浮体浅水波浪载荷数值计算方法研究
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摘要
[目的]在浅水环境下,对波浪中浮体的响应进行求解时,其主要难点在于对有限水深格林函数及其偏导数的准确求解和快速计算。[方法]为此,利用改进的Gauss-Laguerre积分法,提出一种可精确计算有限水深格林函数及其偏导数的方法,结合循环矩阵原理,给出对称性的处理方法和简化的级数求解公式。并将所提方法与其他商业软件计算结果进行对比分析。[结果]结果表明,所提计算方法精确度较高。[结论]该方法可用于准确评估浅水中的浮体运动和波浪载荷。
[Objectives] For figuring out the response of floating structures in the waves of shallow water,the main difficulty lies in the accurate solution and efficient calculation of Green's function and its partial derivative of the finite water depth. [Methods] Therefore, a method is proposed to accurately calculate the Green's function and its partial derivative by using the improved Gauss-Laguerre quadrature; then by combining this method with circulant matrix principle, one approach for dealing with symmetry problem and a simplified way of series for solving the formula are given. Finally, the numerical results of this method are compared with those of other commercial software. [Results] The analysis results show that the method proposed in this paper has high accuracy. [Conclusions] This proposed method can be used to accurately estimate motions and wave loads of the floating structures in shallow water.
[Objectives] For figuring out the response of floating structures in the waves of shallow water,the main difficulty lies in the accurate solution and efficient calculation of Green's function and its partial derivative of the finite water depth. [Methods] Therefore, a method is proposed to accurately calculate the Green's function and its partial derivative by using the improved Gauss-Laguerre quadrature; then by combining this method with circulant matrix principle, one approach for dealing with symmetry problem and a simplified way of series for solving the formula are given. Finally, the numerical results of this method are compared with those of other commercial software. [Results] The analysis results show that the method proposed in this paper has high accuracy. [Conclusions] This proposed method can be used to accurately estimate motions and wave loads of the floating structures in shallow water.
引文
[1]Li L.Numerical seakeeping predictions of shallow water effect on two ship interactions in waves[D].Halifax,Nova Scotia:Dalhousie University,2001.
[2]谢永和,李润培,舒志.有限水深复合格林函数的数值计算[J].船舶力学,2005,9(1):23-28.Xie Y H,Li R P,Shu Z.Numerical calculation of finite water-depth composite Green function[J].Journal of Ship Mechanics,2005,9(1):23-28(in Chinese).
[3]刘日明,任慧龙,李辉.有限水深格林函数及其导数的改进Gauss-Laguerre算法[J].船舶力学,2008,12(2):188-196.Liu R M,Ren H L,Li H.An improved Gauss-Laguerre method for finite water depth Green function and its derivatives[J].Journal of Ship Mechanics,2008,12(2):188-196(in Chinese).
[4]Wehausen J V,Laitone E V.Surface waves,handbuch der physik[M].Berlin:Springer-Verlag,1960:446-778.
[5]John F.On the motion of floating bodies II:simple harmonic motions[J].Communications on Pure and Applied Mathematics,1950,3(1):45-101.
[6]Newman J N.Algorithms for the free-surface green function[J].Journal of Engineering Mathematics,1985,19(1):57-67.
[7]Newman J N.The exciting forces on a moving body in waves[J].JournalofShip Research,1965,9(3):190-199.
[8]卢诚波.几类循环矩阵的快速算法研究[D].上海:上海大学,2011:17.Lu C B.Fast algorithm for several circulant matrix[D].Shanghai:Shanghai University,2011:17(in Chinese).
[9]戴仰山,沈进威,宋竞正.船舶波浪载荷[M].北京:国防工业出版社,2007:27-31.Dai Y S,Shen J W,Song J Z.Ship wave load[M].Beijing:National Defense Industry Press,2007:27-31.
[10]ISSC.Very large floating structures[C]//16thInternational Ship and Offshore Structures Congress.Southampton,UK:ISSC,2006.
[2]谢永和,李润培,舒志.有限水深复合格林函数的数值计算[J].船舶力学,2005,9(1):23-28.Xie Y H,Li R P,Shu Z.Numerical calculation of finite water-depth composite Green function[J].Journal of Ship Mechanics,2005,9(1):23-28(in Chinese).
[3]刘日明,任慧龙,李辉.有限水深格林函数及其导数的改进Gauss-Laguerre算法[J].船舶力学,2008,12(2):188-196.Liu R M,Ren H L,Li H.An improved Gauss-Laguerre method for finite water depth Green function and its derivatives[J].Journal of Ship Mechanics,2008,12(2):188-196(in Chinese).
[4]Wehausen J V,Laitone E V.Surface waves,handbuch der physik[M].Berlin:Springer-Verlag,1960:446-778.
[5]John F.On the motion of floating bodies II:simple harmonic motions[J].Communications on Pure and Applied Mathematics,1950,3(1):45-101.
[6]Newman J N.Algorithms for the free-surface green function[J].Journal of Engineering Mathematics,1985,19(1):57-67.
[7]Newman J N.The exciting forces on a moving body in waves[J].JournalofShip Research,1965,9(3):190-199.
[8]卢诚波.几类循环矩阵的快速算法研究[D].上海:上海大学,2011:17.Lu C B.Fast algorithm for several circulant matrix[D].Shanghai:Shanghai University,2011:17(in Chinese).
[9]戴仰山,沈进威,宋竞正.船舶波浪载荷[M].北京:国防工业出版社,2007:27-31.Dai Y S,Shen J W,Song J Z.Ship wave load[M].Beijing:National Defense Industry Press,2007:27-31.
[10]ISSC.Very large floating structures[C]//16thInternational Ship and Offshore Structures Congress.Southampton,UK:ISSC,2006.