﻿ 固定式海洋平台的时域振动响应研究
 舰船科学技术  2016, Vol. 38 Issue (8): 52-56 PDF

1. 中国计量学院 浙江流量计量技术重点实验室, 浙江 杭州 310018 ;
2. 浙江水利水电学院 机械与汽车工程学院, 浙江 杭州 310018

Time domain vibration response of the fixed offshore platform
XIE Zhuo1, ZHANG Huo-ming1, FANG Gui-sheng2, KONG Ling-bin1
1. Zhejiang Provincial Key Laboratory of Flow Measurement Technology, China Jiliang University, Hangzhou 310018, China ;
2. Zhejiang Water Conservancy and Hydropower College, Mechanical and Automotive Engineering, Hangzhou 310018, China
Abstract: The study of offshore structures is an important subject in the field of ocean engineering. Based on Airy linear wave theory and Morrison equation, the equation of motion of the platform was derived. The wave force was simplified to two nodes, and the response characteristics of the structure were analyzed from the point of view of dynamics. A simplified fixed platform was used as an example. The displacement response, velocity response and acceleration response of the structure were analyzed and compared with different incident waves. Research results show that the intensity of incident wave increases the structure vibration becomes more intense and structural vibration response is not only related to the incident wave period and wave height, and the wave form of also have certain relationship.
Key words: fixed offshore platform     time domain     vibration response
0 引言

1 理论分析

Airy线性波理论是波浪理论中最基本最常用的波浪理论。Airy波浪理论将非线性的波浪自由面条件，近似以线性的边界条件代替，这一线性边界适应于波高很小的情况。Airy线性波的速度势为:

 $\varphi (x,t) = \frac{{gH}}{{2\omega }}\frac{{\cos h kz}}{{\cos h kd}}\sin (kx-\omega t)\text{，}$ (1)

 $\eta (x,t) = \frac{H}{2}\cos (kx-\omega t)\text{，}$ (2)

 $L = T\sqrt {\frac{{gL}}{{2{\rm{\pi }}}}\tan h\frac{{2{\rm{\pi }}d}}{L}} 。$ (3)
 图 1 波浪示意图 Fig. 1 Schematic diagram of wave

θ=kx-ωt，由线性波速度势可以得到波浪水质点速度和加速度的表达式为:

 $u = \frac{{\partial \varphi }}{{\partial x}} = \frac{{gkH}}{{2\omega }}\frac{{\cos h kz}}{{\cos h kd}}\cos \theta \text{，}$ (4)
 $\mathop u\limits^. = \frac{{\partial u}}{{\partial t}} = \frac{{gkH}}{2}\frac{{\cos h kz}}{{\cos h kd}}\sin \theta \text{。}$ (5)

 $f = {C_M}{A_I}\mathop u\limits^. + {C_D}{A_D}u\left| u \right| \text{。}$ (6)

 $\begin{array}{*{20}{c}} {f(x,t) = {C_M}{A_I}\frac{{gkH}}{2}\frac{{\cos hkz}}{{\cos hkd}}\sin \theta + }\\ {\sqrt {\frac{8}{{\rm{\pi }}}} {C_D}{A_D}{\sigma _u}\frac{{gkH}}{{2\omega }}\frac{{\cos hkz}}{{\cos hkd}}\cos \theta ,}\\ {f(x,t) = {C_M}{A_I}gk\frac{{\cos hkz}}{{\cos hkd}}\eta (x,t + T/4) + }\\ {\sqrt {\frac{8}{{\rm{\pi }}}} {C_D}{A_D}{\sigma _u}\frac{{gk}}{\omega }\frac{{\cos hkz}}{{\cos hkd}}\eta (x,t)} \end{array}{\rm{ }}$ (7)

 $\sigma _{{u}}^2 = \int_0^\infty {{{(\omega \displaystyle\frac{{\cosh kz}}{{\sinh kh}})}^2}{S_\eta }(\omega )} {\rm d}\omega$

 $M\ddot Y + C\dot Y + KY = P(t)。$ (8)

 $y(t) = \sum\limits_{i = 1}^n {{\phi _i}{q_i}(t)} \text{，}$ (9)

 $v(t) = \sum\limits_{i = 1}^n {{\phi _i}{{\mathop q\limits^. }_i}(t)} \text{，}$ (10)
 $a(t) = \sum\limits_{i = 1}^n {{\phi _i}{{\mathop q\limits^{..} }_i}(t)} \text{。}$ (11)
2 算例分析

 图 2 平台结构示意图 Fig. 2 Schematic diagram of platform structure
2.1 参数设置

2.2 计算结果

 图 3 一年一遇海况规则波面高程 Fig. 3 Once a year the sea surface elevation rule

 图 4 平台位移对比图 Fig. 4 Platform displacement contrast diagram

 图 5 平台速度对比图 Fig. 5 Platform speed comparison chart

 图 6 平台加速度对比图 Fig. 6 Platform acceleration contrast diagram

 图 7 三种海况下结构上甲板位移响应图 Fig. 7 Comparison of displacement response of structure on deck

 图 8 三种海况下结构下甲板位移响应图 Fig. 8 Comparison of displacement response of structure under deck

 图 9 三种海况下结构上甲板速度响应图 Fig. 9 Comparison of speed response of structure on deck

 图 10 三种海况下结构下甲板速度响应图 Fig. 10 Comparison of speed response of structure under deck

 图 11 三种海况下结构上甲板加速度响应图 Fig. 11 Comparison of acceleration response of structure on deck

 图 12 三种海况下结构下甲板加速度响应图 Fig. 12 Comparison of acceleration response of structure under deck

Pierson-Moskowitz波高谱于1966年被国际船模水池会议定为标准海浪谱，目前广泛应用于海浪研究及有关工程问题。采用以P-M谱为随机波浪谱作为入射波，取波浪周期12.39 s，有义波高12.5 m，其波面高程如图 13所示。计算结构位移、速度和加速度响应并与同条件下以规则波为入射波所得振动响应结果进行比较，限于篇幅这里仅给出位移响应的对比结果，如图 14图 15所示。

 图 13 P-M谱的波面高程 Fig. 13 Wave height of P-M spectrum

 图 14 结构上甲板位移响应对比图 Fig. 14 Comparison of displacement response of structure on deck

 图 15 结构上甲板位移响应对比图 Fig. 15 Comparison of displacement response of structure under deck

3 结语

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