Experimental study on the nonlinear pressure acting on a high-speed vessel in irregular waves

The present study focuses on the nonlinear behavior of pressure on the hull surface of a high-speed vessel in irregular waves, particularly the pressure responses of alternately wet and dry areas near the waterline and on the bow zone. The vessel has high deadrise angles that may be subject to slight impact and water pile-up effects. A series of experiments in regular and irregular head waves were conducted, and the validity of applying Volterra modeling was investigated. In a previous article using experimental data in regular waves, it was confirmed that the approximate third-order Volterra model adequately simulated the variation of pressure responses in regular waves of different steepness up to a wave amplitude with a wavelength ratio of 0.01, even for the highly nonlinear pressures acting on the abovementioned areas of the hull surface. In this article, further validation for the second part of the study was obtained using experimental data in irregular waves. The frequency response functions obtained from the previous study’s experimental data in regular waves were applied to the third-order Volterra model by combining the input of irregular waves to simulate the responses in irregular waves of sea state five. Then, the spectra and statistics were analyzed. For the motions, accelerations, and pressure responses in irregular waves (as well as for the simulated time histories) variance spectra and statistics such as cumulative distributions of peak values and probability density functions were compared with the experimental results. It was confirmed that even for highly nonlinear and non-Gaussian pressures on the abovementioned areas of the hull surface, the approximate third-order Volterra model simulates the pressure responses in irregular head waves up to a sea state of five with adequate accuracy on deterministic and statistical bases.     

Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large containership model in severe head and oblique seas

Vertical bending moment (VBM) is of crucial importance in ensuring the survival of vessels in rough seas. With regard to conventional vessels, wave-induced maximum VBM is normally considered to be experienced in head seas. It is conservative to determine the extreme VBM based on either numerical simulations or model tests in long-crested head seas. Extensive model tests have been conducted in head seas with focus on the nonlinear vertical responses in severe seas, and the measured results were compared with numerical calculations for validation. Unexpected phenomena, however, were observed during the model tests of an ultra-large containership. The maximum sagging and hogging VBMs were encountered in oblique seas. Furthermore, the significant wave height used in oblique seas was even smaller than that used in head seas. The nonlinear vertical load effects in oblique seas require further investigations for this particular vessel. Limited experimental results in oblique seas have been reported, in which the lateral responses were always more concerned than the vertical responses. Up to now, rare systematic comparisons of the nonlinear vertical responses between head and oblique seas have been published, especially when the hydroelastic effects are also accounted for. A 13000-TEU ultra-large containership model, which was designed by Hyundai Heavy Industries (HHI), has been tested in the towing tank and the ocean basin at the Marintek center in Trondheim. The experimental results in regular waves are first compared between head and oblique seas. The statistical characteristics of the VBM amidships under nineteen irregular wave conditions are then investigated. Next, the extreme hogging and sagging VBMs are compared under different wave conditions with focus on the extreme hogging VBMs. At the end of the paper, the uncertainties in the experiments are discussed.     

船体在波浪中的非线性水动压力

本文提出了一个预报船体在波浪中大幅运动时非线性水动压力场的二维时域理论。船体扰动势用时域自由面格林函数和在入射波下的瞬时湿表面上的分布源求解；与非线性水动压力场相匹配的船体运动用差分法求得。为提高计算效率和避免数值过程发散，采用了改进的数值模型和方案。通过线性理论计算与模型试验结果的比较，指出了线性切片理论在预报水动压力场时的不足，水动压力与波高的非线性关系及正负水动压力沿船体表面的分布在Wigley船的计算比较中得到了说明。初步计算表明，该理论的实用化发展前景是令有鼓舞的。相应的计算机程序可在PC机上运行。     

超大型 VLCC 波激振动和砰击振动模型试验研究

船舶的波激振动和砰击振动对船舶结构的安全性有较大影响。文章以一艘超大型 VLCC 为研究对象,通过变截面梁分段模型试验方法对船舶在规则波和不规则波中波激振动和砰击振动响应进行了比较分析,介绍了船模波浪载荷试验中模型的设计原则,通过静水试验得到了船体梁垂向振动频率特性、振动阻尼和静水兴波弯矩等参数,通过规则波和不规则波试验分析了波高、波浪周期和装载状态等因素对波激振动和砰击振动的影响。该文的研究结果对大型船舶的结构设计具有一定的指导意义。     

中高速船加装减纵摇组合附体模型试验

对某常规单体排水式圆舭导弹护卫艇进行加装减纵向运动组合附体的模型快速性试验和耐波性试验。首先进行了小尺度模型的静水阻力试验和规则波试验，优选出阻力和减摇效果均较优的方案。进行了较大尺度模型的静水阻力试验、规则波试验和不规则波试验。试验结果表明减纵向运动组合附体可显著抑制舰船的纵向运动，包括垂荡、纵摇、艏、中、艉部加速度，以及砰击、上浪、波浪增阻等，经优化设计的组合附体尺度和布局对艇静水阻力基本没有影响。     

New insight into the wave-induced nonlinear vertical load effects of ultra-large container ships based on experiments

Accurate estimation of the wave-induced extreme hogging vertical bending moment (VBM) is of vital importance for the design of container ships because container ships are normally under hogging conditions in still water. According to the empirical formulas proposed by the classification society rules, the design hogging VBM can be approximately 20 % smaller than the design sagging VBM for vessels with small block coefficients. High-order harmonic components in the vertical load effects, which are induced by the nonlinearities in the hydrodynamic forces and ship hull geometry, contribute to the asymmetry. Previous studies have shown that the nonlinear hydrostatic and Froude–Krylov forces increase the sagging VBM significantly. Current numerical tools are able to reveal this asymmetry to a certain extent. There is, however, little focus on the nonlinear pressure under the bow bottom, which is a more likely contributor to the hogging VBM. Several unexpected phenomena have been observed for large container ships. The wave-frequency sagging and hogging VBMs followed each other closely, and hence did not reflect the significant nonlinear factors as expected. In this paper, the test data of two (8600-TEU and 13000-TEU) ultra-large containership models in both regular and irregular head waves are systematically studied. In regular waves, the influence of the second and third harmonics on the fundamental hogging peaks and sagging troughs is estimated by comparing both the amplitude and phase difference relative to the first harmonic peaks. In irregular waves, the focus is on the statistical characteristics of the wave-induced nonlinear vertical load effects. To achieve a balance between results in regular and irregular waves, the influence of the second harmonics is evaluated through bispectral analysis.     

基于模型试验与三维水弹性理论的船舶波激振动响应研究

船体波激振动使得船体结构中产生高频、持续和具有一定幅值的振动应力,可能引起结构发生严重的疲劳损伤,因而对船舶结构的安全性带来严峻的挑战。文章以一艘大型LNG船为研究对象,采用三维线性水弹性理论与水池模型试验方法对船舶波激振动响应进行了比较分析,研究了规则波与不规则波中的波激振动特性。改变该LNG船的刚度,并保持船型、重量分布等其它主船体特征不变,在模型试验和理论计算中探讨了刚度对波激振动的影响。通过两种刚度船体梁的模型试验与理论计算结果的比较分析,给出了波浪周期和船体刚度的变化对波激振动影响的几点结论。     

明基床上局部开孔沉箱防波堤反射系数的近似计算方法

给出了明基床上局部开孔沉箱防波堤在规则波和不规则波作用下反射系数的近似计算方法。将明基床假定为一直立墙，用匹配特征函数展开法给出计算规则波作用下整体结构反射系数的理论解。利用线性传递函数法得到不规则波作用下开孔沉箱防波堤反射波频谱，得到频率平均的反射系数。将反射系数计算结果与已有研究者的试验结果进行了比较，符合良好。     

Hydroelastic analysis of a very large floating plate with large deflections in stochastic seaway

The hydroelasticity of a very large floating plate with large deflections in multidirectional irregular waves is discussed. After a brief introduction on wave loads on a flexible structure, the paper derives the generalised fluid force acting on a floating structure in multidirectional irregular waves. The nonlinear sectional forces induced by the membrane forces in the plate are deduced. The hydroelastic response equations of a floating plate with large deflections in multidirectional irregular waves are established, and a solution method in the frequency domain is discussed including extreme value statistics. A very large floating structure is chosen as an example. The numerical results show that the influence of the membrane forces on the vertical displacements and the bending moments is noticeable but not that large.     

不同海况下艏部砰击及鞭状效应的试验与数值分析

为了更深入地研究船舶的鞭状效应,在拖曳水池中对某船进行了艏部砰击及鞭状效应分段模型试验研究。提出了一种可以考虑砰击力的非线性水弹性计算方法。并改进了传统的分段模型,采用变截面梁对船体刚度进行模拟以更好地接近实船。在规则波迎浪下观察到了严重的艏部砰击现象。试验数据表明,当波高从5.6m增大到21m时,由于鞭状效应原因,总弯矩相比低频波浪弯矩的增大值从24.64%增长到92.02%。最后,将不同海况下的测量结果与基于线性与非线性水弹性理论的计算结果进行了比较分析,初步验证了文中方法和程序在预报船体波浪载荷中的适用性。     

S-175集装箱船舶波浪载荷的船模试验与线性切片理论计算的比较

本文就日本S-175集装箱船舶的波浪载荷进行了船模试验与线性切片理论计算的比较,发现线性切片理论对于波浪载荷沿船长的纵向分布以及中拱与中垂的不同分量都与试验值存在着相当大的差异,仅纵向运动较为满意;揭示了对于在高浪级下快速舰船的波浪载荷,特别是砰击载荷应致力于开展非线性理论和试验研究。     

考虑晃荡耦合船舶运动的晃荡压力算法（英文）

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid(VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiationdiffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.     

Practical estimation methods of the design loads for primary structural members of tankers

Various design loads used in the strength evaluation of ship structures have been introduced currently by classification societies. As most of these design loads have been determined as the standard loads for the sake of convenience, the relationships between the design loads and the sea states actually encountered by ships seem to be weak. Accordingly, it may be difficult to refer and utilize them as the fundamental design concepts for ship designers or the operational guidelines for ship operators. To overcome these difficulties, the authors have developed practical estimation methods of the design loads having transparent and consistent backgrounds to the actual loads acting on primary structural members of tankers. In this paper, the design sea states that closely resemble the actual sea states which are considered as the most severe for hull structures are firstly proposed. Secondly, the practical estimation methods of the design sea states are proposed by parametric studies using the results of series calculation of representative tankers. Thirdly, the practical estimation methods of design regular waves resulting in the same level of stresses with that induced in irregular waves under the design sea states are proposed. Finally, the practical estimation methods of the design loads such as ship motions, accelerations, hull girder bending moments and hydrodynamic pressures that are induced under design regular waves are proposed.     

系泊浮体运动响应分析的非线性水动力学方法（英文）

Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.     

A unified seakeeping and maneuvering analysis of ships in regular waves

The behavior of a ship in regular waves during maneuvering was studied by using a two-time scale model. The maneuvering analysis was based on Söding’s (Schiffstechnik 1982; 29:3–29) nonlinear slender-body theory generalized to account for heel. Forces and moments due to rudder, propeller, and viscous cross-flow follow from the state-of-the-art procedures. The developed unified theory of seakeeping and maneuvering was verified and validated for calm water by comparing it with experimental and calculated zigzag and circle maneuvers. Linear wave-induced motions and loads were determined by generalizing the Salvesen-Tuck-Faltinsen (Trans SNAME 1970; 78:250–287) strip theory. The mean second-order wave loads in incident regular deep water waves in oblique sea conditions were estimated by the potential flow theories of Faltinsen et al. (Proc 13th Symp Naval Hydrody 1980), Salvesen (Proc Intl Symp Dynam Mar Vehicl Struct Wave 1974), and Loukakis and Sclavounos (J Ship Res 1978; 22:1–19). The considered theories cover the whole range of important wavelengths. Comparisons between the different mean second-order wave load theories and available experimental data were carried out for different ship hull forms when the ship was advancing forward on a straight course. The mentioned methods have been incorporated into the maneuvering model. Their applicability from the perspective of the maneuvering ability of the selected types of ships was investigated in given wave environments. The wave conditions are valid for realistic maneuvering cases in open coastal areas. It was demonstrated that the incident waves may have an important influence on the maneuvering behavior of a ship. The added resistance, mean second-order transverse force, and yaw moment also play important roles.     

迎浪规则波中小水线面双体船纵向运动及波浪载荷非线性特性数值分析

基于RANS方程和VOF模型求解船体粘性兴波流场,开展了小水线面双体船(Small Waterplane Area Twin Hulls,SWATH)迎浪规则波中纵向运动及波浪载荷的非线性特性研究.通过数值计算结果与模型试验结果的对比分析,验证了文中方法的有效性;在此基础上,较为系统地分析了SWATH船的垂荡及纵摇运动响应、垂向加速度和波浪载荷的一阶及二阶量随入射波高的变化规律,指出SWATH船的运动响应及载荷与波高存在非线性的关系,尤其体现在响应共振区附近;相比于船体垂荡和纵摇运动,垂向加速度及波浪载荷的非线性特性更为显著.     

Investigation on the nonlinear effects of the vertical motions and vertical bending moment for a wave-piercing tumblehome vessel based on a hydro-elastic segmented model test

Although the nonlinear effects of the ship motions, wave-induced loads and structural responses of conventional vessels have been investigated experimentally and numerically in recent years, similar studies on the wave-piercing tumblehome (WPTH) vessels are rare, in spite of the urgent necessary due to their extensive applications. This paper experimentally investigated the nonlinear effects of the vertical motions and vertical bending moment (VBM) for a WPTH vessel based on a hydro-elastic segmented model test. The model test was carried out in head regular waves for three amplitudes, in the towing tank at Harbin Engineering University. Based on the band-pass filter technique, four kinds of decomposed harmonics are defined by mean offset, linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibration. Meanwhile, based on mean offset, three kinds of combined responses are defined by considering linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibrations step by step. The transfer functions of vertical motions and VBM are presented as function of the incident wave frequency, and the measured data and VBM were compared with numerical calculations for validation. With the method proposed above, the results of VBM are analyzed by focusing on the influences of decomposed harmonics on the amplitudes and asymmetry of combined responses. Strong nonlinear effects are observed in the VBM. The nonlinearity of VBM can be identified by the significant amplitudes of decomposed harmonics, variation of amplitude with the wave amplitude and remarkable asymmetry about the zero axis. The hogging VBM of WPTH vessel can be even larger than the sagging VBM, which is in contrast to the general experiences from conventional vessels. Combined the calculated relative motion with the decomposed and combined histories of VBM, the occurrence of the transient impact and its characteristics are discussed, and these are then used to analyze the unconventional asymmetry of VBM. Furthermore, the influences of the bow shape over the vertical motions and VBM are discussed. At the end of the paper, the uncertainties in the test are provided.     

Simplified estimation for the dynamic behavior and reliability analysis of very large floating structures under wave-induced loads

This paper deals with the dynamic response and strength of very large floating structures (VLFS) in regular and irregular waves, considering the propagation of the hydroelastic deflection wave of the structure. First, a simplified estimation method is presented for the dynamic response and strength of the structure in regular waves. Then, the validity of the method is demonstrated by comparing its results with analytical results and experimental results for a mat-type floating structure model. Next, a simplified estimation method for dynamic responses under long crested irregular wave conditions is presented by using the above results and by combining them with irregular sea wave spectra. Finally, the applicability of the method is investigated through numerical examples carried out for a 4,800-m class VLFS under trial design. Characteristics of the hydroelastic waves, short-term responses, and reliability levels are numerically identified. Received for publication on April 14, 1999; accepted on Sept. 10, 1999     

舰船波浪弯矩响应的频率特性

非直壁式舰船在高浪级和高航速下的弯矩响应中,除了含有低频遭遇频率成分外,还存在着一定数量的遭遇频率的倍频成分及船体各谐调的垂向总振动频率成份,它们都会对舰船波浪弯矩的非线性响应产生相应的影响。如果舰船的第一谐调垂向总振动频率正好是遭遇频率的整数倍,这时弯矩的非线性响应将达到极值。本文从模型试验及理论计算两方面分析了舰船波浪弯矩的频率特性,对船体载荷响应理论的发展及设计载荷的确定具有指导意义。     

船体非线性波浪载荷的水弹性分析

本文采用水弹性分析方法研究船舶在规则波及不规则波中迎浪航行时的结构动力响应（运动、剪力和弯矩等）。确定流体载荷时应用了扩展的切片理论，其中计及由于船体的非直舷、剖面吃水的瞬时变化和船体振荡的非简谐特性所导致的非线性，同时还考虑了波浪冲击、出水和上浪的影响。运动方程是在时域内步进求解。数值计算结果与规则波中的模型试验相比较，符合程度令人满意。