. Hughes.(1992). An arbitrary lagrangian-eulerian finite element method interaction of fluid and a rigid body. Computer methods in applied mechanics and engineering. 95, 115-138P.
[71] Takashi Nomura. (1994). ALE finite element computations of fluid-structure interaction problems. Computer methods in applied mechanics and engineering. 112: 291-308P.
[72] Vincenzo Armenio and Michele La Rocca.(1996). On the analysis of sloshing of water in rectangular containers: numerical study and experimental validation. Ocean Engrg. Vol. 23 No.8, pp 705-739P.
[73] V. J. Modi, M. L. Seto. (1997). Suppression of flow-induced oscillations using sloshing liquid dampers: analysis and experiments. Journal of Wind Engineering and Industrial Aerodynamics 67 & 68 611-625P.
[74] V. J. Modi and S. R. Munshi. (1998). An efficient liquid sloshing damper for vibration control. Journal of Fluids and structures. 12: 1055-1071P.
[75] V. J. Modi and A. Akinturk. (2002). An efficient liquid sloshing damper for control of wind-induced instabilities. Journal of Wind Engineering and Industrial Aerodynamics. 90:1907-1918P.
[76] Wan D. C., Miao G. P. and Dai S.Q.(1997). The VOF method for study of wave run up and breaking on sloping structure. J. Hydrodyn. Ser. B. 9(4): 88-96P.
[77] Waterhouse D. D. (1994). Resonant sloshing near a critical depth. J. Fluid Mechanics. 281:313-318P.
[78] Welch J. E., Harlow EH., Shannon J. P., and Daly B. J.(1965). The MAC method: a computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surface. Los Alamos Scientific Laboratory Rep. 1965, La-3425.
[79] Waldie, B. and White, G.(2000). Damping characteristics of baffles for suppression of marine motion effects in primary separators. Chemical Engineering Research & Design 78(A5), 698-706P.
[80] Wing Kam Liu, Ted Belytschko and Herman Chang.(1986). An arbitray lagrangian-eulerian finite element method for path-dependent materials. Computer methods in applied mechanics and engineering. 58, 227-245P.
[81] Wing Kam Liu.(1981). Finite element procedures for fluid-structure interactions and application to liquid storage tanks. Nuclear Engineering and Design. 65: 221-238P.
[82] Y. Kim.(2001). Numerical simulation of sloshing flows with impact load. Applied Ocean Research 23, 53-62P.
[83] Young-Warm Kim. Young-Shin Lee. (2005). Coupled Vibration analysis of liquid-filled rigid cylindrical storage tank with an annular plate cover. Journal of Sound and Vibration. 279: 217-235P.
[84] ZHU Ren-qing, WU You-sheng, Neeeik Atilla. (2004). Numerical Simulation of Liquid Sloshing-a Review. Ship Building of China. Vol. 45 No.2.
[85] ZHU Ren-qing, Wang Zhi-dong, Fang Zhi-yong.(2004). Prediction of pressure induced by large amplitude sloshing in a tank. Journal of ship mechanics. Vol. 8 No. 6.
[86] 陈震．(2005)．海洋结构物入水砰击载荷与响应研究．上海交通大学博士学位论文．
[87] 戴遗山．舰船在波浪中运动的频域与时域势流理论．北京：国防工业出版社，1998年．
[88] 丁文镜，曾长庆．(1992)．晃动液体单摆模型动力学参数的频率识别．振动工程学报．5(3)：211-218页．
[89] 方良玉．(1991)．圆环形挡板的液体晃动阻尼效果和优化设计探讨．强度与环境．第四期，47-51页．
[90] 方良玉．(1989)．组合式储箱中液体晃动固有频率的试验研究．强度与环境．73：11-15页．
[91] 郭兆璞，陈浩然，项晨，包小兵．(1994)空间复合材料加筋板流固耦合振动分析．中国造船．No．3．
[92] 胡欲立．赵寅生．刘永长(1999)．用ALE法数值模拟MPC排气系统的三维流动．中国造船．No．4．
[93] 金咸定，赵德有．(2000)．船体振动学．上海交通大学出版社．
[94] 刘儒勋，刘晓平，张磊，王志峰．(2004)．运动界面的追踪和重构方法．应用数学和力学．第25卷第3期．
[95] 刘泽民．液舱晃荡的有限元计算．哈尔滨船舶工程学院博士学位论文．1993年3月．
[96] 刘泽民．(1995)．液体晃荡的有限元分析．华中理工大学学报．Vol．23 No．3．
[97] 李德元，徐国荣，水鸿寿．(1987)．二维非定常流体力学数值方法．科学出版社．北京．
[98] 李谊乐，刘应中，缪国平．(2000)．舱内晃荡对船舶横摇影响的数值分析．上海交通大学学报．Vol．34 No．1．
[99] 李喆．(2003)．油轮晃荡载荷模型试验报告．上海交通大学船舶与海洋工程学院结构力学试验室．
[100] 梁波，周科健．(1992)．有柔性防晃挡板时贮液圆柱壳内液体晃动研究．强度与环境．第2期．1-8页．
[101] 刘应中，缪国平．船舶在波浪上的运动理论．上海：上海交通大学出版社，1987年．
[102] 陆鑫森编著．(1993)．高等结构动力学．上海交通大学出版社．
[103] 聂武，孙丽萍编．(2000)．船舶计算结构力学．哈尔滨工程大学出版社．
[104] 尼基福罗夫．船体结构声学设计．国防工业出版社翻译出版．1998．
[105] 娜日萨．VLCC液舱晃荡载荷计算及结构强度校核报告．2005．
[106] 彭如海．(2003)．船舶工程中的力学问题．力学与实践．第25卷第5期．
[107] 秦洪德．船舶运动与波浪载荷计算的非线性方法研究．哈尔滨工程大学博士学位论文，2003年．
[108] 任慧龙．非线性波浪载荷与船体极限强度．哈尔滨工程大学博士学位论文，1995年．
[109] 沈国光．(1997)．矩形容器内流体晃动的数值模拟．水动力学研究与进展．Ser A 12(3)：281-288页．
[110] 沈国光．(1990)．柱形容器内储液的驻留运动和地震响应．水动力学研究和进展．A辑，5(4)：68-75页．
[111] 陶智祥，戴仰山．外张砰击载荷．中国造船，1991年第4期：43-51页．
[112] 万水，朱德懋．(1998)．液固耦合内流问题及防晃研究进展．工程力学．Vol．15 No．3．
[113] 王仁，熊祝华，黄文彬著．(1998)．塑性力学基础．科学出版社．
[114] 王德禹，李龙渊，施其．(2000)．三自由度晃荡模拟装置及其模态分析．海洋工程．Vol．18 No．4．
[115] 王德禹，金咸定，李龙渊．(1998)．液舱流体晃荡德模型试验．上海交通大学学报．Vol．32 No．11．
[116] 王建军，陆明万，张雄等．(2001)．自由液面流体大晃动有限元方法．水动力学研究与进展．A辑第16卷第3期．
[117] 王建军，李其汉，朱梓根，陆明万，张雄．(2001)．自由液面大晃动的流固耦合数值分析方法研究进展．力学季刊．Vol．22 No．4．
[118] 王献孚等．计算船舶流体力学．上海交通大学出版社．1992．
[119] 王永学．任意容器三维液体晃荡的数值模拟．大连理工大学博士学位论文．1989．
[120] 王自力．船舶碰撞损伤机理与结构耐撞性研究．上海交通大学博士学位论文．2000年．
[121] 温德超，郑兆昌，孙焕纯．(1996)．用ALE和时间分裂步法分析三维粘性流体大幅晃动的非线性问题．振荡与冲击．Vol．15 No．3．
[122] 吴望一．流体力学．北京大学出版社．1981．
[123] 夏益霖．(1995)．液体晃动非线性阻尼的描述方法．强度与环境．第4期．
[124] 夏益霖，许婉丽．(1988)．火箭液体推进剂防晃试验研究．强度与环境．(6)：24-30页．
[125] 夏益霖．(1991)．液体晃动等效力学模型的参数识别．应用力学学报，8(4)：24-35页．
[126] 项晨，陈浩然，郭兆璞．(1996)．复合材料加筋结构的流固耦合振动及动力响应分析．复合材料学报．Vol．13 No．3．
[127] 谢楠，程军，郜焕秋．(1998)．舰船在波浪中运动时间历程的数值模拟．船舶力学．Vol．2 No．6．
[128] 颜开．(1987)．MAC方法的思想、发展和应用．水动力学研究与进展．A辑，2(3)：133-142页．
[129] 杨代盛，桑国光，李维扬，戴仰山．船舶强度的概率方法．哈尔滨：哈尔滨工程大学出版社，1994年．
[130] 郁时炼，周科健．(1991)．半圆形挡板防晃特性的计算．强度与环境．第4期．30-36页．
[131] 张兴福．三维弹性容器内晃荡问题的二阶频域解．上海交通大学博士学位论文．1998年1月．
[132] 张海彬．FPSO储油轮与半潜式平台波浪载荷三维计算方法研究．哈尔滨工程大学博士学位论文．2004．
[133] 张雄，陆明万，王建军．(1997)．任意拉格朗日—欧拉描述发研究进展．计算力学学报．Vol．14 No．(2)．
[134] 邹志利，邱大洪，王永学．(1996)．VOF法模拟波浪槽中二维非线性波．水动力学研究与进展．Ser．A
[135] 周叮．(1991)．贮液圆筒在水中的弯曲自由振动．应用数学和力学．11(5)：439-446页．
[136] 周叮，丁文镜．(1990)．储箱内液体晃动特性及其力学参数的识别问题．强度与环境．79：11-25页．
[137] 朱仁庆，吴有生，彭兴宇，沈进威．船舶液体晃荡动力学的研究方法及进展．华东船舶工业学院学报．Vol．13 No．1．
[138] 朱仁庆，颜开，吴有生．盛液容器内液体二维晃荡的数值模拟．(1998)．华东船舶工业学院学报．Vol．12 No．2．
[139] 朱仁庆，吴有生．(2002)．液舱内流体晃荡特性数值研究．中国造船．Vol．43 No．2．
[140] 朱仁庆．液体晃荡及其与结构的相互作用．中国船舶科学研究中心博士学位论文．
[141] 庄惠忠．船舶在波浪中的载荷与压力分布研究．哈尔滨工程大学硕士学位论文，1994年12月．
[2] ABS. ABS presentation for large LNG designs to MARIC. 2005.
[3] Alain Cariou, Guido Casella. Liquid sloshing in ship tanks: a comparative study of numerical simulation. Marine Structures. 12 183-198P.
[4] A.A. Fediw, N. Isyumov, B.J. Vickery.(1995). Performance of a tuned sloshing water damper. Journal of wind engineering and industrial aerodynamics 57, 237-247P.
[5] Antonio Huerta and Wing Kam Liu. (1988). Viscous flow with large free surface motion. Computer methods in applie mechanics and engineering. 69: 277-324P.
[6] Bang-Fuh Chen, Hsuen-Weng Chiang. (2000). Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank. Ocean Engineering. 953-977P.
[7] Bass R.L.,Bowles E.B. and Cox P.A. (1980) Liquid dynamic loads in LNG cargo tanks. SNAME Transactions. 88: 103-126P.
[8] Belytschko T and Kennedy J M.(1978). Computer models for subassembly simulation. Nucl. Engrg. Design. 49: 17-38P.
[9] Belytschko T and Kennedy J M. et al. (1980). Quasi-eulerian finite element formulation for fluid-structure interaction. J. Pressure Vessel Technol. ASME. 102: 62-69P.
[10] Chen S., Merriman B. and Osher S.A.(1997). A simple level set method for solving Stefan problems. J. Comput. Phys. 135: 8-29P.
[11] Chen, B.F. and Chiang, H.W.(2000). Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank. Journal of Ocean Engineering 27:9, 953-977P.
[12] Cho, J.R., Lee, J.K., Song, J.M., Park, S.H. and Lee, J.N.(2000). Free vibration analysis of above ground LNG-storage tanks by the finite element method. KSME International Journal 14: 6,633-644P.
[13] Cho, J. R. and Song, J. M. (2001). Assessment of classical numerical models for the separate fluid-structure modal analysis. Journal of Sound and Vibration 239:5. 995-1012P.
[14] Cleary W. A. Jr. (1982) Subdivision, stability, liability. Marine Technology. 18: 38-50P.
[15] C. W. Hirt, A.A.Amsden, and J.L. Cook.(1974). An arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds. Journal of computational physics 135, 203-216P.
[16] C. Z. Wang, B. C. Khoo.(2005). Finite element analysis of two-dimensional nonlinear sloshing problems in random excitations. Ocean Engineering. 32 107-133P.
[17] Faltinsen, O. M. and Timokha, A. N.(2001). An adaptive multimodal approach to nonlinear sloshing in a rectangular tank. Journal of Fluid Mechanics 432, 167-200P.
[18] Faltinsen, O. M.(2000). Hydroelastic slamming. Journal of Marine Science and Technology 5, 49-65P.
[19] Faltinsen, O. M.(1974). A nonlinear theory of sloshing in rectangular tanks. Journal of ship research. 18(4): 224-241P.
[20] Faltinsen, O. M.(1978). A numerical nonlinear method of sloshing in tanks with two-dimensional flow. Journal of ship research. 22(3): 193-202P.
[21] ED. Fischer, F. G.. Rammerstorfer.(1999). A refined analysis of sloshing effects in seismically excited tanks. Pressure Vessels and Piping. 76 69.3-709P.
[22] Gao Huanqiu, Xie nan, Shen Wanan Qian Yaoxin.(1998). Experimental Study on Effect of Sloshing on Ship Roll Motion. Journal of Ship Mechanics. Vol. 2 No.6.
[23] Gavin. So, S. Eren Semerciail.(2004). A note on a natural sloshing absorber for vibration control. Journal of Sound and Vibration. 269, 1119-1127P.
[24] G. X. Wu, Q. W. Ma, R.Eatock Taylor(1998). Numerical simulation of sloshing waves in a 3D tank based on a finite element method. Applied Ocean Research 20, 337-355E
[25] Hakan Akyildiz, Eredm Unal. (2005). Experimental investigation of pressure distribution on a rectangular tank due to the liquid sloshing. Ocean Engineering 32, 1503-1516P.
[26] H Lee, JW Kim, C Whang. (2004). Dynamic strength analysis of membrane type LNG Containment system. The international conference on design and operation of gas carriers. Sept 22-25, 2004, London, UK.
[27] Hamlin, N. A. et al. (1986). Liquid sloshing in slack ship tanks-theory. Observations and experiments. 94: 159-195P.
[28] Hayama, S. et al. (1983). Nonlinear sloshing in tectangular container(in Japanese). Trans. JSME. Part C. 54(501):1102-1107P.
[29] Hirt C. W., Nichols B. D. (1981). Volume of fluid (VOF) method for the dynamics of free surface fluidflow. J. Compute Physics. 39: 201-225P.
[30] Huerta A., Liu W. K.(1988). Viscous flow structure interaction. J. of pressure Vessel tchnolog. 110: 15-21P
[31] Hughes TJR, Liu WK, Zimmerman TK. (1981). Lagrangian-eulerian finite element formulation for incompressible viscous flows. Comput. Meths. Appl. Mech. Engrg. 29: 329-349P.
[32] Jannette B. Frandsen.(2004). Sloshing motion in excited tanks. Journal of Computational Physics. 196, 53-87P.
[33] Jean Donea.(1983). Arbitrary Lagrangian-Eulerian Finite Element Methods. Computational Methods for Transient Analysis. Chapter 10, 473-516P.
[34] J. Donea, E Fasoli Stella, et al.(1977). Lagrangian and eulerian finite element techniques for transient dynamic fluid-structure interaction problems. Paper B1/2, Trans SMIRT-4P.
[35] J. Donea, E Fasoli Stella, S. Giuliani, J.E Halleux, A.V. Jones.(1979). An arbitrary lagrangian-eulerian finite element procedure for transient dynamic fluid-structure interaction problems. Paper B1/3, Trans SMIRT-5, Germany.
[36] J. Donea, S.Giuliani and J. P. Halleux.(1982). An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interaction. Computer methods in applied mechanics and engineering. 33: 689-723P.
[37] J. G. Anderson, S. E. Semercigil and O. E Turan.(2000). A standing-wave-type sloshing absorber to control transient osciliations. Journal of sound and vibtation. 232 839-856P.
[38] J. G. Anderson, S. E. Semercigil and O. F. Turan.(2000). An improved stand-wave-type sloshing absorber. Journal of sound and vibration. 235(4) 702-710P.
[39] J. R. Cho, H. W. Lee.(2004). Numerical study on liquid sloshing in baffled tank by nonlinear finite element method. Comput. Methods Applied Mech. Engrg. 193 2581-2598P.
[40] K. Kimura, K. Ogura, T. Mieda, K. Yamamoto, Y. Eguchi. S. Moriya, et al. (1995). Experimental and analytical studies on the multi-surface sloshing characteristics of a top entry loop type FBR. Nuclear Engineering and Design 157, 49-63P.
[41] Katsuya Umemoto, Takao, Hodaka Shimizu, Akio Murakami.(1996). An experimental study on sloshing loads of double hull tankers and a consideration on structural response. Proceedings of SNAJ.
[42] Li, Y. L., Liu, Y. Z. and Miao, G. P.(2000a). Numerical analysis of the sloshing effects on ship roll motion. Journal of Shanghai Jiaotong University. 34:1, 6-9P.
[43] Liu W. K.,(1981). Finite element procedures for fluid-structure interactions with application to liquid storage tanks. Nucl. Engrg. Design. , 65:221-238P.
[44] Liu W. K. and Belytschko T. (1983). Fluid structure interaction with sloshing. In: Trans SMIRT-7, Vol. B, Chicago, L,11-18P.
[45] Liu Z., Huang Y.(1994). A new method for large amplitude sloshing problems. J. sound vibration. 175(2):185-195P.
[46] Liu WK., Belytschko T, et al. (1986). An arbitrary lagrangian-eulerian finite element method for path-dependent materials. Comput. Meths. Appl. Mech. Engrg., 58: 227-245P.
[47] Lou YK, Choi H.(1987). Spatial pressure vibrations and Three-dimensional effects on liquid sloshing loads. US Mar Admin Rep Ma-RD-760-87036.
[48] LR. Sloshing loads and scatling assessment. 2002.
[49] LR. Structural design assessment.
[50] M. Serdar Celebi, Hakan Akyildiz.(2002). Nonlinear modeling of liquid sloshing in a moving rectangular tank. Ocean Engineering. 29 1527-1553P.
[51] Mansour and R. C. Ertekin, Proceedings of the 15th international Ship and offshore structures congress Vol.1.
[52] Marco Anghileri, Luigi-M. L. Castelletti, Maurizio Tirelli.(2005). Fluid-structure interaction of water filled tanks during the impact with the ground. International Journal of Impact Engineering. 31,235-254P.
[53] Matauura Y., Matsumoto K.(1986). On a mean to reduce excite-vibration with the sloshing in a tank. SNAJ160.
[54] Michele La Rocca, Giampiero Sciortino, Maria Antonietta Boniforti.(2000). A fully nonlinear model for sloshing in a rotation container. Fluid Dynamics Research. 27 23-52P.
[55] Mikelis N.E., Miller J. K., et al. (1984). Sloshing in partially filled liquid tanks and its effects on ship motions: numerical simulations and experimental verification. Transactions of the Roral institute of Naval Architect. 126: 267-281P.
[56] Mikelis N. E. and J. M. J. Journee.(1984). Experimental and Numerical simulation of sloshing behaviour in liquid cargo tanks and its effect on ship motions. Delft University of Technology, Ship Hydromenchanics Laboratory, Report 0661-P.
[57] MSC. MSC. Dytran user's manual.
[58] N. C. Pal, S. K. Bhatacharry, P. K. Sinha.(2003). Non-linear coupled slosh dynamics of liquid-filled laminated composite containers: a two dimensional finite element approach. Journal of sound and vibration 261 729-749P.
[59] Noh W. F. (1964). CEL: A time-dependent weo-space-dimensional coupled Eulerian-lagrangian code, in B. Alder, S. Fernbach and M. Rotenberg, eds. Methods in Computaional Physics 3, (Academic press, New York, 1964)
[60] Osher S. and Sethian J. A. (1988). Fronts propagation with curvature-dependent speed: algorithms based on Hamilton-Jacobin formulations. J. Comput. Phys. 79:2
[61] P. K. Ojak, L. Konieczny, H. Michniewicz.(2001). Comparison of the ship tank structure response to sloshing determined experimentally and using MSC/Dytran computer code. Fourth ICMT 23-25 may 2001, Poland.
[62] R. K. Gupta.(1995). Sloshing in shallow cylindrical tanks. Journal of sound and vibration. 180(3), 397-415P.
[63] S. H. Lee, J. Y. Kim, K. J. Lee, J. M. Kang, D.J. Yum, Y.S. Seol, S. Rashed, A. Kawahara.(1995) Simulation of 3-D sloshing and structural response in ship's tanks taking account of fluid-structure interaction. SNAME.
[64] Sethian J.A. Level set methods. Cambrige Univ. Press. Cambridge UK. 1996.
[65] Shahrouz Aliabadi, Andrew Johnson, Jalal Abedi.(2003). Comparison of finite element and pendulum models for simulation of sloshing. Computers & Fluids. 32, 535-545P.
[66] Sudo S. and Hashimoo H. (1988). Unsteady pressure response of a liquid in a cylindrical container subject to horizontal vibration. Trans. JSME. Part B. 31(2): 227-233P.
[67] S. Subhash Babu and S.K. Bhattaharyya. (1996). Finite element analysis of fluid-structure interaction effect on liquid retaining structures due to sloshing. Computers & Structures Vol.59, No.6, 1165-1171P.
[68] S. Valsgard, Trym Tveitnes, Wouter Pastoor. Gas Carriers Developments and sloshing load determination for new operations and trades. DNV AS Paper Series No. 2003-P014.
[69] T. Ikeda and N. Nakagawa.(1997). Non-linear vibration of a structure caused by water sloshing in a rectangular tank. Journal of sound and vibration. 201(1), 23-41P.
[70] Takashi. Nomura, Thomas J. R. Hughes.(1992). An arbitrary lagrangian-eulerian finite element method interaction of fluid and a rigid body. Computer methods in applied mechanics and engineering. 95, 115-138P.
[71] Takashi Nomura. (1994). ALE finite element computations of fluid-structure interaction problems. Computer methods in applied mechanics and engineering. 112: 291-308P.
[72] Vincenzo Armenio and Michele La Rocca.(1996). On the analysis of sloshing of water in rectangular containers: numerical study and experimental validation. Ocean Engrg. Vol. 23 No.8, pp 705-739P.
[73] V. J. Modi, M. L. Seto. (1997). Suppression of flow-induced oscillations using sloshing liquid dampers: analysis and experiments. Journal of Wind Engineering and Industrial Aerodynamics 67 & 68 611-625P.
[74] V. J. Modi and S. R. Munshi. (1998). An efficient liquid sloshing damper for vibration control. Journal of Fluids and structures. 12: 1055-1071P.
[75] V. J. Modi and A. Akinturk. (2002). An efficient liquid sloshing damper for control of wind-induced instabilities. Journal of Wind Engineering and Industrial Aerodynamics. 90:1907-1918P.
[76] Wan D. C., Miao G. P. and Dai S.Q.(1997). The VOF method for study of wave run up and breaking on sloping structure. J. Hydrodyn. Ser. B. 9(4): 88-96P.
[77] Waterhouse D. D. (1994). Resonant sloshing near a critical depth. J. Fluid Mechanics. 281:313-318P.
[78] Welch J. E., Harlow EH., Shannon J. P., and Daly B. J.(1965). The MAC method: a computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surface. Los Alamos Scientific Laboratory Rep. 1965, La-3425.
[79] Waldie, B. and White, G.(2000). Damping characteristics of baffles for suppression of marine motion effects in primary separators. Chemical Engineering Research & Design 78(A5), 698-706P.
[80] Wing Kam Liu, Ted Belytschko and Herman Chang.(1986). An arbitray lagrangian-eulerian finite element method for path-dependent materials. Computer methods in applied mechanics and engineering. 58, 227-245P.
[81] Wing Kam Liu.(1981). Finite element procedures for fluid-structure interactions and application to liquid storage tanks. Nuclear Engineering and Design. 65: 221-238P.
[82] Y. Kim.(2001). Numerical simulation of sloshing flows with impact load. Applied Ocean Research 23, 53-62P.
[83] Young-Warm Kim. Young-Shin Lee. (2005). Coupled Vibration analysis of liquid-filled rigid cylindrical storage tank with an annular plate cover. Journal of Sound and Vibration. 279: 217-235P.
[84] ZHU Ren-qing, WU You-sheng, Neeeik Atilla. (2004). Numerical Simulation of Liquid Sloshing-a Review. Ship Building of China. Vol. 45 No.2.
[85] ZHU Ren-qing, Wang Zhi-dong, Fang Zhi-yong.(2004). Prediction of pressure induced by large amplitude sloshing in a tank. Journal of ship mechanics. Vol. 8 No. 6.
[86] 陈震．(2005)．海洋结构物入水砰击载荷与响应研究．上海交通大学博士学位论文．
[87] 戴遗山．舰船在波浪中运动的频域与时域势流理论．北京：国防工业出版社，1998年．
[88] 丁文镜，曾长庆．(1992)．晃动液体单摆模型动力学参数的频率识别．振动工程学报．5(3)：211-218页．
[89] 方良玉．(1991)．圆环形挡板的液体晃动阻尼效果和优化设计探讨．强度与环境．第四期，47-51页．
[90] 方良玉．(1989)．组合式储箱中液体晃动固有频率的试验研究．强度与环境．73：11-15页．
[91] 郭兆璞，陈浩然，项晨，包小兵．(1994)空间复合材料加筋板流固耦合振动分析．中国造船．No．3．
[92] 胡欲立．赵寅生．刘永长(1999)．用ALE法数值模拟MPC排气系统的三维流动．中国造船．No．4．
[93] 金咸定，赵德有．(2000)．船体振动学．上海交通大学出版社．
[94] 刘儒勋，刘晓平，张磊，王志峰．(2004)．运动界面的追踪和重构方法．应用数学和力学．第25卷第3期．
[95] 刘泽民．液舱晃荡的有限元计算．哈尔滨船舶工程学院博士学位论文．1993年3月．
[96] 刘泽民．(1995)．液体晃荡的有限元分析．华中理工大学学报．Vol．23 No．3．
[97] 李德元，徐国荣，水鸿寿．(1987)．二维非定常流体力学数值方法．科学出版社．北京．
[98] 李谊乐，刘应中，缪国平．(2000)．舱内晃荡对船舶横摇影响的数值分析．上海交通大学学报．Vol．34 No．1．
[99] 李喆．(2003)．油轮晃荡载荷模型试验报告．上海交通大学船舶与海洋工程学院结构力学试验室．
[100] 梁波，周科健．(1992)．有柔性防晃挡板时贮液圆柱壳内液体晃动研究．强度与环境．第2期．1-8页．
[101] 刘应中，缪国平．船舶在波浪上的运动理论．上海：上海交通大学出版社，1987年．
[102] 陆鑫森编著．(1993)．高等结构动力学．上海交通大学出版社．
[103] 聂武，孙丽萍编．(2000)．船舶计算结构力学．哈尔滨工程大学出版社．
[104] 尼基福罗夫．船体结构声学设计．国防工业出版社翻译出版．1998．
[105] 娜日萨．VLCC液舱晃荡载荷计算及结构强度校核报告．2005．
[106] 彭如海．(2003)．船舶工程中的力学问题．力学与实践．第25卷第5期．
[107] 秦洪德．船舶运动与波浪载荷计算的非线性方法研究．哈尔滨工程大学博士学位论文，2003年．
[108] 任慧龙．非线性波浪载荷与船体极限强度．哈尔滨工程大学博士学位论文，1995年．
[109] 沈国光．(1997)．矩形容器内流体晃动的数值模拟．水动力学研究与进展．Ser A 12(3)：281-288页．
[110] 沈国光．(1990)．柱形容器内储液的驻留运动和地震响应．水动力学研究和进展．A辑，5(4)：68-75页．
[111] 陶智祥，戴仰山．外张砰击载荷．中国造船，1991年第4期：43-51页．
[112] 万水，朱德懋．(1998)．液固耦合内流问题及防晃研究进展．工程力学．Vol．15 No．3．
[113] 王仁，熊祝华，黄文彬著．(1998)．塑性力学基础．科学出版社．
[114] 王德禹，李龙渊，施其．(2000)．三自由度晃荡模拟装置及其模态分析．海洋工程．Vol．18 No．4．
[115] 王德禹，金咸定，李龙渊．(1998)．液舱流体晃荡德模型试验．上海交通大学学报．Vol．32 No．11．
[116] 王建军，陆明万，张雄等．(2001)．自由液面流体大晃动有限元方法．水动力学研究与进展．A辑第16卷第3期．
[117] 王建军，李其汉，朱梓根，陆明万，张雄．(2001)．自由液面大晃动的流固耦合数值分析方法研究进展．力学季刊．Vol．22 No．4．
[118] 王献孚等．计算船舶流体力学．上海交通大学出版社．1992．
[119] 王永学．任意容器三维液体晃荡的数值模拟．大连理工大学博士学位论文．1989．
[120] 王自力．船舶碰撞损伤机理与结构耐撞性研究．上海交通大学博士学位论文．2000年．
[121] 温德超，郑兆昌，孙焕纯．(1996)．用ALE和时间分裂步法分析三维粘性流体大幅晃动的非线性问题．振荡与冲击．Vol．15 No．3．
[122] 吴望一．流体力学．北京大学出版社．1981．
[123] 夏益霖．(1995)．液体晃动非线性阻尼的描述方法．强度与环境．第4期．
[124] 夏益霖，许婉丽．(1988)．火箭液体推进剂防晃试验研究．强度与环境．(6)：24-30页．
[125] 夏益霖．(1991)．液体晃动等效力学模型的参数识别．应用力学学报，8(4)：24-35页．
[126] 项晨，陈浩然，郭兆璞．(1996)．复合材料加筋结构的流固耦合振动及动力响应分析．复合材料学报．Vol．13 No．3．
[127] 谢楠，程军，郜焕秋．(1998)．舰船在波浪中运动时间历程的数值模拟．船舶力学．Vol．2 No．6．
[128] 颜开．(1987)．MAC方法的思想、发展和应用．水动力学研究与进展．A辑，2(3)：133-142页．
[129] 杨代盛，桑国光，李维扬，戴仰山．船舶强度的概率方法．哈尔滨：哈尔滨工程大学出版社，1994年．
[130] 郁时炼，周科健．(1991)．半圆形挡板防晃特性的计算．强度与环境．第4期．30-36页．
[131] 张兴福．三维弹性容器内晃荡问题的二阶频域解．上海交通大学博士学位论文．1998年1月．
[132] 张海彬．FPSO储油轮与半潜式平台波浪载荷三维计算方法研究．哈尔滨工程大学博士学位论文．2004．
[133] 张雄，陆明万，王建军．(1997)．任意拉格朗日—欧拉描述发研究进展．计算力学学报．Vol．14 No．(2)．
[134] 邹志利，邱大洪，王永学．(1996)．VOF法模拟波浪槽中二维非线性波．水动力学研究与进展．Ser．A
[135] 周叮．(1991)．贮液圆筒在水中的弯曲自由振动．应用数学和力学．11(5)：439-446页．
[136] 周叮，丁文镜．(1990)．储箱内液体晃动特性及其力学参数的识别问题．强度与环境．79：11-25页．
[137] 朱仁庆，吴有生，彭兴宇，沈进威．船舶液体晃荡动力学的研究方法及进展．华东船舶工业学院学报．Vol．13 No．1．
[138] 朱仁庆，颜开，吴有生．盛液容器内液体二维晃荡的数值模拟．(1998)．华东船舶工业学院学报．Vol．12 No．2．
[139] 朱仁庆，吴有生．(2002)．液舱内流体晃荡特性数值研究．中国造船．Vol．43 No．2．
[140] 朱仁庆．液体晃荡及其与结构的相互作用．中国船舶科学研究中心博士学位论文．
[141] 庄惠忠．船舶在波浪中的载荷与压力分布研究．哈尔滨工程大学硕士学位论文，1994年12月．