﻿ 深海立管固有频率影响因素分析
 舰船科学技术  2018, Vol. 40 Issue (1): 70-74 PDF

1. 中国计量大学 浙江省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

The analysis of influence factors on natural frequency of deep-sea risers
KONG Ling-bin1, ZHANG Huo-ming1, CHEN Yang-bo1, FANG Gui-sheng2
1. College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018;
2. Mechanical and Automotive Engineering College, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018
Abstract: Deep-sea risers work in a complex marine environment. Vortex-induced vibration occurred when the vibration frequency gets close to the riser's natural frequency, it would caused risers' damage or even failure. By using the numerical simulation method, the effects of different factors (such as boundary condition, physical parameters of risers and top tension) on natural frequency of risers were researched. Firstly, a simplified riser model was established in the finite element software-Abaqus, and the vibration characteristics of risers' under three kinds of different boundary conditions were analyzed. Then based on the third boundary condition, the effects of above factors on natural frequency of risers were considered. At the end of this paper, based on the above research work, some meaningful conclusions were drawn.
Key words: deep sea risers     natural frequency     boundary condition     bending moment     numerical simulation
0 引 言

1 立管运动方程及边界条件的处理

 $EI\frac{{{\partial ^4}y}}{{\partial {z^4}}} - \left( {{T_0} + T\cos \omega t} \right)\frac{{{\partial ^2}y}}{{\partial {z^2}}} + {\rm{c}}\frac{{\partial {\rm{y}}}}{{\partial t}} + m\frac{{{\partial ^2}{\rm{y}}}}{{\partial {t^2}}} = {F_{\rm{y}}}\left( {z,t} \right),$ (1)

Fyzt） 为沿着y方向上每单位长度的流体总作用力，可视作漩涡串作用产生的升力FLzt） 和张力腿由于横向运动而产生的流体阻尼力Frzt） 两部分组成，即

 ${F_y}\left( {z,t} \right) = {F_L}\left( {z,t} \right) - {F_r}\left( {z,t} \right){\text{。}}$ (2)

 ${F_L}\left( {z,t} \right) = \frac{1}{2}\rho D{\left( {{V_c} + u} \right)^2}{C_L}\cos {\omega _s}t{\text{。}}$ (3)

 图 1 不同边界条件示意图 Fig. 1 The schematic of different boundary conditions

 \begin{aligned}& \!\!\!\left\{ {\begin{array}{*{20}{c}}\!\!\!{y(0,t) = y(l,t) = 0,\;\;\;\;\;}\\\!\!\!\!{\displaystyle\frac{{\partial {y^2}(0,t)}}{{\partial {z^2}}} \!\!=\!\! \displaystyle\frac{{\partial {y^2}(l,t)}}{{\partial {z^2}}} \!\!=\!\! 0}{\text{。}}\end{array}} \right.\!\!\!\!\!\;\;\left\{ {\begin{array}{*{20}{c}}\!\!\!\!{y(0,t) = 0\;\;y(l,t) = d},\\\!\!\!\!{\displaystyle\frac{{\partial {y^2}(0,t)}}{{\partial {z^2}}} \!\!=\!\! 0\;\;\displaystyle\frac{{\partial {y^3}(l,t)}}{{\partial {z^3}}}\!\! =\!\! 0}{\text{。}}\end{array}} \right.\!\!\!\;\; \\ & \left\{ {\begin{array}{*{20}{c}}{y(0,t) = 0\;\;\;\;\;\;\;\frac{{\partial y(l,t)}}{{\partial z}} = 0},\\{\displaystyle\frac{{\partial {y^2}(0,t)}}{{\partial {z^2}}} = 0\;\;\;\;\displaystyle\frac{{\partial {y^3}(l,t)}}{{\partial {z^3}}} = 0}{\text{。}}\end{array}} \right.\end{aligned}\!\!\!\!\!\!\!\!\! (4)

 $y(z,t) = \sum\limits_{n = 1}^\infty {{y_n}\left( t \right)} \sin {\lambda _n}z{\text{。}}$ (5)

1.1 算例验证

 ${f_n} = \frac{1}{{2\pi }}{\left( {\frac{{n\pi }}{L}} \right)^2}\sqrt {\frac{{EI}}{{\rho A}}} {\text{。}}$ (6)

 图 2 简支梁前10阶频率计算结果比较 Fig. 2 The comparison of simple-supported beam′s frequencies
1.2 不同边界条件比较

 图 3 第1类边界条件 Fig. 3 The first boundary condition

 图 4 第2类边界条件 Fig. 4 The second boundary condition

 图 5 第3类边界条件 Fig. 5 The third boundary condition

 图 6 不同边界条件下的立管固有频率 Fig. 6 Riser′s natural frequencies under different boundary conditions

2 立管固有频率的影响因素分析

 图 7 自重对立管固有频率的影响 Fig. 7 The effect of self-weight on riser′s natural frequency

 图 8 内容物对立管固有频率的影响 Fig. 8 The effect of contents on riser′s natural frequency

 图 9 不同长度立管1阶固有频率 Fig. 9 The first natural frequencies of different lengths

 图 10 不同外径立管1阶固有频率 Fig. 10 The first natural frequencies different diameter

 图 11 不同壁厚立管1阶固有频率 Fig. 11 The first natural frequencies of different thickness

 图 12 不同顶张力立管1阶固有频率 Fig. 12 The first natural frequencies of different top tensions

1）立管的1阶固有频率随着立管长度、外径和管壁厚度的增加而减小。其中，立管长度对固有频率的影响最为显著，在设计深海石油开发平台时需进行考虑。

2）当立管的顶张力较小时，立管的1阶固有频率随着顶张力的增加而快速增加；而随着顶张力的继续增加，幅度越来越小。考虑到立管强度校核的要求，可以适当地加大立管顶张力，以预防立管发生共振。

3 总结与展望

1）立管的固有频率与其边界条件中的初始位移密切相关，但与该位移的运动无关；

2）立管自重和管内流体密度对立管的1阶固有频率有影响。其中，立管自重对对立管1阶固有频率的影响更大。当不考虑立管的自重和管内流体的密度时，立管的前10阶频率均会偏大；

3）随着立管长度、外径和壁厚的增加，立管的固有频率会降低。其中，立管的长度对于固有频率的影响最为显著，随着立管长度的增加，立管的固有频率急剧降低；

4）立管的顶部张力对立管的固有频率有影响。当立管的顶张力较小时，立管的1阶固有频率随着顶张力的增加而快速增加；而随着顶张力的继续增加，其增幅会越来越小。

 [1] 张杰, 唐友刚. 深海立管固有振动特性的进一步分析[J]. 船舶力学, 2014, 18 (1-2): 165–171. ZHANG Jie, TANG You-gang. Further analysis on natural vibration of deep-water risers[J]. Journal of Ship Mechanics, 2014, 18 (1-2): 165–171. [2] 张杰, 唐友刚, 黄磊, 等. 参数激励下深海立管多模态耦合振动特性分析[J]. 振动与冲击, 2013, 32 (19): 51–56. ZHANG Jie, TANG You-gang, HUANG Lei, et al. Multi-mode coupled vibration behavior of a deep-water riser under parametric excitations[J]. Journal of Vibration and Shock, 2013, 32 (19): 51–56. DOI: 10.3969/j.issn.1000-3835.2013.19.010 [3] 雷松, 郑向远, 张文首, 等. 海洋立管悬挂状态的固有频率和振型[J]. 船舶力学, 2015, 19 (10): 1267–1274. LEI Song, ZHENG Xiang-yuan, ZHANG Wen-shou, et al. Natural frequencies and mode shapes of free-hanging risers[J]. Journal of Ship Mechanics, 2015, 19 (10): 1267–1274. DOI: 10.3969/j.issn.1007-7294.2015.10.012 [4] 郭磊, 段梦兰, 张新虎, 等. 浮式平台对深水立管振动的影响及共振研究[J]. 石油机械, 2014, 42 (9): 59–64. GUO Lei, DUAN Meng-lan, ZHANG Xin-hu, et al. The influence of floating platform on deep-water riser vibration and resonance[J]. ChinaPetroleum Machinery, 2014, 42 (9): 59–64. [5] MONTOYA-HERNÁNDEZ D J,VÁZQUEZ-HERNÁNDEZ A O, CUAMATZI R, et al. Natural frequency analysis of a marine riser considering multiphase internal flow behavior[J]. Ocean Engineering, 2014(92): 103–113. [6] 王在刚. 海洋立管流固耦合动力特性分析[D]. 兰州: 兰州理工大学, 2013. WANG Zai-gang. Analysis on dynamic characteristics of fluid-structure interactionfor marine risers[D]. Lanzhou: Lanzhou University of Technology, 2013. [7] 王东, 任帅, 陈磊, 等. 基于ANSYS的浅海天然气立管模态分析[J]. 管道技术与设备, 2014 (3): 9–11. WANG Dong, REN Shuai, CHEN Lei, et al. Shallow gas riser modal analysis based on Ansys[J]. Pipeline Technique and Equipment, 2014 (3): 9–11. [8] 姜峰, 郑运虎, 梁瑞, 等. 海洋立管湿模态振动分析[J]. 西南石油大学学报(自然科学版), 2015, 37 (5): 159–166. JIANG Feng, ZHENG Yun-hu, LIANG Rui, et al. An analysis of the wet modal vibration of marine riser[J]. Journal of Southwest Petroleum University (Science & Technology Edition), 2015, 37 (5): 159–166. DOI: 10.11885/j.issn.1674-5086.2013.11.11.03 [9] 王红霞, 李喆. 钢悬链线立管振动响应影响因素分析[J]. 噪声与振动控制, 2011, 31 (4): 26–28. WANG Hong-xia, LI Zhe. Factors analysis of influencing of steel catenary riser[J]. Noise and Vibration Control, 2011, 31 (4): 26–28. [10] 潘佳. 深水立管涡激振动响应和疲劳损伤分析[D]. 大连: 大连理工大学, 2015. PAN Jia. Vortex-induced vibration response and damage analysis of riser in deep water[D]. Dalian: Dalian University of Technology, 2015. [11] 孙传栋, 黄维平, 曹静. Abaqus在深水顶张力生产立管模态分析中的应用[J]. 中国水运月刊, 2009, 9 (2): 181–182. SUN Chuan-dong, HUANG Wei-ping, CAO Jing. Application of Abaqus in modal analysis of standpipe in deep water tension production[J]. China Water Transport, 2009, 9 (2): 181–182. [12] 黄祥鹿. 海洋工程流体力学及结构动力响应[M]. 上海: 上海交通大学出版社, 1992. [13] 马驰, 董艳秋. 海洋平台张力腿在两种边界条件下的涡激非线性振动的比较研究[J]. 船舶力学, 2000, 4 (1): 56–65. MA Chi, DONG yan-qiu. Comparative study of vortex-induced nonlinear oscillation of TLP tethers under two different boundary conditions[J]. Journal of Ship Mechanics, 2000, 4 (1): 56–65.