一个变系数非线性演化方程新的精确解

通过推广的F-展开法研究一个变系数非线性演化方程的精确解.首先通过线性变换将变系数非线性演化方程约化为标准椭圆方程形式,再由标准方程行波解的结构求出原方程的解,从而得到了变系数非线性演化方程丰富的精确解.     

变系数BBM方程的精确解

通过推广的F-展开法研究了变系数BBM(Benjamin,Bona and Mahony)方程的精确解,通过线性变换将变系数BBM方程约化为标准椭圆方程形式,由标准方程的行波解的结构求出原方程的解,从而得到了变系数BBM方程丰富的精确解.同时研究了解随参数的变化而变化的情况.     

船舶非线性参激横摇运动方程的主参数共振

运用多尺度法和数值计算方法研究了非线性参激横摇运动方程的主参数共振,得到了二阶一致有效近似解,并分析了方程稳态解的稳定性,以及分岔与混沌行为.     

船舶非线性参激横摇运动方程的主参数共振

运用多尺度法和数值计算方法研究了非线性参数横摇运动方程的主要参数共振,得取了二阶一致有效近似解,并分析了方程稳态解的稳定性,以及分岔与混沌行为。     

一类p-Laplacian方程周期解的存在唯一性

利用 Man＆#225;sevich-Mawhin 连续定理研究一类二阶 p-Laplacian 方程（p（x＇））＇= f（t，x，x＇）- e（t）周期解的存在与唯一性，在非线性项 f = g ＋ h 分别满足一定增长性的条件下，得到了一个新的周期解存在唯一性定理。     

锚泊线一阶运动响应对二阶锚链阻尼的影响

本文主要研究锚泊线的一阶运动响应对二阶锚链阻尼的影响。在频域内采用摄动方法分析系泊结构物慢漂运动时,锚链二阶方程可分解成非齐次方程和齐次方程。其解分别与锚链的一阶运动响应和浮式结构物的二阶运动有关。为了探讨锚泊线一阶运动的影响,本文通过求解非齐次和齐次方程,分别求得相应的二阶锚链阻尼和二阶锚链力。从计算结果可以看出,尽管由非齐次方程得到的二阶锚链力占总的二阶锚链力成分很小,但其所提供的二阶锚链阻尼却与二阶齐次方程解同量级。故在分析二阶锚链阻尼时,不能忽略非齐次方程解的影响。     

中等细环壳轴对称变形问题的一般解

为探讨环壳在海洋工程和船舶结构方面的应用，本文对Ｂ．Ｂ．诺沃日洛夫＾［１］环壳方程提出了以α＝α／Ｒ为摄动参数的一般摄动解法，并推导了一阶、二阶摄动解的表达式。本文解可用于计算参数α值较小的中等细环壳和细环壳中的应力、位移。     

基于粒子系统的船行波建模与绘制

基于船行波理论和粒子系统理论实时生成三维船行波的方法，以矩形基本粒子对船行波粒子进行造型，采用动态纹理映射技术和透明度扰动方法，模拟船行波的辐射效果，根据船行波所受外力构建其运动方程，来描述船行进过程中船首波、船尾波粒子的运动效果，采用与视点相关技术实时生成船在海上航行的三维场景：与传统的基于物理模型的船行波模拟算法相比，该算法既正确模拟船行进时产生的船行波的运动行为和辐射行为，降低计算复杂性，真实再现船行波的三维视觉效果，在满足实时交互漫游的前提下表现出较强的真实感。实验结果表明，此方法能满足船行波实时模拟的需要。     

关于一类二阶共轭矩阵方程的解

考虑一类二阶共轭矩阵方程 B*X*AXB+B*X*C+C*XB+D=O 其中，B∈Cp×m，A∈n×n，C∈Cn×m，D∈Cm×m，在A＞O及A≥O，C或B为列满秩阵两种情况 下，此方程可解的充分必要条件，并在有解的情况下，给出了通解的显式表示。     

关于一类二阶共轭矩阵方程的解

考虑一类二阶共轭短阵方程BXAXB＋BXC＋CXB＋D＝0其中，B∈C^p*m,A∈C^n*n,C∈Cn*m,D∈Cm*m,在A＞O及A大于等于O，C或B为列满秩阵两种情况下，此方程可解的充分必要条件，并在有解的情况下，给出了妥的显式表示。     

Three-dimensional vortex-induced vibrations of a circular cylinder predicted using a wake oscillator model

This paper reports a numerical study based on a wake oscillator model, to determine the three-dimensional vortex-induced vibration (VIV) responses on a flexible cylinder with pinned-pinned boundary conditions subjected to a uniform flow. Four different aspect ratios have been selected for the study. The coupling equations of the structural oscillator models and wake oscillator models in both the cross-flow (CF) and in-line (IL) directions have been solved using a standard central difference method of the second order. The structural displacement, structural frequency, response wave pattern, response trajectory, and lift force coefficient, for four aspect ratios, have been compared. The numerical results establish that, for a small aspect ratio, the CF displacements have absolute standing wave behaviors without travelling wave behaviors, and the IL displacements have dominant standing wave behaviors with slight travelling wave behaviors. Further, the VIV trajectory is repeatable and displays figure-eight shapes. However, for a large aspect ratio, the CF displacements display identical characteristics with the IL displacements for a small aspect ratio, and the IL displacements for a large aspect ratio are simultaneously dominated by standing and travelling wave behaviors. Moreover, the VIV trajectory is apparently aperiodic and shows chaotic shapes.     

波浪在不平坦海岸底床上传播的平面二维数学模型

基于线性波浪理论,利用摄动理论中的多重尺度法,以坡度ε为小参数,Liu和Shit·帷导出波浪在不平坦底床传播的波幅方程,以及一阶势函数的解析解。为验证该模型是否可用于平面二维波浪传播问题,利用有限差分法,分别对波幅方程和边界条件进行离散和求解,得到因折射、绕射引起的波幅和波向的变化。通过引入绕射因子,使该模型的应用范围更为广泛,并且计算精度得到提高。将计算得到的波向和波高与Berkhoff、Berkhoff等翻椭圆形浅滩试验值进行比较,表明该模型可以应用于平面二维问题。     

高阶呼吸子式畸形波波形的数值研究

畸形波是一种波高极大的罕见波浪,对海洋平台的结构以及工作人员的人身安全具有极大威胁。由于在开阔海域中对畸形波的观测存在困难,通过数值手段对其波形进行研究具有十分重要的意义。四阶非线性薛定谔方程又被称为Dysthe方程,能够更加准确地描述波浪的非线性演化。该文通过数值求解Dysthe方程,研究了三阶非线性薛定谔方程的高阶呼吸子解(最高至5阶解)的演化过程。提出了四阶离散步长—虚拟波谱法,得到了具有更高守恒精度的数值解。同时,通过坐标变换以及拟合对高阶呼吸子式畸形波的波形进行了深入研究。     

线性水波理论中远场无波势的构建(英文)

Various water wave problems involving an infinitely long horizontal cylinder floating on the surface water were investigated in the literature of linearized theory of water waves employing a general multipole expansion for the wave potential. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation (for non-oblique waves in two dimensions) or two-dimensional Helmholz equation (for oblique waves) satisfying the free surface condition and decaying rapidly away from the point of singularity. The method of constructing these wave-free potentials is presented here in a systematic manner for a number of situations such as deep water with a free surface, neglecting or taking into account the effect of surface tension, or with an ice-cover modelled as a thin elastic plate floating on water.     

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.     

具有高阶导数自由表面边界条件的两层流体无波势和多级的构建（英文）

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace's equation(or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace's equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.     

Construction of wave-free potentials and multipoles in a two-layer fluid having free-surface boundary condition with higher-order derivatives

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.     

On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth

A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6–10 iterations are required to obtain a numerically converged solution.     

水深对三体船运动和波浪载荷的影响

利用三维势流理论和简单格林函数计算了迎浪航行时不同航速和不同水深组合下的波浪运动响应和载荷传递函数,研究不同水深和航速组合对三体船的波浪运动响应和波浪载荷的影响,并对船舯垂向弯矩和舯后1/4船长处剪力进行了长期预报.将预报值与规范值进行比较,结果令人满意.计算结果表明三体船在不同水深下航行时,水深对其运动响应和波浪载荷都会产生显著影响.     

基于扭转弹性波理论的船舶柴油机推进轴系扭振研究

本文建立了连续轴模型中沿轴向传播的扭振弹性波的波动方程组,结合方程组的初始条件和边界条件及波动方程解的行波表达式,导出了各轴段扭转弹性波传播的解析表达式,利用数值迭代方法可求解;利用弹性波分析理论对船舶柴油机推进轴系的连续模型进行了扭振响应计算的研究,在激励力上可同时计及各谐次的综合作用,可精确计算共振及非共振工况的强迫振动响应,使计算过程与扭振实测分析过程完全对应.研究中,对某船舶柴油机推进轴系的扭转振动振形和轴系扭振响应进行了计算,获得了较好的效果.