Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation

In the research field of nonlinear dynamical system theory, it is well known that a homoclinic/heteroclinic point leads to unpredictable motions, such as chaos. Melnikov’s method enables us to judge whether the system has a homoclinic/heteroclinic orbit. Therefore, in order to assess a vessel's safety with respect to capsizing, Melnikov’s method has been applied for investigations of the chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper (Maki et al. in J Mar Sci Technol 15:102–106, 2010), a formula to predict the capsizing boundary by applying Melnikov’s method to analytically obtain the non-Hamiltonian heteroclinic orbit was proposed. However, in that paper, only limited numerical investigation was carried out. Therefore, further comparative research between the analytical and numerical results is conducted, with the result being that the formula is validated.     

Analytical formulae for predicting the surf-riding threshold for a ship in following seas

Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation. Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees reasonably well with that obtained experimentally for an unconventional vessel.     

波高对桩柱最大水平波浪力新算法精确性影响

对Morison方程进行适当变形、推演,得到了一种可直接计算近海平台支撑物所受最大水平波浪力的计算方法。将此计算方法与经典计算法进行对比。对比发现,当阻力相对于惯性力起主要作用时,新算法与经典算法所得结论完全一致。当惯性力相对于阻力起主要作用时,新算法存在一定偏差,在该情况下,使用Matlab辅助计算,得到了波高对桩柱最大水平波浪力新算法精确性的影响曲线。     

基于随机Melnikov方法的甲板上浪船舶混沌运动研究

应用随机Melnikov方法和庞加莱截面研究甲板上浪时船舶的混沌运动。考虑甲板上浪对船舶静稳性的影响,建立随机横浪中船舶横摇运动方程。由随机Melnikov过程结合均方准则确定船舶产生混沌运动的参数域,计算不同参数域中船舶横摇响应的庞加莱截面和时间历程。结果表明,增加船舶阻尼将抑制混沌运动的发生。甲板上浪时船舶横摇响应的庞加莱截面上有两个吸引域,船舶运动过程有两个横摇中心。在非混沌参数域中,船舶只围绕其中的一个横摇中心运动;在混沌参数域中,发生由一个横摇中心到另一个横摇中心的随机跳跃。     

航行于波浪中的肥大型船波浪增阻计算研究(英文)

Under the background of the energy saving and emission reduction, more and more attention has been placed on investigating the energy efficiency of ships. The added resistance has been noted for being crucial in predicting the decrease of speed on a ship operating at sea. Furthermore, it is also significant to investigate the added resistance for a ship functioning in short waves of large modern ships. The researcher presents an estimation formula for the calculation of an added resistance study in short waves derived from the reflection law. An improved method has been proposed to calculate the added resistance due to ship motions, which applies the radiated energy theory along with the strip method. This procedure is based on an extended integral equation (EIE) method, which was used for solving the hydrodynamic coefficients without effects of the irregular frequency. Next, a combined method was recommended for the estimation of added resistance for a ship in the whole wave length range. The comparison data with other experiments indicate the method presented in the paper provides satisfactory results for large blunt ship.     

同心球壳-球体系感应磁场的解析解

考虑薄壳体和非薄壳体结构的感应磁场可提高舰艇感应磁场数值建模精度,开发相应的磁场数值程序包时,磁场解析解模型是验证程序包数值准确性的有效手段。同心球壳-球体系模型是验证同时考虑薄壳体和非薄壳体感应磁场数值准确性的理想模型。基于分离变量法推导了该模型感应磁场的解析解,以积分方程法和有限元法为参照,解析解误差均在5%以内,表明了导出解析解表达式的准确性。     

回转体-螺旋桨组合体之推力减额的一个数值预测方法

作者把计算回转体绕流的Landweber方法推广到带有运转螺旋桨时回转体绕流问题的计算,导出了附加螺旋桨影响后的物面速度分布的第一类Fredh-olm积分方程。对该方程的迭代求解则用新的加速迭代公式替代常用的Land-weber迭代公式。通过对带与不带运转螺旋桨时回转体上压力差的积分可以得到推力减额。两条模型(分别在风洞、水池的试验)的数值例子表明:本方法的迭代速度要比Landweber迭代公式快,而计算得的推力减额和表面压差分布与试验结果的一致性很好,优于Huaug用Hess-Smith方法算得的结果。     

准周期激励非线性隔振系统的混沌研究

建立了准周期激励下非线性隔振系统的模型;应用Poincare映射方法对系统进行降维处理后,在Poincare截面上分析了系统稳定流形和不稳定流形的行为。应用Melnikov方法确定了系统产生混沌的参数区域。结果表明双曲不变环面的稳定流形和不稳定流形之间同宿横截相交是导致该系统产生混沌的根本原因,并给出了系统出现混沌时的相图、Poincare截面图,计算了Lyapunov指数。     

基于多次透射公式和无奇异边界元法模拟全非线性数值波浪水池

文章基于势流理论对全非线性的三维数值水池进行了模拟,其控制方程由无奇异边界积分方程法(Desingularized Boundary Integral Equation Method,DBIEM)进行离散求解,在求解全非线性的自由面微分方程时,文中采用混合欧拉—拉格朗日法(Mixed Eulerian-Lagrangian,MEL)和四阶Adams-Bashforth-Moulton(ABM4)预报—修正方法,为了避免结果发散即增强数值稳定性,文中采用B样条法来光顺波面.同时,在远方辐射控制面上采用多次透射公式方法(Multi-transmitting Formula,MTF)来进行消波,文中得到的结果与理论解进行了比较,结果表明该方法可用来有效模拟全非线性的数值波浪水池.     

海洋平台立管系统的三维动态响应仿真研究

海洋平台立管是其生产系统的主要组成部分,立管系统的动力学特性直接影响生产平台的稳定性和安全性,针对海洋平台立管系统动态响应特性的数值分析显得尤为重要。本研究以凝集参数时域分析法对海洋平台立管系统进行三维仿真模拟,用四阶Runge--Kutta法进行积分求解,分析惯性坐标系下海洋平台立管系统的动态响应。     

具有淹水舱的舰船横摇运动建模探讨

舰船在风浪中横摇运动特性是影响舰船航行安全的主要因素,而当舰船由于碰撞、搁浅等意外事故造成船体破损进水后,具有淹水舱的舰船在风浪中的横摇运动将变得更加复杂,更加危险,文章系统地分析了具有淹水舱的舰船在波浪中横摇运动时船和舱内水的能量耦合作用,根据拉格朗日方程建立了具有淹水舱的舰船横摇运动两自由度微分方程,并在此基础上,用Melnikov方法对某实船破损进水后的横摇运动进行了非线性分析,验证了所建模型的实用性,为进一步分析破损进水舰船在风浪中的横摇运动特性提供了可行的数学模型.     

基于综合刚度原理水平承载桩计算的改进方法

目前应用的综合刚度原理双参数法所推导的公式,深度幂次数的取值范围受限,且与实际不符,加之对桩的计算没有结合实际进行分段,而是对整个桩取统一参数,造成桩的下半段计算误差较大。基于综合刚度原理,提出水平承载桩计算的改进方法,即先对桩的求解表达式中深度幂次数进行修正,推导微分方程的解,并进行实例计算;然后对桩进行分界点确定,运用反力积分法对桩的后半段进行计算。实例计算结果的对比表明,用该方法不仅拓宽参数的取值范围,而且桩的后半段计算精度有较大提高。     

基于无奇异边界元法模拟三维全非线性液舱晃荡

文章基于全非线性势流理论对三维液舱晃荡进行了数值模拟,其控制方程由无奇异边界积分方程法(Desingular-ized Boundary Integral Equation Method,DBIEM)进行离散求解,在求解全非线性的自由面微分方程时,文中采用混合欧拉—拉格朗日法(Mixed Eulerian-Lagrangian,MEL)和四阶Adams-Bashforth-Moulton(ABM4)预报—修正方法,为了避免结果发散即增强数值稳定性,文中采用B样条法来光顺自由面.在微幅水平激励下,该文中得到的结果与解析解吻合较好.     

Numerical prediction of the surf-riding threshold of a ship in stern quartering waves in the light of bifurcation theory

In order to develop design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge-sway-yaw-roll model in quartering waves, the relevant bifurcation condition is formulated with a rigorous mathematical background. Then an efficient numerical solution procedure suitable for tracing the surf-riding threshold hypersurface is presented with successful examples. This deals with all state and control variables in parallel, and excludes backward time integration and an orthogonal condition in the iteration process. The bifurcation conditions identified were compared with the results from a direct numerical simulation in the time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and nonperiodic motions such as surf-riding and broaching.     

Equivalent design pressure for ship plates subjected to moving slamming impact loads

When a ship navigates at sea, the slamming impact can generate significant load pulses which move up along the hull plating. The effect of the moving pressure has so far not been explicitly considered in the Rules and Regulations for the Classification of Ships. Based on a modal superposition method and the Lagrange equation, this paper derives analytical solutions to study the elastic dynamic responses of fully clamped rectangular plates under moving pressure impact loads. The spatial variation of the moving slamming impact pressure is simplified to three types of impact loads, i.e. a rectangular pulse, a linearly decaying pulse and an exponentially decaying pulse. The dynamic responses of fully clamped rectangular plates under the moving slamming impact pressure are calculated in order to investigate the influence of the load pulse shapes and moving speed on the plate structural behaviour. It is found that the structural response of the plate increases with the increase of the moving speed. The response of the plate subjected to a moving pressure impact load is smaller than the case when the plate is subjected to a spatially uniform distributed impact load with the same load amplitude and load duration. In order to quantify the effect of the moving speed on the dynamic load, a Dynamic Moving Load Coefficient (DMLC) is introduced as the ratio between the dynamic load factor for the moving impact load and that under the spatially uniform distributed impact load. An expression for DMLC is proposed based on analyses of various scenarios using the developed analytical model. Finally an empirical formula which transforms the moving impact loads to an equivalent static load is proposed.     

双材料中矩形裂纹问题的超奇异积分方程方法

使用超奇异积分方程方法,对双材料空间中垂直于界面的矩形裂纹Ⅰ型问题进行了研究.首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程.根据裂纹面上位移函数的分布特性,通过将位移间断函数表示为特征函数和一组多项式乘积的形式,为其建立了数值方法.数值结果表明,该方法不仅具有较好的收敛性和较高的数值计算精度,而且能够精确满足裂纹面上的边界条件.在此基础上,对不同材料组合界面对裂纹前沿应力强度因子的影响进行了分析,取得了较好的数值结果.     

用Melnikov方法研究船舶在随机横浪中的倾覆

本文应用Melnikov函数和相空间转移率研究船舶在随机波浪中的强非线性横摇运动及其倾覆问题,分析了波浪特征频率、特征波高、船舶非线性恢复力臂以及阻尼特性对相空间转移率的影响.以长30.7m、宽6.9m的渔船为例,采用ISSC波浪谱,在时域内计算了Melnikov函数,得到了相空间转移率与Melnikov函数之间的关系以及有义波高对相空间转移率的影响.研究表明:随有义波高增大,相空间转移率不断增大,船舶航行的安全域迅速减小.从而揭示了相空间转移率与船舶倾覆内在的密切联系,为船舶的设计和稳性衡准提供了有价值的参考.     

一般边界条件下矩形薄板振动声辐射特性分析

基于改进傅立叶级数方法,将矩形板振型函数表示为包含正弦三角级数的改进傅立叶级数,从而有效地克服结构在边界处存在的不连续性,建立了一般边界条件下矩形薄板结构振动声辐射的分析方法,并对薄板结构的振动声辐射特性进行了研究。文中还建立了薄板结构的位移容许函数,然后基于最小势能原理求解了系统的Lagrange函数,最后利用Rayleigh-Ritz法对方程求解从而获得薄板自由振动的模态信息;在此基础上,基于Rayleigh积分公式推导出了薄板振动、辐射声压和声功率的表达式,研究了结构特性参数及边界条件对薄板振动声辐射的影响,通过有限元软件和参考文献的比对分析,验证了改进方法的正确性和有效性。     

防空导弹对直杆型杀伤模型单发杀伤概率计算

针对直杆型杀伤模型,在建立弹目之间有关脱靶量以及脱靶方位角的圆柱坐标系模型的基础上,利用概率密度积分法,首先进行简化解析法计算,对防空导弹单发杀伤概率的值进行估算,然后将制导误差的概率密度函数,战斗部的条件杀伤概率,以及引信战斗部联合杀伤概率等计算公式进行了优化,得出了计算防空导弹单发杀伤概率的流程,并对这一方法进行了验证.