浮体二阶非线性水弹性力学分析方法
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摘要
浮体水弹性力学将浮体结构力学和浮体水动力学有机地结合起来，为评估柔性浮
体结构的总体性能提供了一个更具一致性和合理性的方法。水弹性理论至今已发展了
20多年，着重研究线性问题（Bishop ＆ Price，1979；Wu，1984；杜双兴，1996；王大
云，1996）。线性理论着重研究小运动浮体及在流体中的结构频率特征处于波频范围
内或大于波频频段的弹性体。在高海况条件下浮体作大幅运动时其刚体运动引起的二
阶力及瞬时湿表面变化引起的二阶流体力可能对浮体产生较大的非线性影响。当海洋
浮体的尺度大为增加，远远超过常规船舶的尺度时，他们的低频特征十分显著，在波
浪中的运动也会不同于一般的浮体。在这些情况下，就有必要研究二阶及高阶波浪力
对浮体水弹性响应的影响。本文的目的之一就是建立浮体二阶水弹性力学分析方法，
分析上述二阶波浪力对浮体水弹性分析的影响。基于多类浮体都要靠锚泊系统定位，
而关于锚泊系统与可变形体的相互作用尚缺乏深入的研究，本文的目的之二就是建立
锚泊浮体的一阶及二阶水弹性分析理论并开发相应的计算程序。
基于上述两个目的，作者在完成本文的过程中所做的主要工作包括：
（1）对二维与三维水弹性力学理论及与二阶波浪力相关的分析方法的国内外研
究情况作了简要的回顾。
（2）简要介绍了三维线性水弹性力学的基本理论和分析方法。
（3）在考虑一阶速度势和一阶响应对二阶作用力影响的情况下，推导了带航速
浮体三维非线性水弹性分析中二阶水动力系数的广义形式，建立了航行浮体三维频域
非线性水弹性分析理论。
（4）讨论了锚链系统的非线性特征，分析了对称式布置锚链系统的线性化方法，
推导了重力式锚链和张力式锚链的锚链恢复力刚度矩阵。
（5）推导得出了锚泊浮体所受水动力的广义形式，建立了锚泊浮体三维线性及
非线性频域水弹性力学运动方程。在航行浮体线性水弹性力学分析程序（吴有生、杜
双兴，1992）的基础上开发了锚泊浮体线性水弹性分析程序，使得只需简单的输入锚
链参数即可考虑锚泊系统的影响。对锚泊长方箱形的浮动均匀梁（后文简称浮式箱梁）
模型进行了线性水弹性分析预报。对预报结果进行了较为详细的分析讨论，得出了一
些可供工程应用参考的结论。
（6）开发了锚泊浮体三维非线性水弹性分析程序，并对锚泊浮式箱梁模型进行了
摘要
二阶水弹性分析预报，给出了浮式箱梁在不规则波中的和频和差频响应主坐标，计算
了位移、弯矩、剪力的时间响应和锚链系泊力，并与线性水弹性分析结果进行了比较。
详细讨论了和频和差频响应对总响应的影响和不同二阶力对总响应的贡献，以及不同
刚体模态和弹性模态间的耦合作用问题。
本文得出的主要结论有：
（l）对于对称式布置的锚链系统，在进行水动力或水弹性分析时，锚链的作用可
以近似作线性化处理，可以预先求解锚泊系统的线性刚度矩阵，将其并入水动力或水．
弹性分析的总恢复力矩阵。
（2）在波频接近于浮体在水中的湿固有频率时会出现谐振现象。所以当浮体结构
较柔，也即其固有频率较低而处于波频范围内时必须考虑浮体的水弹性响应。
门）对于系泊浮体，在水弹性响应的刚体模态即耐波性响应会出现低频谐振现象，
而且会跟后面的弹性模态产生耦合而影响结构的安全（如疲劳寿命），在系泊系统设
计阶段必须对这些现象引起注意。
门）浮式箱梁二阶水弹性分析的和频和差频主坐标与一阶主坐标类似，在各波向 学－
角时均会出现谐振现象，且谐振点的出现位置与一阶主坐标的分析结果一致。
（5）二阶力对浮体的运动有影响，受二阶力影响较大的为纵荡、横荡、垂荡、艄
摇、二节点垂弯、四节点垂弯、一节点扭转、二节点扭转等运动模态，受影响较小的
是横摇、纵摇、各阶水平弯曲、三节点垂弯和五节点垂弯等运动模态，总的规律是二
阶力对纵荡、横荡和脂摇以及与他们无耦合效应的运动模态的贡献较大，而对与他们
有耦合效应的运动模态的贡献较小。另外，总体上差频的影响大于和频。
瞩）浮体的垂向位移、弯矩和剪力受H阶力的影响都比较大，在波向角p司35 f
“和p＝1“”时，二阶非线性的分析结果的最大值一般比线性分析的结果要大。
门）锚链力在波向角p＝135”和p叫旷 时，二阶非线性效应不可忽略，其分析
结果比线性结果显著增大。
（8）在高海况下，二阶力的主要贡献是刚体的二阶转动引起的二阶力，其它二阶
力的影响则较小。
Hydroelasticity theories of ships and floating marine structures, which embody the full
complexities of the dynamics of the structure concerned and the fluid around it, provide more
consistent and more rational approaches for the assessment of the overall behavior of a
flexible marine structure. The existing theories have been developed for more than 20 years,
however mainly focus on linear problems (Bishop and Price, 1979; Wu, 1984; Du, 1996;
Wang, 1996). The linear theories are suitable for investigating a floating body with small
amplitude of motion or an elastic structure in waves with resonant frequencies within or
higher than the range of the wave frequencies. When responding to high waves with large
amplitude, the floating structure may apparently suffer from non-linear responses due to the
second order hydrodynamic forces induced by the rigid body rotations of motion and the
effect of the instantaneous wetted surface. For a marine structure with the scale much larger
than a conventional ship, its resonant frequencies in water will be very low, and its behavior
in waves will be quite different than a usual vessel. In these circumstances it is obviously
necessary to investigate the influence of the second and higher order hydrodynamic actions
on the hydroelastic responses of a floating structure. The first objective of the present thesis
is therefore to establish a second order hydroelasticity theory and the corresponding
numerical method for investigating the effect of the above mentioned second order wave
forces on the structural behavior of the floating body.
Most of the floating marine structures are kept stationary by a mooring system.
However there has still been a lack of deepening study about the interaction between a
慺lexible?structure in waves and its mooring system. The second objective of the present
thesis is to develop the second order hydroelastic analysis method and the corresponding
computer program for predicting the responses of a moored flexible floating structure to
waves.
To achieve these two objectives, the following efforts have been made and the results are
presented in the present thesis. These include:
(1) The existing two and three dimensional hydroelasticity theories and the analysis
methods for the second order wave forces are briefly reviewed.
(2) The fundamental contents and the analysis methods of three-dimensional
hydroelasticity theories are briefly introduced.
(3) Under the condition that only the contributions of the first order velocity potentials
and responses to the second order hydrodynamic forces are considered in the analysis, a
frequency domain non-linear three-dimensional hydroelasticity theory for a floating body
either traveling or stationary in waves is presented. The general formulations of the second
order hydrodynamic coefficients appearing in the non-linear three-dimensional hydroelastic
equations of motion of the floating body are also included.
(4) The non-linear characteristics of the mooring system are discussed. The linearized
III
Abstract
representations of the mooring effects, together with the stiffness matrices respectively for
symmetrically disposed tensional and gravitational mooring systems are introduced.
(5) The linear and non-linear three-dimensional hydroelastic equations of motion of the
moored floating system in frequency domain are presented. Based on the computer
program suite of linear three-dimens
体结构的总体性能提供了一个更具一致性和合理性的方法。水弹性理论至今已发展了
20多年，着重研究线性问题（Bishop ＆ Price，1979；Wu，1984；杜双兴，1996；王大
云，1996）。线性理论着重研究小运动浮体及在流体中的结构频率特征处于波频范围
内或大于波频频段的弹性体。在高海况条件下浮体作大幅运动时其刚体运动引起的二
阶力及瞬时湿表面变化引起的二阶流体力可能对浮体产生较大的非线性影响。当海洋
浮体的尺度大为增加，远远超过常规船舶的尺度时，他们的低频特征十分显著，在波
浪中的运动也会不同于一般的浮体。在这些情况下，就有必要研究二阶及高阶波浪力
对浮体水弹性响应的影响。本文的目的之一就是建立浮体二阶水弹性力学分析方法，
分析上述二阶波浪力对浮体水弹性分析的影响。基于多类浮体都要靠锚泊系统定位，
而关于锚泊系统与可变形体的相互作用尚缺乏深入的研究，本文的目的之二就是建立
锚泊浮体的一阶及二阶水弹性分析理论并开发相应的计算程序。
基于上述两个目的，作者在完成本文的过程中所做的主要工作包括：
（1）对二维与三维水弹性力学理论及与二阶波浪力相关的分析方法的国内外研
究情况作了简要的回顾。
（2）简要介绍了三维线性水弹性力学的基本理论和分析方法。
（3）在考虑一阶速度势和一阶响应对二阶作用力影响的情况下，推导了带航速
浮体三维非线性水弹性分析中二阶水动力系数的广义形式，建立了航行浮体三维频域
非线性水弹性分析理论。
（4）讨论了锚链系统的非线性特征，分析了对称式布置锚链系统的线性化方法，
推导了重力式锚链和张力式锚链的锚链恢复力刚度矩阵。
（5）推导得出了锚泊浮体所受水动力的广义形式，建立了锚泊浮体三维线性及
非线性频域水弹性力学运动方程。在航行浮体线性水弹性力学分析程序（吴有生、杜
双兴，1992）的基础上开发了锚泊浮体线性水弹性分析程序，使得只需简单的输入锚
链参数即可考虑锚泊系统的影响。对锚泊长方箱形的浮动均匀梁（后文简称浮式箱梁）
模型进行了线性水弹性分析预报。对预报结果进行了较为详细的分析讨论，得出了一
些可供工程应用参考的结论。
（6）开发了锚泊浮体三维非线性水弹性分析程序，并对锚泊浮式箱梁模型进行了
摘要
二阶水弹性分析预报，给出了浮式箱梁在不规则波中的和频和差频响应主坐标，计算
了位移、弯矩、剪力的时间响应和锚链系泊力，并与线性水弹性分析结果进行了比较。
详细讨论了和频和差频响应对总响应的影响和不同二阶力对总响应的贡献，以及不同
刚体模态和弹性模态间的耦合作用问题。
本文得出的主要结论有：
（l）对于对称式布置的锚链系统，在进行水动力或水弹性分析时，锚链的作用可
以近似作线性化处理，可以预先求解锚泊系统的线性刚度矩阵，将其并入水动力或水．
弹性分析的总恢复力矩阵。
（2）在波频接近于浮体在水中的湿固有频率时会出现谐振现象。所以当浮体结构
较柔，也即其固有频率较低而处于波频范围内时必须考虑浮体的水弹性响应。
门）对于系泊浮体，在水弹性响应的刚体模态即耐波性响应会出现低频谐振现象，
而且会跟后面的弹性模态产生耦合而影响结构的安全（如疲劳寿命），在系泊系统设
计阶段必须对这些现象引起注意。
门）浮式箱梁二阶水弹性分析的和频和差频主坐标与一阶主坐标类似，在各波向 学－
角时均会出现谐振现象，且谐振点的出现位置与一阶主坐标的分析结果一致。
（5）二阶力对浮体的运动有影响，受二阶力影响较大的为纵荡、横荡、垂荡、艄
摇、二节点垂弯、四节点垂弯、一节点扭转、二节点扭转等运动模态，受影响较小的
是横摇、纵摇、各阶水平弯曲、三节点垂弯和五节点垂弯等运动模态，总的规律是二
阶力对纵荡、横荡和脂摇以及与他们无耦合效应的运动模态的贡献较大，而对与他们
有耦合效应的运动模态的贡献较小。另外，总体上差频的影响大于和频。
瞩）浮体的垂向位移、弯矩和剪力受H阶力的影响都比较大，在波向角p司35 f
“和p＝1“”时，二阶非线性的分析结果的最大值一般比线性分析的结果要大。
门）锚链力在波向角p＝135”和p叫旷 时，二阶非线性效应不可忽略，其分析
结果比线性结果显著增大。
（8）在高海况下，二阶力的主要贡献是刚体的二阶转动引起的二阶力，其它二阶
力的影响则较小。
Hydroelasticity theories of ships and floating marine structures, which embody the full
complexities of the dynamics of the structure concerned and the fluid around it, provide more
consistent and more rational approaches for the assessment of the overall behavior of a
flexible marine structure. The existing theories have been developed for more than 20 years,
however mainly focus on linear problems (Bishop and Price, 1979; Wu, 1984; Du, 1996;
Wang, 1996). The linear theories are suitable for investigating a floating body with small
amplitude of motion or an elastic structure in waves with resonant frequencies within or
higher than the range of the wave frequencies. When responding to high waves with large
amplitude, the floating structure may apparently suffer from non-linear responses due to the
second order hydrodynamic forces induced by the rigid body rotations of motion and the
effect of the instantaneous wetted surface. For a marine structure with the scale much larger
than a conventional ship, its resonant frequencies in water will be very low, and its behavior
in waves will be quite different than a usual vessel. In these circumstances it is obviously
necessary to investigate the influence of the second and higher order hydrodynamic actions
on the hydroelastic responses of a floating structure. The first objective of the present thesis
is therefore to establish a second order hydroelasticity theory and the corresponding
numerical method for investigating the effect of the above mentioned second order wave
forces on the structural behavior of the floating body.
Most of the floating marine structures are kept stationary by a mooring system.
However there has still been a lack of deepening study about the interaction between a
慺lexible?structure in waves and its mooring system. The second objective of the present
thesis is to develop the second order hydroelastic analysis method and the corresponding
computer program for predicting the responses of a moored flexible floating structure to
waves.
To achieve these two objectives, the following efforts have been made and the results are
presented in the present thesis. These include:
(1) The existing two and three dimensional hydroelasticity theories and the analysis
methods for the second order wave forces are briefly reviewed.
(2) The fundamental contents and the analysis methods of three-dimensional
hydroelasticity theories are briefly introduced.
(3) Under the condition that only the contributions of the first order velocity potentials
and responses to the second order hydrodynamic forces are considered in the analysis, a
frequency domain non-linear three-dimensional hydroelasticity theory for a floating body
either traveling or stationary in waves is presented. The general formulations of the second
order hydrodynamic coefficients appearing in the non-linear three-dimensional hydroelastic
equations of motion of the floating body are also included.
(4) The non-linear characteristics of the mooring system are discussed. The linearized
III
Abstract
representations of the mooring effects, together with the stiffness matrices respectively for
symmetrically disposed tensional and gravitational mooring systems are introduced.
(5) The linear and non-linear three-dimensional hydroelastic equations of motion of the
moored floating system in frequency domain are presented. Based on the computer
program suite of linear three-dimens
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