NAGESH , GUPTA N K . Response of thin-walled metallic structures to underwater explosion: a review [J ] . International Journal of Impact Engineering , 2021 , 156 : 103950 . DOI: 10.1016/j.ijimpeng.2021.103950 http://doi.org/10.1016/j.ijimpeng.2021.103950 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21001378 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21001378

PHUONG T , CHANG L W , MICHAEL S , et al . Composite structures subjected to underwater explosive loadings: a comprehensive review [J ] . Composite Structures , 2021 , 263 : 113684 . DOI: 10.1016/j.compstruct.2021.113684 http://doi.org/10.1016/j.compstruct.2021.113684 https://linkinghub.elsevier.com/retrieve/pii/S0263822321001458 https://linkinghub.elsevier.com/retrieve/pii/S0263822321001458

沈超 , 张磊 , 周章涛 , 等 . 水下近距和接触爆炸载荷作用下板架结构动态响应机理 [J ] . 兵工学报 , 2023 , 44 ( 4 ): 1050 - 1061 .

SHEN C , ZHANG L , ZHOU Z T , et al . Mechanism of dynamic responses of grillage structures under loads of close-in and contact underwater explosions [J ] . Acta Armamentarii , 2023 , 44 ( 4 ): 1050 - 1061 . (in Chinese) DOI: 10.12382/bgxb.2022.0037 http://doi.org/10.12382/bgxb.2022.0037 This paper designs grillage structure models based on a specific protective structure of a surface ship, and conducts close-in and contact underwater explosion experiments on 10 grillage models under 7 working conditions with various charges and distances. The velocities of typical points are measured with the Photonic Doppler Velocimetry system, the fragments of the grillage structure are gathered, and the damage forms after each experiment are recorded. The experimental results compare well with the numerical results, verifying the generality of the experiment and the accuracy of the simulation. The analyses of experimental and numerical results reveal several conclusions. The grillage structure is susceptible to shear and tear at reinforcing ribs and diaphragm plates, leading to the formation of fragments. The number and weight of fragments depend on the explosive charges, distances, and structures of the grillage. The velocities of points on the surface of the grillage decrease exponentially with increasing distance between the measuring point and center point. The center point is the projection point of the explosive charge on the grillage surface. When the ratio of the explosion distance to explosive charge radius is not less than 2, the velocity of center point remains nearly constant, even though the explosive charge mass changes.

苏标 , 姚熊亮 , 孙龙泉 , 等 . 水下接触爆炸作用下双层加筋板架结构的损伤特征 [J ] . 兵工学报 , 2021 , 42 ( 增刊1 ): 127 - 134 .

SU B , YAO X L , SUN L Q , et al . Damage characteristics of double reinforced plate frame structure under the action of underwater contact explosion [J ] . Acta Armamentarii , 2021 , 42 ( S1 ): 127 - 134 . (in Chinese)

LEI Z , DU Z P , GAO P , et al . Research advance of damage load of surface ship cabin explosion [J ] . Scientia Sinica Physica, Mechanica & Astronomica , 2021 , 51 ( 12 ): 124605 .

RAMAJEYATHILAGAM K , VENDHAN C P . Deformation and rupture of thin rectangular plates subjected to underwater shock [J ] . International Journal of Impact Engineering , 2004 , 30 ( 6 ): 699 - 719 . DOI: 10.1016/j.ijimpeng.2003.01.001 http://doi.org/10.1016/j.ijimpeng.2003.01.001 https://linkinghub.elsevier.com/retrieve/pii/S0734743X04000132 https://linkinghub.elsevier.com/retrieve/pii/S0734743X04000132

SURESH C , RAMAJEYATHILAGAM K . Large deformation behavior of thin mild steel rectangular plates subjected to underwater explosion loading under air and water backed conditions [J ] . Applied Ocean Research , 2021 , 114 : 102780 . DOI: 10.1016/j.apor.2021.102780 http://doi.org/10.1016/j.apor.2021.102780 https://linkinghub.elsevier.com/retrieve/pii/S014111872100256X https://linkinghub.elsevier.com/retrieve/pii/S014111872100256X

YUAN Y , TAN P J . Deformation and failure of rectangular plates subjected to impulsive loadings [J ] . International Journal of Impact Engineering , 2013 , 59 : 46 - 59 . DOI : 10.1016/j.ijimpeng.2013.03.009 http://doi.org/10.1016/j.ijimpeng.2013.03.009 https://linkinghub.elsevier.com/retrieve/pii/S0734743X13000730 https://linkinghub.elsevier.com/retrieve/pii/S0734743X13000730

REN S F , ZHAO P F , WANG S P , et al . Damage prediction of stiffened plates subjected to underwater contact explosion using the machine learning-based method [J ] . Ocean Engineering , 2022 , 266 : 112839 . DOI: 10.1016/j.oceaneng.2022.112839 http://doi.org/10.1016/j.oceaneng.2022.112839 https://linkinghub.elsevier.com/retrieve/pii/S0029801822021229 https://linkinghub.elsevier.com/retrieve/pii/S0029801822021229

KISHORE S , SENOL K , NAIK P P , et al . Underwater implosion pressure pulse interactions with submerged plates [J ] . Journal of the Mechanics and Physics of Solids , 2020 , 143 : 104051 . DOI: 10.1016/j.jmps.2020.104051 http://doi.org/10.1016/j.jmps.2020.104051 https://linkinghub.elsevier.com/retrieve/pii/S0022509620302854 https://linkinghub.elsevier.com/retrieve/pii/S0022509620302854

TOHID M M , ALI G , ALI M , et al . Closed-form analytical analysis on the effect of coupled membrane and bending strains on the dynamic plastic behavior of fully clamped thin quadrangular plates due to uniform and localized impulsive loading [J ] . Thin-Walled Structures , 2018 , 123 : 48 - 56 . DOI: 10.1016/j.tws.2017.11.010 http://doi.org/10.1016/j.tws.2017.11.010 https://linkinghub.elsevier.com/retrieve/pii/S0263823117307528 https://linkinghub.elsevier.com/retrieve/pii/S0263823117307528

GUPTA N K , PAWAN K , HEGDE S . On deformation and tearing of stiffened and un-stiffened square plates subjected to underwater explosion — a numerical study [J ] . International Journal of Mechanical Sciences , 2010 , 52 ( 5 ): 733 - 744 . DOI: 10.1016/j.ijmecsci.2010.01.005 http://doi.org/10.1016/j.ijmecsci.2010.01.005 https://linkinghub.elsevier.com/retrieve/pii/S0020740310000068 https://linkinghub.elsevier.com/retrieve/pii/S0020740310000068

WANG H , PEI D M , ZHANG P , et al . The plastic dynamics and failure analysis of ship broadside protection structures subjected to contacted UNDEX: energy dissipation model and simulation [J ] . Ships and Offshore Structures , 2022 , 17 ( 4 ): 728 - 741 . DOI: 10.1080/17445302.2020.1865715 http://doi.org/10.1080/17445302.2020.1865715 https://www.tandfonline.com/doi/full/10.1080/17445302.2020.1865715 https://www.tandfonline.com/doi/full/10.1080/17445302.2020.1865715

ZHANG J , SHI X H C , GUEDES S . Experimental study on the response of multi-layered protective structure subjected to underwater contact explosions [J ] . International Journal of Impact Engineering , 2017 , 100 : 23 - 34 . DOI: 10.1016/j.ijimpeng.2016.10.004 http://doi.org/10.1016/j.ijimpeng.2016.10.004 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16305231 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16305231

JIN Q K , DING G Y . A finite element analysis of ship sections subjected to underwater explosion [J ] . International Journal of Impact Engineering , 2011 , 38 ( 7 ): 558 - 566 . DOI: 10.1016/j.ijimpeng.2010.11.005 http://doi.org/10.1016/j.ijimpeng.2010.11.005 https://linkinghub.elsevier.com/retrieve/pii/S0734743X10002009 https://linkinghub.elsevier.com/retrieve/pii/S0734743X10002009

朱锡 , 张振华 , 刘润泉 , 等 . 水面舰艇舷侧防雷舱结构模型抗爆试验研究 [J ] . 爆炸与冲击 , 2004 ( 2 ): 133 - 139 .

ZHU X , ZHANG Z H , LIU R Q , et al . Surface ship outboard mine protection compartment structural model of blast resistance test research [J ] . Explosion and Shock Waves , 2004 ( 2 ): 133 - 139 . (in Chinese)

KONG X S , WU W G , LI J , et al . Experimental and numerical investigation on a multi-layer protective structure under the synergistic effect of blast and fragment loadings [J ] . International Journal of Impact Engineering , 2014 , 65 : 146 - 162 . DOI: 10.1016/j.ijimpeng.2013.11.009 http://doi.org/10.1016/j.ijimpeng.2013.11.009 https://linkinghub.elsevier.com/retrieve/pii/S0734743X13002200 https://linkinghub.elsevier.com/retrieve/pii/S0734743X13002200

YAO S J , CHEN F P , WANG Y J , et al . Experimental and numerical investigation on the dynamic response and damage of large-scale multi-box structure under internal blast loading [J ] . Thin-Walled Structures , 2023 , 183 : 110430 . DOI: 10.1016/j.tws.2022.110430 http://doi.org/10.1016/j.tws.2022.110430 https://linkinghub.elsevier.com/retrieve/pii/S026382312200982X https://linkinghub.elsevier.com/retrieve/pii/S026382312200982X

GANNON L . Simulation of underwater explosions in close-proximity to a submerged cylinder and a free-surface or rigid boundary [J ] . Journal of Fluids and Structures , 2019 , 87 : 189 - 205 . DOI: 10.1016/j.jfluidstructs.2019.03.019 http://doi.org/10.1016/j.jfluidstructs.2019.03.019 https://linkinghub.elsevier.com/retrieve/pii/S0889974618306856 https://linkinghub.elsevier.com/retrieve/pii/S0889974618306856

张之凡 , 谢宇杰 , 王成 , 等 . 近自由面水下爆炸气泡与破损结构耦合作用机理研究 [J ] . 北京理工大学学报 , 2022 , 42 ( 9 ): 909 - 917 .

ZHANG Z F , XIE Y J , WANG C , et al . Coupling mechanism between damaged structure and underwater explosion bubble near free surface [J ] . Transactions of Beijing institute of Technology , 2022 , 42 ( 9 ): 909 - 917 . (in Chinese)

LIU L T , WANG J X , TANG K . Coupling characteristics of bubbles with a free surface initially disturbed by water waves [J ] . Physics of Fluids , 2022 , 34 ( 4 ): 042117 . DOI: 10.1063/5.0090098 http://doi.org/10.1063/5.0090098 https://pubs.aip.org/pof/article/34/4/042117/2844662/Coupling-characteristics-of-bubbles-with-a-free https://pubs.aip.org/pof/article/34/4/042117/2844662/Coupling-characteristics-of-bubbles-with-a-free The interactions between bubbles and water waves have important applications in ocean engineering, and their coupling characteristics are strongly associated with the wave phase angle, wavelength, and wave amplitude. Based on the assumption that the liquid is inviscid and incompressible, the coupling characteristics between bubbles and water waves are solved by the Euler equations with the finite volume method, and the bubble surface and water wave surface are tracked by the front tracking method. The accuracy of the numerical method is verified by comparison with a spark-generated bubble experiment. Compared with the bubble near the initially plane free surface, the rising height of the water spike is reduced by water waves in the crest state, where a concave shape forms on the falling water wave during bubble contraction when the wavelength λ≤ 4.00 and the wave amplitude h≥ 0.364. The rising height of the water spike is significantly strengthened by water waves in the trough state with smaller wavelengths and larger wave amplitudes, which produce a thinner and higher water spike. The bubble cycle is shortened by water waves in the crest state with smaller wavelengths and prolonged by water waves in the trough state with smaller wavelengths and larger wave amplitudes. The results presented in this paper provide guidance for the study of underwater explosions in complex water wave environments.

ZHANG A M , LI S M , CUI P , et al . A unified theory for bubble dynamics [J ] . Physics of Fluids , 2023 , 35 ( 3 ): 033323 . DOI: 10.1063/5.0145415 http://doi.org/10.1063/5.0145415 https://pubs.aip.org/pof/article/35/3/033323/2882023/A-unified-theory-for-bubble-dynamics https://pubs.aip.org/pof/article/35/3/033323/2882023/A-unified-theory-for-bubble-dynamics In this work, we established a novel theory for the dynamics of oscillating bubbles such as cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we proposed bubble dynamics equations that can simultaneously take into consideration the effects of boundaries, bubble interaction, ambient flow field, gravity, bubble migration, fluid compressibility, viscosity, and surface tension while maintaining a unified and elegant mathematical form. The present theory unifies different classical bubble equations such as the Rayleigh–Plesset equation, the Gilmore equation, and the Keller–Miksis equation. Furthermore, we validated the theory with experimental data of bubbles with a variety in scales, sources, boundaries, and ambient conditions and showed the advantages of our theory over the classical theoretical models, followed by a discussion on the applicability of the present theory based on a comparison to simulation results with different numerical methods. Finally, as a demonstration of the potential of our theory, we modeled the complex multi-cycle bubble interaction with wide ranges of energy and phase differences and gained new physical insight into inter-bubble energy transfer and coupling of bubble-induced pressure waves.

WANG Y N , WANG Z , LIANG S H , et al . Experimental and numerical study on the failure modes of ship stiffened plate structure under projectile perforation [J ] . International Journal of Impact Engineering , 2023 , 178 : 104590 . DOI: 10.1016/j.ijimpeng.2023.104590 http://doi.org/10.1016/j.ijimpeng.2023.104590 https://linkinghub.elsevier.com/retrieve/pii/S0734743X2300101X https://linkinghub.elsevier.com/retrieve/pii/S0734743X2300101X

LI G L , SHI D Y , CHEN Y Y , et al . A study on damage characteristics of double-layer cylindrical shells subjected to underwater contact explosion [J ] . International Journal of Impact Engineering , 2022 , 172 : 104428 . DOI: 10.1016/j.ijimpeng.2022.104428 http://doi.org/10.1016/j.ijimpeng.2022.104428 https://linkinghub.elsevier.com/retrieve/pii/S0734743X22002688 https://linkinghub.elsevier.com/retrieve/pii/S0734743X22002688

刘文思 , 陆越 , 周庆飞 , 等 . 鱼雷近场爆炸复杂载荷及对舰船毁伤模式 [J ] . 兵工学报 , 2021 , 42 ( 4 ): 842 - 850 .

LIU W S , LU Y , ZHOU Q F , et al . Complex load of torpedo near-field explosion and its damage mode to ships [J ] . Acta Armamentarii , 2021 , 42 ( 4 ): 842 - 850 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.04.018 http://doi.org/10.3969/j.issn.1000-1093.2021.04.018 A numerical analysis model of near-boundary underwater explosion was established based on nonlinear explicit dynamic analysis software LS-DYNA in order to evaluate the damage efficiency of torpedo underwater explosion to ships. The calculated results of explosion load under near-free liquid surface boundary conditions were compared with the calculated results of empirical formulas in Ref.［6］ and the experimental results in Ref.［17］, verifying that the proposed numerical simulation method can well reflect the shock wave pressure of the near-field underwater explosion and the multiple bubble pulsation processes. The technology is used to build a numerical simulation model close to the actual combat boundary conditions, and calculate and analyze the damage mode of the torpedo near-field explosion to the ship under multiple conditions. The results show that different boundary conditions in the near field have an important effect on the pulsating load of underwater explosion bubbles. Under different conditions, shock wave, bubble pulsation and water jet load have complex coupling effects with ship structure. The effect of torpedo on the ship in the near field under different conditions shows different energy output structures, which is closely related to the final damage mode of ship, and there is an optimal detonation distance to maximize the total energy of torpedo acting on the ship.

秦健 , 艾东民 , 吴成 , 等 . 几种炸药水下爆炸能量损失特性分析研究 [J ] . 兵工学报 , 2015 , 36 ( 增刊2 ): 38 - 42 .

QIN J , AI D M , WU C , et al . Research on energy dissipation characteristics of underwater explosion of explosives [J ] . Acta Armamentarii , 2015 , 36 ( S2 ): 38 - 42 . (in Chinese)

孟龙 , 黄瑞源 , 王金相 , 等 . 小当量梯恩梯水下爆炸气泡脉动的数值模拟 [J ] . 兵工学报 , 2020 , 41 ( 增刊1 ): 64 - 71 .

MENG L , HUANG R Y , WANG J X , et al . Numerical simulation of bubble pulsation of small scaled TNT in underwater explosion [J ] . Acta Armamentarii , 2020 , 41 ( S1 ): 64 - 71 . (in Chinese)

张杜江 , 赵振宇 , 贺良 , 等 . 基于Johnson-cook本构模型的高强度装甲钢动态力学性能参数标定及验证 [J ] . 兵工学报 , 2022 , 43 ( 8 ): 1966 - 1976 . DOI: 10.12382/bgxb.2021.0409 http://doi.org/10.12382/bgxb.2021.0409 具有高屈服强度的某装甲钢广泛应用于我国装甲车辆。为准确模拟该装甲钢的动态力学行为，开展基于Johnson-Cook（J-C）本构模型的动态本构参数标定及验证。采用万能材料试验机对该装甲钢进行不同温度下的准静态拉伸试验，同时采用分离式霍普金森压杆开展不同应变率下的压缩性能测试。基于实验数据和J-C本构模型，拟合得到该装甲钢的本构参数。基于轻气炮开展泡沫铝弹丸冲击均质梁的实验研究，分别采用J-C本构模型和理想弹塑性模型进行有限元仿真计算，并将冲击实验与数值结果进行对比分析。结果表明：该装甲钢具有应变率强化效应，且温度软化效应显著；采用J-C本构模型仿真的均质梁峰值挠度与试验结果的相对误差为1.7%~6.1%，残余挠度相对误差为0.6%~7.6%。

ZHANG D J , ZHAO Z Y , HE L , et al . Calibration and verification of dynamic mechanical properties of high-strength armored steel based on Johnson-Cook constitutive model [J ] . Acta Armamentarii , 2022 , 43 ( 8 ): 1966 - 1976 . (in Chinese)

WANG G H , WANG Y X , LU W B , et al . On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion [J ] . Applied Ocean Research , 2016 , 59 : 1 - 9 . DOI: 10.1016/j.apor.2016.05.011 http://doi.org/10.1016/j.apor.2016.05.011 https://linkinghub.elsevier.com/retrieve/pii/S014111871630150X https://linkinghub.elsevier.com/retrieve/pii/S014111871630150X

吴林杰 , 侯海量 , 朱锡 , 等 . 水下接触爆炸下防雷舱舷侧空舱的内压载荷特性仿真研究 [J ] . 兵工学报 , 2017 , 38 ( 1 ): 143 - 150 . DOI: 10.3969/j.issn.1000-1093.2017.01.019 http://doi.org/10.3969/j.issn.1000-1093.2017.01.019 为研究水下接触爆炸下防雷舱舷侧空舱的内压载荷特性，在水下爆炸气泡第1次脉动周期的约3倍时间范围内，利用LS_DYNA软件对水下爆炸气泡与防雷舱舷侧空舱的相互作用过程和舷侧空舱的内压载荷特性进行了仿真分析，并通过模型试验对仿真结果及分析进行了验证。研究结果表明：伴随着水下爆炸气泡膨胀或收缩，爆炸产物气体从外板破口处流入或流出舷侧空舱，外板也相应地向里凹陷或向外凸出运动；舷侧空舱内部空间被外板花瓣隔成两个区域，舷侧空舱的内压载荷在花瓣前面和花瓣背面具有不同特性；采用有限元方法评估舷侧空舱外板的最大破坏程度时，可将计算时间取为气泡第1次脉动周期的5%.

WU L J , HOU H L , ZHU X , et al . Numerical simulation on inside load characteristics of broadside cabin of defensive structure subjected to underwater contact explosion [J ] . Acta Armamentarii , 2017 , 38 ( 1 ): 143 - 150 . (in Chinese)

HUANG C , LIU M B , WANG B , et al . Underwater explosion of slender explosives: directional effects of shock waves and structure responses [J ] . International Journal of Impact Engineering , 2019 , 130 : 266 - 280 . DOI: 10.1016/j.ijimpeng.2019.04.018 http://doi.org/10.1016/j.ijimpeng.2019.04.018 https://linkinghub.elsevier.com/retrieve/pii/S0734743X19300946 https://linkinghub.elsevier.com/retrieve/pii/S0734743X19300946