船舶结构耦合动力学问题
吴有生，司马灿，刘建湖
(中国船舶科学研究中心，江苏 无锡 214082)
摘 要：海洋是当今世界经济、军事竞争的重要领域。海洋的开发利用，必须依靠海洋装备。海洋装备技术的发展有赖于大量力学科学与应用技术的突破。海洋装备所处的复杂流场环境决定了其关键技术中相当部分与流固耦合动力学紧密相关。船舶结构与流体的耦合动力学的第一个主要研究范畴是流场环境因素(波浪、砰击、上浪、水下或空中爆炸等)引起的结构和设备的稳态、瞬态和随机动响应；第二个主要研究范畴是船舶振动与声辐射的预报与控制。在第一个范畴中，有船舶流固耦合水弹性力学的研究，中、高海况条件下船舶的大幅运动、砰击与甲板上浪均会引起船体的非线性载荷与响应，飞机降落引起的航行中船舶的甲板结构动响应，航行中由砰击引起的船舶甲板瞬态动响应与动屈曲，船舶的水下爆炸动响应及其防护技术等问题。属于第二范畴的船舶结构耦合动力学问题，亦即与舰船声隐身技术相关的耦合动力学/声学问题有着极为丰富的内涵。本文主要对第一研究范畴的国内外研究现状和发展趋势进行了回顾和展望。
关键词：船舶与海洋结构；流固耦合；船舶水弹性力学；船舶非线性载荷与响应
The Coupled Dynamics of Ship Structures
You-Sheng Wu, Can Sima, Jian-Hu Liu
（China Ship Scientific Research Center，Jiangsu, Wuxi, 214082）
Abstract: Ocean is the important space of the present world for economic and military competitions and combats, as well the vast resource storage for sustainable development of mankind. The ocean exploitation and utilization has to largely rely on the technology of marine vehicles and equipments. The development of marine technology depends on the breakthrough of variety of subjects in theoretical and applied mechanics. The severe surrounding environment of marine objects definitely indicates that marine technology is closely related to the coupled dynamics of fluid-structure interaction. The fluid-environment (waves, slamming, green water, under-water explosion etc.) induced steady state, transient state and random featured dynamic responses of ship structures and onboard equipments are the first kind of problems investigated by the coupled fluid-structure dynamics of ships. The machinery and propeller induced vibration and noise radiation of ships are the second kind of problems being studied by the coupled fluid-structure dynamics of ships. In the research of the first kind of coupled fluid-structure dynamic problems, there are the hydroelasticity theories, non-linear loads and responses induced by the large motions of the ship, slamming and green water effects in rough seas, dynamic response of deck structure induced by aircraft landing, transient response and dynamic buckling of the ship deck structure induced by the slamming, responses of a ship induced by the underwater explosion, etc. The second kind of coupled dynamic problems of ships, namely the acoustic stealth related vibration and noise radiation are of extremely broad contents. In the presentation, present state and perspectives in the first kind of coupled fluid-structure dynamic problems are focused. Keywords: ship and marine structures; fluid-structure Interaction; hydroelasticity of ships; non-linear wave loads and responses
吴有生（1942－），男，浙江嵊县人，中国工程院院士，水弹性力学与船舶力学专家。
详细摘要
二十一世纪是海洋的世纪。海洋是当今世界经济、军事竞争的重要领域，也是人类将赖以生存发展，而又未充分开发的资源宝库。海洋的开发利用，必须依靠海洋装备。近20余年，世界海洋运输船舶数量与质量迅猛提升；军民船舶技术取得了突飞猛进的发展。在人类进一步征服海洋的同时，各类新型海洋运载工具正以大为进化了的新面貌出现在波涛浩翰的海洋空间，并进入深海洋底，创造出人类运输、生产、生活的新境界。我国正处这一进展的前列，从1994年起造船产量始终居世界第三位，2006年造船产量占世界年造船总量的18％，产值以年均30％的高速增长，船舶品种向大型化、高新技术、高附加值船方向发展，若干年后即有望成为世界第一造船大国。海洋装备技术的发展有赖于大量力学科学与应用技术的突破。海洋装备所处的复杂流场环境决定了其关键技术中相当部分与流固耦合动力学紧密相关。
船舶结构与流体的耦合动力学的第一个主要研究范畴是流场环境因素(波浪、砰击、上浪、水下或空中爆炸等)引起的结构和设备的稳态、瞬态和随机动响应；第二个主要研究范畴是船舶振动与声辐射的预报与控制。
在第一个范畴中，船舶流固耦合水弹性力学近30年在我国取得了长足的进步，发展与应用内容越来越丰富。
船舶水弹性力学(Hydroelasticity of Ships) 是一个考虑海洋结构的惯性力、变形内力及其界面上的水动力之间相互作用现象的科学分支。它把结构和其周围流场作为统一的整体系统进行分析，描述在海洋环境激励下船体的运动与变形，以及航行或驻留浮体在机械激励下的结构强迫动响应。
自70年代后期船舶二维线性水弹性力学理论诞生以来，线性船舶水弹性力学理论及其分析方法已发展得较为成熟。船舶三维频域线性水弹性力学理论及其基于边界积分的数值计算方法(Price & Wu, 1983; Bishop, Price & Wu, 1986) 的建立已有二十余年。其忽略船体航行时的航速效应及定常兴波流场影响的简化分析方法在零航速极大型浮动结构(VLFS) 、低航速复杂形状海洋结构物和细长航行船舶的运动与安全性评估中获得了较为广泛的应用。其后，进一步发展并形成了计及航速影响与非均匀定常兴波流场影响的更为严格的分析方法(吴与杜，1998；Du, Wu and Price, 1998；Tian & Wu, 2006)，使三维频域线性水弹性分析应用对象的几何形状与航速范围大为扩展，并己在船舶设计中成功应用。期间，成功地发展了三维时域线性水弹性力学理论及采用三维时域Green函数的分折方法（Wang, D.Y.,1996; Wang & Wu, 1998）。
在中、高海况条件下，船舶的大幅运动、砰击与甲板上浪均会引起船体的非线性载荷与响应，成为决定船舶运动与结构安全性的重要因素。我国先后发展了计及瞬时吃水与船舷外飘动量砰击的两种二维非线性水弹性力学理论和分折方法。其中一种方法采用描写自由表面记忆效应的脉冲响应函数的时间卷积(Gu, Wu and Xia, 1989; Gu et al, 1988)；第二种方法采用一个高阶微分表达式描写船体相对波面运动速度与垂向水动力之间的关系，避免了时域卷积（Wang, Z.H., 1992; Wang, Xia and Wu,1995）。该两种二维非线性分析方法已广泛用于预报波浪和砰击引起的护卫舰、油船、散货船等多类船舶的结构响应，显示了与试验与实测结果吻合的良好效果，但只限于单体细长船舶。1997年，Wu, Maeda & Kinoshita 提出了一个三维二阶船舶非线性水弹性力学理论，考虑了高海情条件下船体大幅运动刚体转动和瞬时湿表面变化对可变形航行浮体的水动力作用的影响。该理论主要计及了一阶速度势及一阶运动与变形响应对二阶流场作用力与结构响应的贡献。Chen ( 2001)发展了针对零航速系泊浮体的三维二阶分析方法与软件；Tian (2007) 把计及航速影响与非均匀定常兴波流场影响的较为严格的求解一阶速度势及一阶运动与变形响应的线性水弹性分析方法与带有全部航速项的二阶计算方法结合起来，完成了较为完整的将该理论用于航行船体的数值分析方法和计算程序。成功地预报了一艘以设计航速(12节) 在生存海况中航行的1500吨级小水
线面双体海洋考察船的运动、结构载荷与应力，与船模试验结果互为引证，在该船结构设计中应用(Wu, Ni et.al, 2007)。
飞机降落引起的航行中船舶的甲板结构动响应是一个飞机与甲板、船舶与波浪间耦合运动的问题。彭兴宁等（1997）采用非线性二维水弹性力学理论（Gu et al ,1988）预报波浪和砰击引起的甲板结构运动，在时域内求解等效的飞机起落架—轮子的二自由度系统和甲板结构挠曲变形间耦合撞击响应，进而获取了飞机所受的载荷及优化降落方案。
航行中由砰击引起的船舶甲板瞬态动响应与动屈曲是另一类典型的耦合动力学问题。徐向东等(1997) 采用非线性二维水弹性力学理论在时域内预报波浪和砰击引起的船舶弯矩，用与弯矩等效的时变力系求解离散船舶结构的动稳定性方程，建立了波浪中砰击过载引起的船舶甲板动屈曲分析方法，进而分析并观察了甲板弹塑性屈曲现象。
中国船舶科学研究中心在波浪水池中开展了多批弹性船模试验。发展形成了弹性材料船模试验的相似律、设计准则、制作与试验技术。自航可变形船模的波浪试验表明，这类弹性船模试验技术对于验证水弹性力学理论的数值预报效果、观察并理解船舶结构的流固耦合现象，包括非线性载荷与波高的关系、及非线性高阶谐波响应成份的产生机理，是一种十分有效的手段(Lin, et.al., 1991; Li, et al., 1995; Wu et.al., 2003)。
许多情况下，与水面船舶的运动与变形相关的流固耦合动力学问题可以用理想流体来处理。一旦涉及流场的分离与涡的生成，这一近似就远远偏离了现实。例如，水下潜航物体进行空间机动操纵不可避免地要虑流场的分离与涡的作用。Du (1999)与Wu & Du (1999)拓展了Tan (1994)与Price & Tan (1992)发展的粘流边界积分方法，基于Hamilton原理，建立了非惯性坐标系中做机动运动的潜器的结构运动方程，探讨了可变形结构与粘性流体在非惯性坐标系中的耦合作用的理论表达式。然而，其求解将是一项困难的工作，有待进一步研究。潜航物体稳定翼与舵的流激颤振也是一类典型的需采用粘性流理论加以考察的耦合动力学问题。Sima, Zhang and Wu (1999) 用修正的欧辛子作为基函数，发展了一种边界积分法，同时引进了流固耦合界面条件，用以求解受粘性流激励的柔性结构的动响应。修正的欧辛方程大大扩展了适用的雷诺数范围。由流引起的一个弹性二维水翼的颤振的理论分析结果与实验结果比较，在时域及频域中均吻合良好。贮液船舶晃荡问题是另一类由“液体晃动/舱壁变形/船舶刚体运动” 构成的复杂系统的流固耦合动力学问题。朱仁庆(2001) 、朱仁庆和吴有生 (1998) 改进了传统的流体体积法（VOF），用以描述晃荡流场，通过物面边界条件，与结构动力学理论结合，建立了计及粘性流体与弹性壁面耦合作用的液体晃荡水弹性力学理论与分析方法。
各种船舶的直接设计技术要求对流场环境与船舶结构的行为作统一的综合评定。陈瑞章 (1997、2000) 综合利用船舶水弹性力学分析方法，对长度80～180m的84艘船舶进行了波浪载荷设计值的预报计算，并回归给出了船舶的设计波高及波浪载荷的设计公式。
在第一范畴的船舶结构耦合动力学问题中，船舶的水下爆炸动响应及其防护技术具有特殊的重要性。在该领域中，我国开展了较系统深入的理论与实验研究。包括水下爆炸冲击波、气泡脉动流场、船体上压力分布时空特征的计算方法，基于二阶双重渐近近似方法（DAA2）的船舶水下爆炸动响应理论分析方法，船体结构水下爆炸弹塑性变形破坏计算方法，适用于声学复合材料结构与的二阶双重渐近近似方法(ADDA)法等。我国并开展了一系列水面与水下船舶的实验研究。
属于第二范畴的船舶结构耦合动力学问题，亦即与舰船声隐身技术相关的耦合动力学/声学问题有着极为丰富的内涵，在本文中不展开讨论。
船舶流固耦合动力学的理论、试验技术与应用技术正在发展之中。我国在该领域中做了许多工作，相当部分在国际上处于前列，在此只触及了其中的一部分，未提及的内容未必不重要。从提及的内容可见，船舶流固耦合动力学在军民船舶与海洋工程领域有重要的应用背景和广阔的发展前景。随着振动工程领域内涉及的结构与流体两方面理论/计算技术/实验技术的进步，船舶流固耦合动力学将会进一步创新发展，把载荷/内力、强度/稳定/疲劳、振动/噪声等领域的技术融为一体，给出船舶安全性与风险的短期与长期、时域与概率统计的综合评估方法。其内涵在可预见的未来将大为扩展。
Summary
The 21st Century is the Century of Ocean. Ocean is the important space of the present world for economic and military competitions and combats, as well the vast resource storage for sustainable development of mankind. The ocean exploitation and utilization has to largely rely on the technology of marine vehicles and equipments. During the past more than 20 years, the global sea transportation has gained both rapid increases in total shipping amount and tremendous improvements in corresponding technologies. Varity new types of marine vehicles have appeared on the vast ocean, and diving into the deep seas, creating the new era of mankind’s transportation, production and living. China is just at the frontier of this progress. Starting from 1994 China has been the third largest country of shipbuilding. In 2006 ships built by Chinese shipbuilding industry reached 18% of the total world ship products of the year. Meanwhile among the kinds of ships built in China the large, high-tech and high added value ships were getting more and more. In few years later China will no doubt to be the first largest shipbuilding country in the world. The development of marine technology depends on the breakthrough of variety of subjects in theoretical and applied mechanics. The severe surrounding environment of marine objects definitely indicates that marine technology is closely related to the coupled dynamics of fluid-structure interaction.
The fluid-environment (waves, slamming, green water, under-water explosion etc.) induced steady state, transient state and random featured dynamic responses of ship structures and onboard equipments are the first kind of problems investigated by the coupled fluid-structure dynamics of ships. The machinery and propeller induced vibration and noise radiation of ships are the second kind of problems being studied by the coupled fluid-structure dynamics of ships.
In the research of the first kind of coupled fluid-structure dynamic problems, the hydroelasticity theories of ships gained great progress in China during the past nearly 30 years, with rich contents of investigation and profound results of application.
Hydroelasticity of ships is the branch of science that investigates the phenomena involving mutual interactions among inertial, hydrodynamic and elastic forces. The hydroelasticity theories embody the structure and the surrounding fluid as a coupled entity, analyse and describe the motions and structural distortions of a ship responding to severe ocean environment, as well as the machinery excited forced vibrations of a travelling or stationary marine structure.
Since the infancy of two-dimensional hydroelasticity theory in late 70s, the development of linear hydroelasticity theories and the corresponding numerical methods have been relatively mature. The three-dimensional frequency-domain hydroelasticity theory of ships and the numerical method (Price & Wu, 1983; Bishop, Price & Wu, 1986) was established more than 20 years ago. By neglecting the influence of the forward speed effect and the wave making steady flow the simplified method of three-dimensional hydroelasticity theory have been applied successfully to a wide range of problems, including the motion and safety assessments of very large floating structures (VLFS), low speed arbitrary shaped marine structures and travelling slender ships. Later on more rigorous numerical methods accounting for the full forward speed and steady flow effects were further established (Du & Wu，1998；Du, Wu and Price, 1998；Tian & Wu, 2006), and greatly extended the applications of the three-dimensional frequency-domain hydroelasticity theory to more wide geometric forms and forward speed range of the travelling vehicles. These were successfully employed in design procedures of ships. The three-dimensional time-domain hydroelasticity theory and the numerical method employing the time-domain Green function (Wang, 1996; Wang & Wu, 1998) was also established.
In rough seas the large motions of the ship, slamming and green water effects usually introduce non-linear loads and responses, sometimes resulting in the structural failure. Two forms of non-linear two-dimensional hydroelasticity theories were developed, which deal with arbitrary large relative heave motions of ship sections and take into account the non-linear fluid actions due to slamming and the change of the instantaneous wetted surface.
The first one uses a time involution integral of impulsive function describing the free surface memory effect (Gu, Wu and Xia, 1989; Gu et al, 1988). The second one employs a special high order differential formulation between the relative velocity and the corresponding hydrodynamic force and avoids the time involution integral (Wang, 1992; Wang, Xia and Wu, 1995). These methods have been extensively applied to predict the wave and slam induced structural responses of frigates, container ships and bulk carrier etc. and have shown favourable feature in efficiency and coincidence with the experimental results. However are only applicable for mono-hull slender ships. In 1997, Wu, Maeda & Kinoshita presented a three-dimensional second-order non-linear hydroelasticity theory of ships, taking into account the effects of rigid body rotations and variation of instantaneous wetted surface on the hydrodynamic forces acting on the ship travelling in high waves. This theory includes the contributions of the first order potentials, rigid and flexible body responses of the ship to the second order hydrodynamic actions. Based on this theory, Chen (2000) developed the numerical method for a floating body with zero forward speed and investigated the second order structural responses of moored floating structures in waves. Tian (2007) established the complete numerical method of the second order hydroelastic analysis of a ship travelling in waves, combined with the rigorous numerical method of the first order linear hydroelastic analysis accounting for the full forward speed and steady flow effects. The method and corresponding program was used to successfully predict the motions, structural loads and stresses of a 1500 ton small water-plane area twin hull (SWATH) ocean-survey ship travelling with design speed of 12kn in survival wave condition. The predictions showed good correlation with model test results and applied in the structural design of the ship (Wu, Ni et.al, 2007).
Aircraft landing induced dynamic response of deck structure is a coupled aircraft-deck and ship-wave interaction problem. Peng et al (1997) employed the non-linear two-dimensional hydroelasticity theory to predict the wave and slamming induces deck movement, solved the transient interactions of the coupled movement of aircraft landing wheel system and the deck structure deformation, obtained the loads encountered by the aircraft, and optimised the required landing process.
The slamming induced transient response and dynamic buckling of the ship deck structure is another typical coupled dynamic problem. By applying the non-linear two-dimensional hydroelasticity theory to predict the wave and slamming induced time history of the ship encountered longitudinal bending moments, Xue et.al. (1997) obtained the time variant force systems equivalent to the bending moment, and solved the dynamic stability equation of the discretized ship structure. Hence the method of analysing the dynamic buckling of deck structure caused by the slam over load was introduced. The elasto-plastic buckling phenomenon of the deck was investigated.
Experiments of elastic ship models in wave basin or towing tank have been timely carried out at CSSRC (Lin, et.al. 1991; Li, et al., 1995; Wu et.al. 2003). The similitude conditions and design principle of flexible ship model made of elastic materials were initiated. The wave tests on self-propelled, flexible ship models show that the experimental technique is sure to be a useful approach for verification of numerical predictions provided by hydroelastic theories, as well as to gain more insight towards the hydroelastic behaviours of the ship structure, including the non-linear loads with respect to the wave heights, and the responses of high order harmonic components etc.
In many cases, the fluid-structure interaction problems related to motions and distortions of surface ships may be treated by idea fluid. Once there occur the flow separation and vortex shedding, the simplification of idea fluid would be not proper. For example, the manoeuvring of a submerged vehicle will easily induce flow separation and vortex shedding. Du (1999) and Wu & Du (1999) extended the boundary integral method for viscous flow proposed by Tan (1994) and Price & Tan (1992), and introduced the equations of motion of a manoeuvring submerged structure in a non-inertial coordinate system based on the Hamilton principle. However it is still a difficulty to solve the set of equations. More research is evidently needed. The flutter of a stabilizing fin and a rudder is also a kind of coupled dynamic problem that needs to be investigated in account of fluid viscosity. Sima, Zhang and Wu (1999) developed
a boundary integral method with modified Oseenlets being the fundamental functions to solve the coupled responses of a flexible structure excited by viscous flow. The modified Oseen's equation was extended to a much larger range of Reynolds number, and a fluid-structure interface boundary condition was introduced. The theoretical results of the viscous flow induced flutter of an elastic two-dimensional hydrofoil were well compared with the experimental results in time and in frequency domain (Zhang, et.al. 1999). The sloshing phenomenon of liquid container is another kind of complicated coupled problem consisting of liquid sloshing, bulkhead deformation, and the ship motion. Zhu (2001) and Zhu & Wu (1998) modified the VOF method to describe the fluid sloshing, and combined with the structural dynamics in terms of the interface conditions. Thus a hydroelastic sloshing analysis method was created.
Among the first kind of problems investigated by the coupled fluid-structure dynamics of ships, the underwater explosion induced responses of a ship is of great importance. Comprehensive theoretical and experimental research work has been carried out in this field in China. These range from the description of shock wave and bubble pulsation, prediction of pressure distribution over the ship hull, the evaluation of underwater explosion induced responses of ships based on the double asymptotic approximation approach (DAA2), to the creation of a new method referring to as the ADDA2 approach, which allows for the structure fitted with acoustic materials being analysed. Systematic model tests were as well preformed. The second kind of coupled dynamic problems of ships, namely the acoustic stealth related vibration and noise radiation are of extremely broad contents. These will not be discussed in this presentation.
The theory, experimental technique, and applied technology of coupled dynamics of ship structures are steadily progressing. Comprehensive research and development work has been conducted in China, but only some of the advances are mentioned here. Those not referred to in this presentation are not at all not important. However it is evident from the limited contents mentioned here that the coupled dynamics of ship structures have apparent demand of applications and brilliant future for further development for both the naval and civil ships and for other marine structures as well.
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