﻿ 多浮体海上平台水动力响应分析
 舰船科学技术  2017, Vol. 39 Issue (10): 75-78 PDF

Hydrodynamic response analysis for modules-offshore platform
LI Hong-xian, CHEN Yan-mao, LIU Qi-xian
College of Engineering, Sun Yat-sen University, Guangzhou 510006, China
Abstract: Modules-offshore platform is a typical multi-oscillator system with flexible-rigid-fluid coupling. In this paper, the hydrodynamic software AQWA is used to establish the numerical simulation model of the platform. Then, Hydrodynamic analysis of the platform is carried out. The results show that response amplitude of platform appears large oscillation interval with change of the cable stiffness; In the low and high frequency region, the additional damping of the platform is relatively small; Response amplitude of platform is small and has a good stability in the high frequency region. This study could provide guidance for the design of large offshore platform.
Key words: modules-offshore platform     flexible-rigid-fluid coupling     AQWA     hydrodynamic analysis
0 引 言

1 基本理论

 $\phi (\overrightarrow X ,t) = {a_w}\varphi (\overrightarrow X ){e^{ - i\omega t}},$ (1)

 $P = - \rho \frac{{\partial \phi (\overrightarrow X ,t)}}{{\partial t}} = i\omega \rho \varphi (\overrightarrow X ){e^{ - i\omega t}},$ (2)

 ${F_m} = - \iint\nolimits_{{S_0}} {P{n_m}} {\rm{d}}S = - i\omega \rho \iint\nolimits_{{S_0}} {\varphi (\overrightarrow X )} {n_m}{\rm{d}}S,$ (3)

 ${F_m} = \left[ {({F_{Im}} + {F_{dm}}) + \sum\limits_{k = 1}^6 {{F_{rmk}}{X_k}} } \right],$ (4)
 $\left\{ {\begin{array}{*{20}{c}}\!\!\!\!\! {{F_{Im}} = - i\omega \rho \iint\limits_{{S_0}} {{\varphi _I}(\overrightarrow X ){n_m}{\rm{d}}S} },\\\!\!\!\!\! {{F_{dm}} = - i\omega \rho \iint\limits_{{S_0}} {{\varphi _d}(\overrightarrow X ){n_m}{\rm{d}}S} },\\\!\!\!\!\! {{F_{rmk}} = - i\omega \rho \iint\limits_{{S_0}} {{\varphi _{rk}}(\overrightarrow X ){n_m}{\rm{d}}S} }{\text{。}}\end{array}} \right.$ (5)

 $\begin{split}{F_{rmk}} = & - i\omega \rho \iint\limits_{{S_0}} {\left\{ {{\rm{Re}}\left[ {{\varphi _{rk}}(\overrightarrow X )} \right] + i{\mathop{\rm Im}\nolimits} \left[ {{\varphi _{rk}}(\overrightarrow X )} \right]} \right\}{n_m}{\rm{d}}S} = \\ & \omega \rho \iint\limits_{{S_0}} {{\mathop{\rm Im}\nolimits} \left[ {{\varphi _{rk}}(\overrightarrow X )} \right]{n_m}{\rm{d}}S} - \\ & i\omega \rho \iint\limits_{{S_0}} {{\mathop{\rm Re}\nolimits} \left[ {{\varphi _{rk}}(\overrightarrow X )} \right]{n_m}{\rm{d}}S} = {\omega ^2}{A_{mk}} + i\omega {B_{mk}}{\text{。}}\end{split}$ (6)

 $[ - {\omega ^2}{M} - i\omega {C} + {K}]\cdot{U} = {F}{\text{。}}$ (7)

 ${H} = {[ - {\omega ^2}{M} - i\omega {C} + {K}]^{ - 1}},$ (8)

 ${U} = {HF}{\text{。}}$ (9)

2 计算模型

 图 1 多浮体平台 Fig. 1 Modules-offshore platform

 ${T_c} = \left\{ {\begin{array}{*{20}{c}}{{k_c}(L - {L_0}),L \geqslant {L_0}},\\{\!\!\!\!\!\!\!\!\!\!\!\! 0,\;\;\;\;\;L < {L_0}}{\text{。}}\end{array}} \right.$ (10)

 ${T_F} = \left\{ {\begin{array}{*{20}{c}}{\!\!\! {k_1}\Delta L + {k_2}{{(\Delta L)}^2} + {k_3}{{(\Delta L)}^3},\Delta L \geqslant 0};\\{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! 0,\;\;\;\;\;\;\;\;\;\Delta L < 0}{\text{。}}\end{array}} \right.$ (11)

 图 2 有限元模型 Fig. 2 Finite element model

 $S\left( \omega \right) = \alpha {g^2}{\omega ^{ - 5}}{\gamma ^{\exp \left[ { - 0.5{{\left( {\frac{{\omega - {\omega _p}}}{{\sigma {\omega _p}}}} \right)}^2}} \right]}}\exp \left[ { - \frac{5}{4}{{\left( {\frac{\omega }{{{\omega _p}}}} \right)}^{ - 4}}} \right],$ (12)
 $\alpha = \frac{5}{{16}}\left( {\frac{{H_s^2\omega _p^4}}{{{g^2}}}} \right) \cdot \left[ {1 - 0.287\ln \gamma } \right]{\text{。}}$ (13)

 $\sigma = \left\{ {\begin{array}{*{20}{c}}{0.07,\;\;\;\;\;\omega \leqslant {\omega _p}};\\{0.09,\;\;\;\;\;\omega > {\omega _p}}{\text{。}}\end{array}} \right.$ (14)
3 结果与分析

 图 3 浮体响应幅值随缆绳刚度变化（0°波浪角） Fig. 3 Response amplitude of module changes with the cable stiffness

 图 4 附加阻尼随波浪频率的变化规律 Fig. 4 The variation of additional damping with wave frequency

 图 5 M2的幅值响应算子（0°波浪方位角，kc=500 kN/m） Fig. 5 RAOs of M2 (0° azimuth of wave，kc=500 kN/m)
4 结 语

1）浮体响应幅值随连接件刚度变化会出现较大振荡区间现象，这种跳跃的现象与非线性系统弯曲的共振有关，所以在设计连接件刚度时候一定要注意大幅值振荡区间。

2）在低频和高频区域，模块附加阻尼相对较小。

3）得到网络模块在高频区域内，幅值响应较小，稳定性良好。

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