液舱三维晃荡运动二阶共振理论解及特性分析

从无旋运动的理论出发,并利用微扰法,推导了液舱三维晃荡运动二阶共振问题的理论解。考虑纵荡和横荡运动情况,对液舱三维晃荡二阶共振问题进行了分析。当两个晃荡方向的和频(即其外部激发频率的和)或差频(即其外部激发频率的差值)等于液舱固有频率时,二阶共振发生;当某一晃荡方向(横荡或纵荡)外部激发频率与另一晃荡方向(纵荡或横荡方向)液舱某一固有频率的和或差值等于液舱另一固有频率时,二阶共振也会发生。进一步研究了各个二阶共振激发频率下水深变化对晃荡振幅的影响。结果表明,对于两个晃荡方向外部激发频率的和频和单一晃荡方向(纵荡或横荡)某一个激发频率与另一晃荡方向(横荡或纵荡)某一个属于奇模的固有频率的和频所引发的共振情况,水深变化对共振振幅大小的影响比较大;而对于相应差频所引发的共振情况,水深变化对共振振幅大小的影响比较小。     

Experimental Studies on Sloshing Mitigation Using Dual Perforated Floating Plates in A Rectangular Tank

The performance of dual perforated floating plates in a rectangular tank is investigated based on the model tests under different external excitations for different filling rates.It is found that dual perforated floating plates in the tank can remarkably mitigate violent resonant sloshing responses compared with the clean tank,especially when the external excitation frequency is in the vicinity of the first-order resonant frequency.Next,the parametric studies based on different filling rates and external excitation amplitudes are performed for the first-order resonant frequencies.The presence of dual perforated floating plates seldom shifts the sloshing natural frequencies.Further,dual perforated floating plates change the sloshing modes from the standing-wave mode in the clean tank to the Utube mode,which can arise from the sloshing reduction to some extent.     

三维弹性侧壁液舱内液体晃动波面的实验研究

通过物理模型实验,对弹性侧壁液舱和刚性液舱内液体晃荡问题进行了研究。由于流固耦合的影响,弹性侧壁液舱内液体晃荡的最低阶固有频率稍小于同尺寸的刚性液舱内液体晃荡的最低阶固有频率。液舱模型处于纵向简谐激励作用下,其中激励频率在最低阶固有频率附近。实验分析两种相对液深比h/L=0.167和h/L=0.333,在二阶模态的次共振和一阶模态的共振状况下,对弹性侧壁液舱与刚性液舱内不同测点的波面、振幅谱和晃动波高进行对比分析。结果表明:在浅液深(h/L=0.167)一阶共振下,流固耦合对波面形态的影响比较明显,弹性侧壁液舱内测点晃动波高明显大于刚性液舱内对应测点波高;而在一般液深(h/L=0.333)一阶共振下,水弹性效应减弱,弹性侧壁液舱与刚性液舱内对应测点处波高差异较小。     

双浮板液舱晃荡特性的数值研究

基于黏性流理论,采用动网格技术和6自由度模型,以及动量源方法,建立了双浮板液舱晃荡的数值模型。分别采用3种不同空间步长的网格离散计算区域,进行了网格收敛性验证。通过光滑液舱晃荡的模型试验和解析得到的爬高最大值,验证了数值模型的精确性。在载液率为50%,激励幅值为2 mm条件下,对双浮板液舱晃荡进行了数值计算,与光滑液舱相比,双浮板液舱晃荡的最大爬高明显减小。通过一个激励周期内双浮板液舱晃荡的波面显示发现,液舱晃荡模式由光滑液舱的驻波模式变为U管模式,晃荡模式的改变起到了明显地抑制液舱晃荡的效果。     

An alternative approach to the structural motion analysis of wedge-beam offshore structures supporting a load

For convenience of dynamic analysis, some offshore structures such as fixed-type platforms are often modeled as the wedge beams supporting tip lumped masses. It is well-known that, due to the effect of the surrounding water, the natural frequencies of a beam in air (or dry beam) are different from those of the same beam immersed in water (or wet beam). However, if the natural frequencies and the associated mode shapes of a dry beam are calculated by taking account of the “added mass” for the immersed beam, then the last natural frequencies and mode shapes will be equal to the corresponding ones of the wet beam. Based on the last concept, the closed form solutions for natural frequencies and the associated mode shapes of the dry beam were determined first, then the partial differential equation of motion for the wet beam was transformed into a matrix equation by using the expansion theorem and the foregoing closed form solutions of free vibration responses for the dry beam. Solving the last matrix equation will give the required natural frequencies and the associated mode shapes of the wet beam. The formulation of this paper is available for the fully or partially immersed double tapered beams with either circular, square or rectangular cross-sections. The taper ratio for width and that for depth may be equal or unequal. The numerical results of this paper were compared with the existing results or the finite-element-method results and good agreement was achieved.     

On natural modes in moonpools with recesses

The theoretical model of Molin [6] is extended to the case of rectangular moonpools with one or two recesses, as can be found in some drillships. Obtained natural frequencies and modal shapes of the piston and first sloshing modes are compared with experimental results available in literature, with good agreement. An approximation easy to implement is proposed for the natural frequency of the piston mode. Further illustrative results are presented when some geometrical parameters of the moonpool are being varied.     

水下桩腿长度变化对浮式结构固有频率的影响研究

为了分析带支腿浮式结构水下桩腿处于不同的长度时振动固有频率的变化情况,采用有限元方法和三维线性水弹性理论对一理想的带支腿浮式结构进行研究,分工况计算了3种弹性模态的干、湿固有频率。结果表明对于同一阶弹性模态来说,结构主体平台振型是决定水动力系数大小的主要因素,桩腿水下长度是次要因素,而振型又受到桩腿长度的制约;桩腿水下长度的改变对带支腿浮式结构的干模态固有频率以及湿固有频率都有较明显地调制作用。对于干模态固有频率来说,桩腿关于船身越趋于对称分布时结构的共振频率越高;对于湿固有频率来说,水下桩腿长度地增加有迫使共振频率趋向低频方向移动趋势。     

Internal Resonances for Heave,Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortexinduced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows.The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.     

Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortex-induced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.     

A modal approach to second-order analysis of sloshing using boundary element method

This paper aims at developing a modal approach for the non-linear analysis of sloshing in an arbitrary-shape tank under both horizontal and vertical excitations. For this purpose, the perturbation technique is employed and the potential flow is adopted as the liquid sloshing model. The first- and second-order kinematic and dynamic boundary conditions of the liquid-free surface are used along with a boundary element model which is formulated in terms of the velocity potential of the liquid-free surface. The boundary element model is used to determine the natural mode shapes of sloshing and their corresponding frequencies. Using the modal analysis technique, a non-linear model is presented for the calculation of the first- and second-order potential which can be used to obtain a reduced-order model for the sloshing dynamics. The results of the presented model are verified with the analytical solution for the second-order analysis of sloshing in a rectangular tank and very good results were obtained. Also, the second-order sloshing in some other example tanks with complex bed shapes is studied. The second-order resonance conditions of liquid sloshing in the example tanks are investigated and some conclusions are drawn.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

Motion responses of barge carrying liquid tank

The interaction between the liquid sloshing in a rectangular tank equipped inside the barge and the barge responses has been investigated through a comprehensive experimental program. The barge was subjected to both regular and random wave excitations under beam sea condition. Three relative fill levels (h_s/l) with liquid fill depth (h_s) to length of tank (l) ratio of 0.163, 0.325 and 0.488 were considered. In addition, the barge responses of equivalent dry weight condition corresponding to each fill level were measured to understand the influence of sloshing. While the excitation wave frequency equals to first mode natural sloshing frequency, a noticeable decrease in the sway response has been observed. However, the effect of sloshing oscillation on the heave response is insignificant. A split up of roll resonance was observed for the aspect ratio of 0.163 due to the coupling effect of roll motion and sloshing.     

Roll stabilization by anti-roll passive tanks

Since the most severe roll motion occurs at resonance (known as synchronous rolling), the best way of reducing it is to increase the damping. The most common means of doing so is by the installation of bilge keels. If more control is required, both anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. The use of tanks with liquid free surfaces for reducing roll motion of ships is an old idea. Many researchers have studied the design of anti-roll tanks. However, most of the past effort has concentrated on studying the performance of anti-roll tanks in damping the roll motion of the ship. Little attention has been paid to the fluid motion inside the tank itself. Another important issue is the tank tuning. Proper tuning of the anti-roll tank, to match the ship's natural frequency, is very important in reducing the roll motion. This paper concentrates on the most familiar type, which is the U-tube passive tank as a mechanical absorber of roll motion. A detailed study, covering tank damping, mass, location relative to the ship CG, and tuning, is presented. New suggestions and observations are stated concerning tank damping and tuning.     

弹性液舱内液体晃荡实验研究

通过物理模型实验,对水平简谐激励下弹性矩形液舱内液体晃荡问题进行了研究。实验中给出了不同液深和不同激励振幅下弹性液舱内液体最低阶固有频率。采用影像采集与分析系统获得液舱内自由液面的形状和高度,通过压力采集系统得到舱壁上的压力分布。实验中分析了不同液深、不同激励频率下弹性和刚性液舱内自由液面高度和晃荡压力的变化特性。比较了弹性和刚性液舱内不同位置处自由液面高度随外界激励频率的变化规律,以及舱壁上不同位置处的压力峰值随外界激励频率的变化规律。结果表明:非共振情况下,弹性和刚性实验结果及理论值三者的波高和压力较为接近。共振情况下,弹性和刚性波高基本相等,在近舱壁处二者明显大于理论值,而在远离舱壁处二者与理论值存在一定差别;弹性压力较刚性压力略小,但二者与理论值差别较大。     

Dynamic coupling of a liquid-tank system under transient excitations

It has been observed that the unrestrained free surface of a container can create relatively large liquid movements for even very small motions of the container. This excessive movement may endanger the stability as well as the maneuvering quality of the transporting vehicle. Therefore, the effects of the dynamic coupling of a liquid-tank system are of great concern. This dynamic coupling problem is studied analytically for a two-dimensional, rectangular rigid tank with no baffles. The governing equations of the liquid motion are derived with reference to a moving coordinate system which is fixed to the moving container. With the liquid forces generated by the fluid motion as the external exciting force for the tank, the motions of the liquid-tank system can be described according to Newton's Second Law of Motion. By using the Laplace transformation technique, the dynamic responses of the coupled system can be examined in detail. Numerical results for various types of external excitations and the resultant motions of the fluid-tank system are presented and compared with the equivalent non-shifting cargo system. The results of the comparison indicate that the discrepancy of responses in the two systems can obviously be observed when the ratio of the natural frequency of the fluid and the natural frequency of the tank is close to unity. Also, the amount of fluid inside the tank is a very important factor in determining the responses.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

Analysis of second-order resonance in wave interactions with floating bodies through a finite-element method

A time-domain method is employed to analyse the resonant oscillations of the liquid confined within the two floating bodies. The velocity potentials at each time step are obtained through a finite-element method (FEM) with quadratic shape functions. The matrix equation of the FEM is solved through an iteration. The radiation condition is satisfied through a combination of the damping zone method and the Sommerfeld–Orlanski equation. A detailed analysis is made for two rectangular floating cylinders undergoing forced oscillation. The first-order potential reveals the resonant behaviour of the wave motion at certain frequencies ω_i, which is similar to sloshing in a tank. More interestingly, the second-order theory further reveals that when the oscillation frequency is at ω_i/2 or half of the resonant frequency, no first-order resonance is observed as expected, but the second-order resonant motion becomes evident, which does not seem to have been extensively investigated so far. Detailed results for two rectangular cylinders are provided to show some insights into the resonant effect due to the interaction between the bodies. The first- and second-order resonant phenomena have been observed and the result has shown that the second-order components have significant influence on the wave and force in some cases, especially at the second-order resonance.     

Numerical simulation of nonlinear wave radiation by a moving vertical cylinder

In this paper the fully nonlinear potential model based on a finite element method is used to investigate the nonlinear wave motion around a moving circular cylinder. The results for the cylinder in transient motion are compared with the experimental data and a much better agreement than the linear theory is found. Further simulation for a circular cylinder in sinusoidal motion is made. It is found that when the ratio of the cylinder diameter D to the wavelength L is relatively small at a fixed motion amplitude the nonlinear components of the runup on the cylinder surface at the second- and third-harmonic frequencies become more important and this is confirmed by the experimental data. Results for the hydrodynamic force are also provided for a cylinder oscillating in a channel. It is noticed that when the frequency of the cylinder motion in a channel is between the first and the second natural frequencies of the symmetric mode, the time history has components not only at the frequency of the cylinder motion but also at the first natural frequency. The latter remains significant over the period that the simulation is made. This has important implications to model testing. If measurement is to be made at such a frequency it may take long time for the motion to become periodic at the frequency of the cylinder motion.     

深水AUV系统湿模态分析

以国家科技重大专项研制的深水AUV系统为研究对象,借助商业软件ANSYS,从一个新的角度——AUV湿模态分析,研究了各种外界激励的频率特性。为避免AUV发生共振,应保证AUV所受到的各种外界激励的频率远低于AUV的第7阶固有频率,基于此,我们对AUV航行时的干扰源、AUV搭载的机械结构以及AUV附属结构的对于AUV本体的产生的激励频率进行了计算。计算结果显示,低于AUV本体的固有频率,不会对AUV的稳定性产生影响,实现了AUV本体振动不会影响各传感器的正常工作的设计。     

Experimental Study on A Sloshing Mitigation Concept Using Floating Layers of Solid Foam Elements

A sloshing mitigation concept taking advantage of floating layers of solid foam elements is proposed in the present study. Physical experiments are carried out in a liquid tank to investigate the hydrodynamic mechanism of this concept. Effects of the foam-layer thickness, excitation amplitude, and excitation frequency on the sloshing properties are analyzed in detail. It is found that the floating layers of solid foam elements do not evidently affect the fundamental natural sloshing frequency of the liquid tank evidently among the considered cases. At the resonant condition, the maximum wave height and dynamic pressure are greatly reduced as the foam-layer thickness increases. Higher-order pressure components on the tank side gradually vanish with the increase of the foam-layer thickness. Cases with different excitation amplitudes are also analyzed. The phenomenon is observed when the wave breaking in the tank can be suppressed by solid foam elements.