﻿ THAFTS在大型散货船水弹性响应中的应用
 舰船科学技术  2018, Vol. 40 Issue (12): 37-43, 48 PDF
THAFTS在大型散货船水弹性响应中的应用

Appliction of THAFTS in hydroelastic response of a large bulk carrier
TIAN Chao, GUAN Teng
China Ship Scientific Research Center, Wuxi 214082, China
Abstract: With the dramatic increase of ship size, in the prediction of seakeeping and wave loads of ships, it is necessary to use hydroelastic analysis method to take the fluid and structure interaction into account. In the present paper, THAFTS (Three-dimensional Hydroelastic Analysis of Floating and Translating Structure) software, developed by China Ship Scientific Research Center, was utilized to study the hydroelastic response of a large bulk carrier. At first, the natural frequency and dry mode of the hull in vacuum was analyzed based on FEA method. Then the motions and hydroelastic responses of the ship in the waves were calculated using modal summation theory. The influences of forward speed effects on wave loads were also discussed. Finally, the effects of springing on the fatigue damage of the ship structure were investigated and the conclusions drawn from the results are of great reference value in the structural design of large ships.
Key words: modal analysis     hydroelastic response     wave loads     fatigue damage
0 引　言

1 计算理论模型 1.1 三维水弹性理论

 $\left\{ \begin{array}{l}\overrightarrow u (t) = \sum\limits_{r = 1}^m {\overrightarrow {u_r^0} {p_r}(t)} {\text{，}}\\{\sigma _{ij}}(t) = \sum\limits_{r = 7}^m {{\sigma _{ijr}}{p_r}(t)} {\text{，}}\\V(t) = \sum\limits_{r = 7}^m {{V_r}{p_r}(t)} {\text{，}}\\M(t) = \sum\limits_{r = 7}^m {{M_r}{p_r}(t)} {\text{。}}\end{array} \right.$ (1)

 $[ - {\omega _e}^2([ a] \!+\! [ A]) + i{\omega _e}([ b] \!+\! [ B]) \!+\! ([ c] \!+\! [ C])]\{ p\} \!=\! \{ F\} {\text{，}}$ (2)

 $\left\{ \begin{array}{l}{A_{rk}} = \displaystyle\frac{\rho }{{\omega _e^2}}{\mathop{\rm Re}\nolimits} \iint\limits_{{S_0}} {\overrightarrow n \cdot \overrightarrow {u_r^0} (i{\omega _e} + \overrightarrow W \cdot \nabla ){\phi _k}{\rm d}S}{\text{，}} \\{B_{rk}} = - \displaystyle\frac{\rho }{{{\omega _e}}}{\mathop{\rm Im}\nolimits} \iint\limits_{{S_0}} {\overrightarrow n \cdot \overrightarrow {u_r^0} (i{\omega _e} + \overrightarrow W \cdot \nabla ){\phi _k}{\rm d}S}{\text{，}} \\{C_{rk}} = - \displaystyle\rho g\iint\limits_{{S_0}} {\overrightarrow n \cdot \overrightarrow {u_r^0} [g{\omega _k} + \frac{1}{2}(\overrightarrow {u_r^0} \cdot \nabla ){W^2}]{\rm d}S}{\text{，}} \\{F_r} = \rho \iint\limits_{{S_0}} {\overrightarrow n \cdot \overrightarrow {u_r^0} (i{\omega _e} + \overrightarrow W \cdot \nabla )({\phi _0} + {\phi _D}){\rm d}S}{\text{。}} \end{array} \right.$ (3)

 $\overrightarrow W = U\nabla (\overline \phi - x){\text{。}}$ (4)

 ${\varPhi _{{T}}}(x,y,z,t) = U\overline \varPhi (x,y,z) + \phi (x,y,z,t){\text{，}}$ (5)

 $\phi (x,y,z,t) = [{\phi _I}(x,y,z) + \sum\limits_{r = 1}^{m{\rm{ + }}1} {{\phi _r}(x,y,z)]{e^{i{\omega _e}t}}} {\text{，}}$ (6)

 \left\{ {\begin{aligned}&{{\nabla ^2}{\phi _r} = 0{\text{，}}\quad\quad\quad\quad\quad\quad\quad\;\,{\text{在流域中}}}{\text{；}}\\&\begin{aligned}&- {\omega _e}^2{\phi _r} + g\displaystyle\frac{{\partial {\phi _r}}}{{\partial z}} = 0{\text{，}}\quad\quad\quad\quad\;\;\;\;\,{\text{自由面条件}}{\text{；}}\\&\begin{aligned}{\displaystyle\frac{{\partial {\phi _r}}}{{\partial n}} \!=\! \left\{\begin{aligned}&[i{\omega _e}\overrightarrow {{u_r}} \!+\! \overrightarrow {{\theta _r}} \!\times\! \overrightarrow W \!-\! (\overrightarrow {{u_r}} \cdot \nabla )\overrightarrow W ] \cdot \overrightarrow n{\text{，}} \;\;\;r \!\!=\!\! 1,2,...m{\text{，}}\\& - \displaystyle\frac{{\partial {\phi _I}}}{{\partial n}}{\text{，}}\quad\quad\quad\quad\quad\quad\;\,\,\, r = m + 1{\text{；}}\end{aligned} \right.}(7)\\\begin{aligned}&\displaystyle\frac{{\partial {\phi _r}}}{{\partial z}} = 0{\text{，}}\quad\quad\quad\quad\quad\quad\quad\quad z = - \infty{\text{；}} \\&\mathop {\lim }\limits_{R \to \infty } \sqrt R \left(\displaystyle\frac{{\partial {\phi _r}}}{{\partial R}} - i{k_0}{\phi _r}\right) = 0{\text{，}}\qquad\quad\quad {\text{远场辐射条件}}{\text{。}}\end{aligned}\end{aligned}\end{aligned}\end{aligned}} \right. (7)

1.2 波激振动疲劳谱分析

 ${S_0}\left( \omega \right) = {\left| {{H_0}\left( \omega \right)} \right|^2} \cdot {S_W}\left( \omega \right){\text{，}}$ (8)

 ${\sigma _3} = \sqrt {{m_{1,0}} + {m_{2,0}}} ,{f_3} = \sqrt {f_1^2{m_{1,0}} + f_2^2{m_{2,0}}} {\text{，}}$ (9)
 $\begin{split}{\lambda _3} =& \frac{{{v_p}}}{{{v_c}}}\left[ {\lambda _H^{\frac{m}{2} + 2}\left( {1 - \sqrt {\frac{{{\lambda _W}}}{{{\lambda _H}}}} } \right) + \frac{{m\Gamma \left( {\frac{m}{2} + \frac{1}{2}} \right)}}{{\Gamma \left( {\frac{m}{2} + 1} \right)}}\sqrt {{\text{π}} {\lambda _W}{\lambda _H}} } \right] +\\& \frac{{{v_w}}}{{{v_c}}}\lambda _W^{\frac{m}{2}}{\text{，}}\end{split}$ (10)

 $\begin{array}{l}{v_p} = {\lambda _H}{v_H}\sqrt {1 + \displaystyle\frac{{{\lambda _W}}}{{{\lambda _H}}}{{\left( {\displaystyle\frac{{{v_W}}}{{{v_H}}}\varepsilon } \right)}^2}}{\text{，}} \\{v_c} = \sqrt {{\lambda _H}v_H^2 + {\lambda _W}v_W^2}{\text{，}} \\{\lambda _H} = \displaystyle\frac{{{m_{2,0}}}}{{\sigma _3^2}},{\lambda _W} = \displaystyle\frac{{{m_{1,0}}}}{{\sigma _3^2}},{v_H} = {f_2},{v_W} = {f_1}{\text{，}}\\\varepsilon = \sqrt {1 - \displaystyle\frac{{m_{3,2}^2}}{{{m_{3,0}}{m_{3,4}}}}} {\text{。}}\end{array}$

 $\begin{split}&D = \frac{T}{C}{\left( {2\sqrt 2 } \right)^m}\Gamma \left( {1 + \frac{m}{2}} \right)\times\\&\mathop \sum \limits_{n = 1}^{{n_l}} \mathop \sum \limits_{j = 1}^{{n_s}} \mathop \sum \limits_{i = 1}^{{n_h}} \left[ {{\lambda _{nji}}{p_n}{p_j}{p_i}{f_{nji}}{{\left( {{\sigma _{nji}}} \right)}^m}{\mu _{nji}}} \right]{\text{。}}\end{split}$ (11)

 ${\mu _{{{nji}}}} \!=\! 1 \!-\! \frac{{\Gamma \left[1 + \displaystyle\frac{m}{2},\upsilon _{nji}^2\right] - \upsilon _{nji}^{ - \Delta m}\Gamma \left[1 + \displaystyle\frac{{m + \Delta m}}{2},\upsilon _{nji}^2\right]}}{{\Gamma \left[1 + \displaystyle\frac{m}{2}\right]}}{\text{，}}$ (12)

 ${\nu _{nji}} = \frac{{{S_Q}}}{{2\sqrt 2 {\sigma _{nji}}}}{\text{。}}$

2 大型散货船三维线性水弹性分析

 图 1 大型散货船有限元模型 Fig. 1 FEM model of the bulk carrier

 图 2 船体湿表面网格 Fig. 2 Hydrodynamic panel model
2.1 模态分析

2.2 水动力系数与波浪激励力

 图 3 真空中大型散货船的干模态 Fig. 3 Dry mode of the bulk carrier in vacuum

 图 4 水动力系数计算结果（顶浪） Fig. 4 Results of the hydrodynamic coefficent (head sea)

 图 5 波浪激励力计算结果（顶浪） Fig. 5 Results of the excitation force (head sea)
2.3 主坐标响应

2.4 船体剖面载荷

 图 6 水弹性主坐标响应（顶浪） Fig. 6 Principal coordinate responses of the bulk carrier (head sea)

 图 7 剖面载荷计算结果（顶浪） Fig. 7 Results of the section load (head sea)

 图 8 长期预报结果 Fig. 8 The long-term prediction for vertical bending moment
2.5 疲劳分析

 图 9 疲劳损伤云图 Fig. 9 Fatigue damage cloudimage

3 结　语

1）三维水弹性分析软件THAFTS可以计算大型散货船的运动与波浪载荷，计算结果表明：无论是零航速还是15 kn航速，2节点垂向弯曲主坐标响应和3节点垂向弯曲主坐标响应以及垂向弯矩与垂向剪力在高频处均出现了波激振动现象。

2）航速增大将会引起波激振动峰值增大，且波激振动峰值甚至大于低频共振时的峰值，这必然会增大船体结构的疲劳损伤，在大型船舶的设计中应该考虑波激振动的影响。

3）对此散货船的疲劳分析发现疲劳失效的热点区域主要分布于甲板舱口角隅处以及有开孔的舱壁肋板处，且散货船在60°浪向时的疲劳损伤最大；另外，当考虑波激振动的影响时，船体的疲劳寿命明显减少。

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