﻿ 舰船水下爆炸冲击动弯矩工程化预报
 舰船科学技术  2019, Vol. 41 Issue (1): 20-25 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 华中科技大学 船舶与海洋工程学院，湖北 武汉 430074

Engineering forecast method of shock vibration bending moment of ships subjected to explosion load
GUO Jian-jun1, ZHAO Yu-lin2, ZHANG Hao1, LI Yuan-tai1, XIA Feng1
1. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China;
2. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: Shock vibration bending moment of ships induced by underwater explosion is researched in this paper. Based on the ship hull girder with variable cross section and the formula of Taylor tablet theory shock vibration bending moment is calculated and analyzed, which is verified with test date from ship shock trial. The calculation method is suitable for engineering forecast of the shock vibration bending moment. Then the shock vibration bending moment of various kinds of ships with different ship length and displacement is predicted, as well as analyzed for law of the moment with ship displacement. The shock vibration bending moment calculated above is summed up, and the empirical formula of shock vibration bending moment is get by data processing and date fitting, which is convenient for engineering design.
Key words: ship building engineering     underwater explosion     shock vibration bending moment (SVBM)     engineering forecast method     empirical formula
0 引　言

1 水下爆炸船体冲击动弯矩分析 1.1 简化模型

 图 1 水下爆炸船体梁模型示意图 Fig. 1 Schematic diagram of ship hull girder underwater explosion
1.2 舷外水的影响

 $K = \rho Ag\text{。}$ (1)

 ${m_{av}} = \frac{1}{2}{C_v}{K_i}\rho \pi {b^2}\text{。}$ (2)

 ${P_t}(x,y,t) = 2{P_i}(x,y,t) - \frac{{\rho cv(t)}}{{\cos \alpha (x,y)}}\text{。}$ (3)

1.3 模态叠加法求解冲击动弯矩

 ${ M}\ddot u + { C}\dot u + { K}u = F(t)\text{。}$ (4)

 ${{ \varPhi} ^{\rm T}}{ M}{ \varPhi} \ddot q + {{ \varPhi} ^{\rm T}}{ C}{ \varPhi} \dot q + {{ \varPhi} ^{\rm T}}{ K}{ \varPhi} q = {{ \varPhi }^{\rm T}}F(t)\text{。}$ (5)

 \left\{ \begin{aligned} & {{F_z}({t_i}) = \{ \sum [ 2P(x,y,{t_i}) - \displaystyle\frac{{\rho c\dot u({t_{i - 1}})}}{{\cos \alpha (x,y)}}\delta (x,y,t)] \cdot S{}_z\} }\text{，}\\ & {{ M} = EI\Phi {q^{''}}}\text{，}\\ & {\left[{ M} \right]\left[ {\ddot u({t_i})} \right] + \left[ C \right]\left[ {\dot u({t_i})} \right] + \left[ K \right]\left[ {u({t_i})} \right] = \left[ {{F_z}({t_i})} \right]}\text{。} \end{aligned}\right. (6)

1.4 试验验证

 图 2 动弯矩对比图 Fig. 2 The contrast diagram of shock vibration bending moment

2 不同船型的冲击动弯矩工程化预报

2.1 参数设置

 $C = \frac{{\sqrt W }}{{{R_1}}} \times \frac{{1 + \sin \beta }}{2}\text{。}$ (7)

 图 3 冲击因子工况示意图 Fig. 3 Schematic diagram of keel shock factor (KSF)
2.2 计算结果

 图 4 船A冲击动弯矩（KSF=0.3） Fig. 4 Shock vibration bending moment of ship A (KSF=0.3)

2.3 结果分析

 图 5 冲击因子0.3时动弯矩随排水量的变化曲线 Fig. 5 SVBM curves varying with displacement (KSF=0.3)

 图 6 冲击因子0.5时动弯矩随排水量的变化曲线 Fig. 6 SVBM curves varying with displacement (KSF=0.5)

 图 7 冲击因子0.8时动弯矩随排水量的变化曲线 Fig. 7 SVBM curves varying with displacement (KSF=0.8)

 图 8 冲击因子1.2时动弯矩随排水量的变化曲线 Fig. 8 SVBM curves varying with displacement (KSF=1.2)

3 冲击动弯矩预报的经验公式

 $\left\{ {\begin{array}{*{20}{c}} {{M_{hog}} = kL \cdot \Delta /{C_M}^2} \text{，}\\ {{M_{sag}} = - kL \cdot \Delta /{C_M}^2} \text{。} \end{array}} \right.$ (7)

 \left\{ \begin{aligned} & {{k_{hog}}{\text{ = }}1.22C - 0.24} \text{，}\\ & {{k_{sag}}{\text{ = }} - 1.08C + 0.15} \text{。} \end{aligned} \right. (8)

 图 9 系数k与冲击因子C的线性拟合关系图 Fig. 9 Linear fitting relation graph between coefficient k and KSF C

4 结　语

 [1] 张绮蓉, 马锦华. 水下非接触爆炸对舰船总体强度与局部强度影响的分析028 g实艇水下爆炸试验资料汇编(上册)[M]. 北京: 第六机械工业部船舶系统工程部, 1982: 70–89. ZHANG Qi-rong, MA Jin-hua. Analysis of longitudinal strength and local strength of ship underwater un-contact explosion 028g boat test date[M]. Beijing: Ship System Engineering of Six Machine Industry, 1982: 70–89. [2] 李玉杰, 张效慈, 吴有生, 等. 水下爆炸气泡激起的船体鞭状运动[J]. 中国造船, 2001, 42(3): 1-7. LI Yu-jie, ZHANG Xiao-ci, WU You-sheng, et al. Whipping response of ship hull induced by underwater explosion bubble[J]. Shipbuilding of China, 2001, 42(3): 1-7. DOI:10.3969/j.issn.1000-4882.2001.03.001 [3] 朱锡, 方斌. 舰船静置爆炸气泡时总纵强度计算方法研究[J]. 海军工程大学学报, 2007, 19(6): 6-11. ZHU Xi, FANG Bin. Study on longitudinal strength calculation method of hull standing above an explosion bubble[J]. Journal of Naval University Engineering, 2007, 19(6): 6-11. DOI:10.3969/j.issn.1009-3486.2007.06.002 [4] 李海涛, 朱锡, 张振华. 水下爆炸球面冲击波作用下船体梁的刚塑性动响应特性[J]. 工程力学, 2010, 27(10): 202-207. LI Hai-tao, ZHU Xi, ZHANG Zhen-hua. Dynamic rigid-plastic response of ship-like beam subjected to underwater spherical shock waves[J]. Engineering Mechanics, 2010, 27(10): 202-207. [5] 汪玉, 华宏星. 舰船现代冲击理论及应用[M]. 北京: 科学出版社, 2005: 220–223. [6] 姚熊亮. 舰船振动与噪声[M]. 北京: 国防工业出版社, 2010: 115–121. [7] COLE R H. Underwater explosion[M]. Princeton: Princeton University Press, 1948: 270–352. [8] ZHANG N, ZONG Z. The effect of rigid-body motions on the whipping response of a ship hull subjected to an underwater bubble[J]. Journal of Fluids and Structures, 2011, 27: 1326-1336. DOI:10.1016/j.jfluidstructs.2011.05.004 [9] 金辉, 周学滨, 周华, 等. 水下爆炸中自由场压力和船体壁压的测量与分析[J]. 海军工程大学学报, 2009, 21(5): 82-87. JIN Hui, ZHOU Xue-bin, ZHOU Hua, et al. Measurement and analysis of free-field pressure and ship hull pressure underwater explosion[J]. Journal of Naval University Engineering, 2009, 21(5): 82-87. [10] 顾文彬, 苏青笑, 刘建青, 等. 水下平面爆炸冲击波作用卜空化区域形成及其特征[J]. 爆破, 2004, 21(4): 8-11. GU Wen-bin, SU Qing-xiao, LIU Jian-qiang, et al. Formation process of cavitation region affected by underwater plane blast shock wave and its characteristics[J]. Blasting, 2004, 21(4): 8-11. DOI:10.3969/j.issn.1006-7051.2004.04.003 [11] 刘云龙, 张阿漫, 葛亮, 等. 圆柱壳结构水下爆炸所致鞭状运动特性研究[J]. 振动与冲击, 2013, 32(22): 106-112. LIU Yun-long, ZHANG A-man, GE Liang, et al. Whipping response of a cylindrical shell structure subjected to underwater explosion[J]. Vibration and Shock, 2013, 32(22): 106-112. DOI:10.3969/j.issn.1000-3835.2013.22.020 [12] SCHNEIDER N A, SHIN Y S. Ship shock trial modeling and simulation for USS Winston S. Churchill (DDG81). Tech Report NPS-ME-03–004, Naval Postgraduate School, December 2003.