可计及初始横倾的船舶运动与波浪载荷预报
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摘要
船舶在波浪中的运动响应及波浪载荷预报，对于船体结构有限元分析、可靠性分析及疲劳分析等是十分重要的。当今广泛采用的切片法满足了工程上所需要的精度要求，但一般都只能适用于正浮状态具有横向对称性的船舶。本文尝试对原有的切片法进行扩展，使之能够考虑到船体横倾影响，进而重新建立运动方程，求解处于横倾状态的船舶在波浪中的运动响应及剖面波浪载荷。
首先，本文建立船体横倾的模型，给出横倾后船体的静水力及质量矩阵的算法。然后，采用比例弧法对全剖面进行保角变换并在此基础上用多极展开法计算非对称剖面的辐射流场，进而采用切片理论合成全船的水动力系数并对FLOKSTRA集装箱船进行了考虑横倾影响的运动响应预报。最后，本文给出了处于横倾状态船体的剖面波浪载荷计算方法，并针对实船进行了相应的波浪载荷预报。
Prediction of the motions and wave loads acting on ships sailing on the sea is very important to the FEM, the probability analysis and the fatigue analysis of ship structures. The Strip Theory can meet the demand of shipbuilding engineering. But the common method can only use on ships with lateral symmetry which is in the state of zero trim. This paper will present an improved method which can take account of the transverse inclination and predict the motions and wave loads of a ship in heel.
Firstly, the model of ship with the sate of heel is developed and then the hydrostatic forces and mass matrix of such model is calculated. Secondly, proportional arc length method is used to conformal mapping process of asymmetry sections so as to solute the 2D radiation problem with the method of multipole expansion. On the basis of above, 3D hydrodynamic coefficients are given and motions of the container ship FLOKSTRA are predicted considering the initial heel. In the end, the calculation dealing with the sectional wave load acting on a ship in the state of heel is made.
首先，本文建立船体横倾的模型，给出横倾后船体的静水力及质量矩阵的算法。然后，采用比例弧法对全剖面进行保角变换并在此基础上用多极展开法计算非对称剖面的辐射流场，进而采用切片理论合成全船的水动力系数并对FLOKSTRA集装箱船进行了考虑横倾影响的运动响应预报。最后，本文给出了处于横倾状态船体的剖面波浪载荷计算方法，并针对实船进行了相应的波浪载荷预报。
Prediction of the motions and wave loads acting on ships sailing on the sea is very important to the FEM, the probability analysis and the fatigue analysis of ship structures. The Strip Theory can meet the demand of shipbuilding engineering. But the common method can only use on ships with lateral symmetry which is in the state of zero trim. This paper will present an improved method which can take account of the transverse inclination and predict the motions and wave loads of a ship in heel.
Firstly, the model of ship with the sate of heel is developed and then the hydrostatic forces and mass matrix of such model is calculated. Secondly, proportional arc length method is used to conformal mapping process of asymmetry sections so as to solute the 2D radiation problem with the method of multipole expansion. On the basis of above, 3D hydrodynamic coefficients are given and motions of the container ship FLOKSTRA are predicted considering the initial heel. In the end, the calculation dealing with the sectional wave load acting on a ship in the state of heel is made.
引文
[1] Weinblum, G. and St. Denis, M. On the Motions of Ships at Sea. Trans. SNAME, 1950, Vol.58:184-248P
[2] St. Denis, M. and Pierson, W. J. Jr. On the Motions of Ships in Confused Seas. Trans. SNAME, 1953, Vol.61:280-358P
[3] Korvin-Kroukovsky, B. V. Investigation of Ship Motions in Regular Waves. Tran. SNAME, 1955, Vol.63:386-435P
[4] Korvin-Kroukovsky, B. V. and Jacobs, W. R. Pitching and Heaving Motions of a Ship in Regular Waves. Trans. SNAME, 1957, Vol.65:590-632P
[5] Ogilvie, T. F. and Tuck, E. O. A Rational Strip Theory of Ship Motions. Dept. Nav. Arch. Mar. Eng., Univ. Michigan, Ann Arbor, 1969
[6] Tssai, F. and Takagi, M. Theory and Calculation of Ship Response in Regular Waves. Proc, Symp. on Seaworthiness of Ships, Japan Society of Navel Architects., Tokyo, 1969
[7] Salvesen, N., Tuck, E. O. and Faltinsen, O. Ship Motion and Sea Loads. Trans. SNAME, 1970, Vol.78:250-287P
[8] ISSC. Proceedings of Int. Ship & Offshore Structures Congress, St. John's, Canada. 1994
[9] Jensen, J. J. and Pedersen, P. T. Wave-induced Bending Moments in Ships - A Quadratic Theory. The Royal Institution of Naval Architects, 1978:151-165P
[10] Gerritsma, J. and Beukelman, W. Analysis of the Modified Strip Theory for the calculation of ship motions and wave bending moments. International Shipbuilding Progress, 1967, Vol. 14:319-337P
[11] Meyerhoff, W. K. and Schlachter. An Approach for the Determination of Hull-Girder Loads in a Seaway Including Hydrodynamic Impacts. Ocean Engineering, 1980, Vol.7 (6):305-332P
[12] Cummins, W. E. The Impulse Response Function and Ship Motions. Schiffstechnik, 1962, Vol.9:101-109P
[13] Sding, H. Leckstabilitt im Seegang. Report no.429, Institut fr Schiffbau, Hamburg, 1982
[14] Xia, J., Wang, Z. and Jensen, J. J. Non-linear Wave Loads and Ships Responses by a Time-domain Strip Theory. DCAMM Report no.569, Technical University of Denmark, March 1998
[15] Newman, J. N. The Theory of Ship Motions. Advances in Applied Mechanics, 1978, Vol. 18:221-283P
[16] Newman, J. N. and Sclavounos, P. D. The Unified Theory for Ship Motions. Proceedings, 13th Symp. on Naval Hydrodynamics, Tokyo, 1980
[17] Kashiwagi, M. Prediction of Surge and Its Effect on Added Resistance by Means of the Ship Motion Based on Three-Dimensional Theories. Trans. of West-Japan Soc. Nav. Arch, 1995, Vol.89:77-89P
[18] Sclavounos, P. D. The Unified Slender-body Theory: Ship Motion in Waves. Office of Naval Research Symposium on Naval Hydrodynamics, 1984, Vol.15:177-192P
[19] ITTC. Proceedings of Int. Towing Tank Conference, Kobe, Japan. 1987.
[20] Chapman, R. B. Free-surface Effects for Yawed Surface-piercing Plate. J. Ship Res., 1976, Vol.20:125-136P
[21] Faltinsen, O. and Zhao R. Numerical Prediction of Ship Motions at High Forward Speed. Philosophical Trans. of the Royal Society of London, 1991, Series A 334:241-252P
Motions of Fast Displacement Vessels in Long-crested Head Seas. HPMV, 2000
[23] 马山．基于二维半理论的垂向船舶运动和波浪载荷预报．哈尔滨工程大学硕士学位论文，2002
[24] 张海彬．船舶运动与波浪载荷三维计算方法研究．哈尔滨工程大学硕士学位论文，2001
[25] 邹元杰．船舶在波浪中的脉动压力分布预报．哈尔滨工程大学硕士学位论文，2001
[26] Shin, Y., Cung, J. S., Lin, W. M., Zhang, S. and Engle, A. Dynamic Loadings for Structural Analysis of Fine Form Container Ship Based on a Non-linear Large Amplitude Motions and Loads Method. Trans. SNAME, 1997, Vol.105:127-154P
[27] Yeung, R. W. A Singularity-Distribution Method for Free-Surface Flow Problems with an Oscillating Body. Technical Report NA 73-6, College of Engineering, University of California, Berkeley, August 1973
[28] 戴遗山，贺五洲．简单Green函数法求解三维水动力系数．中国造船，1986(3)：5-10页
[29] Nakos, D. E. and Sclavounos, P. D. Ship Motions by a Three-Dimensional Rankine Panel Method. 18th Syrup. on Naval Hydrodynamics, 1991, 21-39P
[30] Nakos, D. E., Kring, D. C. and Sclavounos, E D. Rankine Panel Methods for Time-Domain Free Surface Flows. 6th Intl. Conference on Numerical Ship Hydrodynamics, University of Iowa, 1993
[31] 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
[32] 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
[33] 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
[34] C. H. Kim, Frank S. Chou and David Tien. Motions and Hydrodynamic Loads of a Ship Advancing in Oblique Waves. Trans. SNAME, 1980, Vol.88:225-256P
[35] Frank, W. Oscillation of Cylinders in or below the Free Surface of Deep Fluids. Naval Ship R&D Center, Report 2375, Washington, D. C., 1967
[36] Ursell, F. On the Heaving Motion of a Circular Cylinder on the Su rface of a Fluid. Quarterly J. of Mech. and Applied Math, 1949, Vol.2:218-231P
[37] Tasai, F. Damping Force and Added Mass of Ships Heaving and Pitching. Soc. Naval Architects of Japan, 1959, Vol. 105:47-56P
[38] Timman, R. and Newman, J. N. The Coupled Damping Coefficients of Symmetric Ships. J. of Ship Research, 1962, Vol.5, No.4
[39] Haskind, M. D. Two Papers on the Hydrodynamic Theory of Heaving and Pitching of a Ship. Technical & Research Bulletin No.1-12, SNAME, Jersey City, N. J., 1953
[40] 戴遗山，顾懋祥，王太舒．船舶适航性计算方法(五个自由度的运动)，船工科技，1978(1)：1-12页
[41] 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
[42] 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论文，1994
[43] 盛振邦，杨尚荣，陈雪深．船舶静力学．上海：上海交通大学出版社，1992年
[44] 秦洪德，孙晓雅，宋竞正．多极展开法求解非对称剖面辐射绕射流场．哈尔滨工程大学学报，2001(3)：17-21页
[2] St. Denis, M. and Pierson, W. J. Jr. On the Motions of Ships in Confused Seas. Trans. SNAME, 1953, Vol.61:280-358P
[3] Korvin-Kroukovsky, B. V. Investigation of Ship Motions in Regular Waves. Tran. SNAME, 1955, Vol.63:386-435P
[4] Korvin-Kroukovsky, B. V. and Jacobs, W. R. Pitching and Heaving Motions of a Ship in Regular Waves. Trans. SNAME, 1957, Vol.65:590-632P
[5] Ogilvie, T. F. and Tuck, E. O. A Rational Strip Theory of Ship Motions. Dept. Nav. Arch. Mar. Eng., Univ. Michigan, Ann Arbor, 1969
[6] Tssai, F. and Takagi, M. Theory and Calculation of Ship Response in Regular Waves. Proc, Symp. on Seaworthiness of Ships, Japan Society of Navel Architects., Tokyo, 1969
[7] Salvesen, N., Tuck, E. O. and Faltinsen, O. Ship Motion and Sea Loads. Trans. SNAME, 1970, Vol.78:250-287P
[8] ISSC. Proceedings of Int. Ship & Offshore Structures Congress, St. John's, Canada. 1994
[9] Jensen, J. J. and Pedersen, P. T. Wave-induced Bending Moments in Ships - A Quadratic Theory. The Royal Institution of Naval Architects, 1978:151-165P
[10] Gerritsma, J. and Beukelman, W. Analysis of the Modified Strip Theory for the calculation of ship motions and wave bending moments. International Shipbuilding Progress, 1967, Vol. 14:319-337P
[11] Meyerhoff, W. K. and Schlachter. An Approach for the Determination of Hull-Girder Loads in a Seaway Including Hydrodynamic Impacts. Ocean Engineering, 1980, Vol.7 (6):305-332P
[12] Cummins, W. E. The Impulse Response Function and Ship Motions. Schiffstechnik, 1962, Vol.9:101-109P
[13] Sding, H. Leckstabilitt im Seegang. Report no.429, Institut fr Schiffbau, Hamburg, 1982
[14] Xia, J., Wang, Z. and Jensen, J. J. Non-linear Wave Loads and Ships Responses by a Time-domain Strip Theory. DCAMM Report no.569, Technical University of Denmark, March 1998
[15] Newman, J. N. The Theory of Ship Motions. Advances in Applied Mechanics, 1978, Vol. 18:221-283P
[16] Newman, J. N. and Sclavounos, P. D. The Unified Theory for Ship Motions. Proceedings, 13th Symp. on Naval Hydrodynamics, Tokyo, 1980
[17] Kashiwagi, M. Prediction of Surge and Its Effect on Added Resistance by Means of the Ship Motion Based on Three-Dimensional Theories. Trans. of West-Japan Soc. Nav. Arch, 1995, Vol.89:77-89P
[18] Sclavounos, P. D. The Unified Slender-body Theory: Ship Motion in Waves. Office of Naval Research Symposium on Naval Hydrodynamics, 1984, Vol.15:177-192P
[19] ITTC. Proceedings of Int. Towing Tank Conference, Kobe, Japan. 1987.
[20] Chapman, R. B. Free-surface Effects for Yawed Surface-piercing Plate. J. Ship Res., 1976, Vol.20:125-136P
[21] Faltinsen, O. and Zhao R. Numerical Prediction of Ship Motions at High Forward Speed. Philosophical Trans. of the Royal Society of London, 1991, Series A 334:241-252P
Motions of Fast Displacement Vessels in Long-crested Head Seas. HPMV, 2000
[23] 马山．基于二维半理论的垂向船舶运动和波浪载荷预报．哈尔滨工程大学硕士学位论文，2002
[24] 张海彬．船舶运动与波浪载荷三维计算方法研究．哈尔滨工程大学硕士学位论文，2001
[25] 邹元杰．船舶在波浪中的脉动压力分布预报．哈尔滨工程大学硕士学位论文，2001
[26] Shin, Y., Cung, J. S., Lin, W. M., Zhang, S. and Engle, A. Dynamic Loadings for Structural Analysis of Fine Form Container Ship Based on a Non-linear Large Amplitude Motions and Loads Method. Trans. SNAME, 1997, Vol.105:127-154P
[27] Yeung, R. W. A Singularity-Distribution Method for Free-Surface Flow Problems with an Oscillating Body. Technical Report NA 73-6, College of Engineering, University of California, Berkeley, August 1973
[28] 戴遗山，贺五洲．简单Green函数法求解三维水动力系数．中国造船，1986(3)：5-10页
[29] Nakos, D. E. and Sclavounos, P. D. Ship Motions by a Three-Dimensional Rankine Panel Method. 18th Syrup. on Naval Hydrodynamics, 1991, 21-39P
[30] Nakos, D. E., Kring, D. C. and Sclavounos, E D. Rankine Panel Methods for Time-Domain Free Surface Flows. 6th Intl. Conference on Numerical Ship Hydrodynamics, University of Iowa, 1993
[31] 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
[32] 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
[33] 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
[34] C. H. Kim, Frank S. Chou and David Tien. Motions and Hydrodynamic Loads of a Ship Advancing in Oblique Waves. Trans. SNAME, 1980, Vol.88:225-256P
[35] Frank, W. Oscillation of Cylinders in or below the Free Surface of Deep Fluids. Naval Ship R&D Center, Report 2375, Washington, D. C., 1967
[36] Ursell, F. On the Heaving Motion of a Circular Cylinder on the Su rface of a Fluid. Quarterly J. of Mech. and Applied Math, 1949, Vol.2:218-231P
[37] Tasai, F. Damping Force and Added Mass of Ships Heaving and Pitching. Soc. Naval Architects of Japan, 1959, Vol. 105:47-56P
[38] Timman, R. and Newman, J. N. The Coupled Damping Coefficients of Symmetric Ships. J. of Ship Research, 1962, Vol.5, No.4
[39] Haskind, M. D. Two Papers on the Hydrodynamic Theory of Heaving and Pitching of a Ship. Technical & Research Bulletin No.1-12, SNAME, Jersey City, N. J., 1953
[40] 戴遗山，顾懋祥，王太舒．船舶适航性计算方法(五个自由度的运动)，船工科技，1978(1)：1-12页
[41] 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
[42] 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论文，1994
[43] 盛振邦，杨尚荣，陈雪深．船舶静力学．上海：上海交通大学出版社，1992年
[44] 秦洪德，孙晓雅，宋竞正．多极展开法求解非对称剖面辐射绕射流场．哈尔滨工程大学学报，2001(3)：17-21页