﻿ 船舶尾部响应特性试验与计算
 舰船科学技术  2022, Vol. 44 Issue (20): 67-70    DOI: 10.3404/j.issn.1672-7649.2022.20.013 PDF

1. 上海交通大学 海洋工程国家重点实验室，上海 200240;
2. 高新船舶与深海开发装备协同创新中心，上海 200240

Experimental and numerical analysis on ship stern vibration response characteristics
YE Xing-hong1,2, XIA Li-juan1,2, WU Bei-ni1,2
1. State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China;
2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Abstract: The ship stern where harmful vibration usually takes place has always been focus of researchers. This paper studies the vibration response of stern structure with model test and finite element (FE) calculation. By comparing experimental results with numerical results, the influence of FE mesh size is investigated. Meanwhile, the accuracy of direct integration method and mode superposition method is analyzed, and the selection of truncation frequency is discussed. Some key points in vibration response calculation of ship structures are summarized.
Key words: stern vibration     model test     finite element calculation     vibration response analysis
0 引　言

1 结构振动响应计算理论 1.1 网格划分准则

 ${c_z} = \sqrt {\frac{E}{{\rho \left( {1 - {\mu ^2}} \right)}}}。$ (1)

 ${c_w} = \sqrt {2{\text{π}} fr{c_z}}，$ (2)
 ${\lambda _w} = \sqrt {\frac{{2{\text{π}} r{c_z}}}{f}}。$ (3)

 $\Delta \leqslant \frac{1}{4}{\lambda _{\min }} = \frac{1}{4}\sqrt {\frac{{2{\text{π}} r{c_z}}}{{{f_{\max }}}}} = \frac{1}{4}\sqrt {\frac{{2{\text{π}} r}}{{{f_{\max }}}}\sqrt {\frac{E}{{\rho \left( {1 - {\mu ^2}} \right)}}} } 。$ (4)
1.2 响应计算方法

 $\left[ M \right]\left\{ {\ddot x} \right\} + \left[ C \right]\left\{ {\dot x} \right\} + \left[ K \right]\left\{ x \right\} = \left\{ {F\left( t \right)} \right\}。$ (5)

 $\left\{ x \right\} = \sum\limits_{i = 1}^n {\left\{ {{\phi _i}} \right\}{\eta _i}} = \left[ \phi \right]\left\{ \eta \right\}。$ (6)

 $\begin{split} {\left[ \phi \right]^{\rm{T}}}\left[ M \right]\left[ \phi \right]\left\{ {\ddot \eta } \right\} + {\left[ \phi \right]^{\rm{T}}} \left[ C \right]\left[ \phi \right]\left\{ {\dot \eta } \right\} + {\left[ \phi \right]^{\rm{T}}}\\ \left[ K \right]\left[ \phi \right]\left\{ \eta \right\} = {\left[ \phi \right]^{\rm{T}}}\left\{ {F\left( t \right)} \right\}。\end{split}$ (7)

 ${\ddot \eta _i} + 2{\omega _i}{\zeta _i}{\dot \eta _i} + {\omega _i}^2{\eta _i} = {f_i}。$ (8)

2 试验模型及有限元模型 2.1 尾部试验模型

 图 1 试验模型典型剖面图 Fig. 1 Typical section profiles of test model

 图 2 激励点及测点位置 Fig. 2 Locations of excitation and measuring points
2.2 有限元模型

 图 3 有限元模型（网格尺寸90 mm） Fig. 3 Finite element model (mesh size = 90 mm)
3 试验与计算结果分析 3.1 网格划分的影响

 图 4 试验结果及3种网格划分下响应计算结果 Fig. 4 Response results of experiment and FE analysis under three mesh schemes

3.2 模态叠加法与直接积分法对比

 图 5 不同截断频率下响应计算结果 Fig. 5 Response calculation results under different truncation frequencies

 图 6 不同截断频率下响应计算结果（堆叠图） Fig. 6 Response calculation results under different truncation frequencies (stacked lines)

 图 7 模态叠加法、直接积分法及试验结果对比 Fig. 7 Comparison of mode superposition method, direct integration method and experiment
4 结　语

 [1] 李志杰. 船舶尾部结构振动特性数值仿真和试验研究[D]. 上海: 上海交通大学, 2016. [2] 张玉奎, 詹蓉, 沈玉琦. 某大型公务船的振动性能评估[J]. 船舶, 2017, 28(2): 43-49. DOI:10.19423/j.cnki.31-1561/u.2017.02.043 [3] LIU C Q, CHE C D, SHEN X H. Experimental and numerical study on vibration of the full-revolving propulsion ship stern[J]. China Ocean Engineering, 2015, 29(1): 33-48. DOI:10.1007/s13344-015-0003-5 [4] 刘西安, 吴广明, 李伟杰. 某科考船艉部舱段振动固有频率计算方法[J]. 中国舰船研究, 2017, 12(4): 110-116. DOI:10.3969/j.issn.1673-3185.2017.04.017 [5] 刘晓之, 夏利娟, 吴嘉蒙. 大型油船阶梯式尾部型式振动特性研究[J]. 舰船科学技术, 2015, 37(10): 26-29+35. DOI:10.3404/j.issn.1672-7649.2015.10.006 [6] HAGEMEN R B, DRUMMEN I. Modal analysis for the global flexural response of ships[J]. Marine Structures, 2019, 63(JAN.): 318-332. [7] 李建彰. 高速型船舶振动响应计算分析[J]. 舰船科学技术, 2018, 40(1): 23-26. DOI:10.3404/j.issn.1672-7649.2018.01.004 [8] 徐孝诚, 尹立中. 关于结构高频响应分析中有限元网格划分的细化标准[J]. 振动与冲击, 2002(1): 54-55+47+104-105. DOI:10.3969/j.issn.1000-3835.2002.01.014 [9] SEPEHRIRAHNAMA S, XU D, ONG E T, et al. Fluid–structure interaction effects on free vibration of containerships[J]. Journal of Offshore Mechanics and Arctic Engineering, 2019, 141(6): 1-27. [10] YE X , XIA L. Experimental Investigation and numerical simulation of ship stern structural vibration model[J]. Journal of Shanghai Jiaotong University (Science), 2020(4).