波-流相互作用的缓坡方程及其波作用量守恒

当表面波从开阔海域传播至近岸水域时,普遍的波一流相互作用经受着海底的强烈影响．运用水波Hamilton变分原理,建立了近岸水域任意水深变化海底上波一流相互作用的缓坡方程．它可包含波、流和水深一般变化的二阶效应,约化为某些典型的缓坡型方程．据此得出广义程函方程,并且证明该缓坡方程的波作用量守恒．     

缓变主流中三维气泡的非线性振动

空化现象和水下噪声机制与液体中气泡的动力学行为密切相关．在无粘势流的假定下，采用多参数摄动分析，研究了缓变主流中三维气泡的非线性体积模态振动．推导了关于缓变泡形展开的各阶扰动方程，获得了一阶振动的演化方程和一些特殊情况下的解析解；并采用高阶有限元离散的边界积分方程方法，对平面固壁和自由面附近三维气泡的固有频率进行了数值计算     

近岸非平整海底上耗散动力系统的广义波作用量守恒方程

为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制，着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响，由基于黏性流体Navie-Stokes方程的平均流方程，建立了近岸耗散动力系统的广义波作用量守恒方程，从中提出垂向速度波作用量和耗散波作用量这两种新概念，使得它们和经典的波作用量相互间达成了一种互补、协调而又主次分明的更为广泛的守恒形式．从而把波作用量这一经典概念从理想的平均流守恒系统引申到实际的平均流耗散系统(即广义守恒系统)中去，为解释沿岸过程和应用于近海、海岸工程提供了一个理论基础．     

缓坡方程的推广

为了描述水波和强烈的环境流在非平整海底上的相互作用,运用无旋运动的Lagrangian变分原理,对经典的Berkhoff缓坡方程进行了改进。假定水流沿水深方向基本上保持均匀性,这正如潮流运动的特征。海底地形由慢变、快变两个分量叠加构成;慢变分量满足缓坡逼近假定,快变分量的波长与表面波波长为同一量级,但其振幅小于表面波的振幅。在以上假定条件下,得到了适用于非平整海底的推广型浅水方程和应用性更加广泛的波－流－非平整海底相互作用的一般缓坡方程,并且从理论上证明一般缓坡方程包含了以下3种著名的缓坡型方程：经典的Berkhoff缓坡方程;波－流相互作用的Kirby缓坡方程、Dingemans关于沙纹海底的缓坡方程。最后,通过与Bragg反射实验数据的比较,表明该模型可以准确地反映快变海底的典型地貌特征。     

波包在后掠翼三维边界层中的演化特征

研究了点源产生的孤立波包在后掠平板三维边界层中的演化特征．理论计算的波包增长路径和ＮｉｔＳＣｈｋｅ－Ｋｏｗｓｔｙ所做流场显示得到的条纹结构一致,证明条纹是波包的等相位线;波包方程的渐近解表明在三维边界层中ｅＮ方法应沿着为实数的方向积分;ｅＮ方法过高预测了扰动幅值的增长率,与Ｄｅｒｈｌｅ的实验结论一致．     

变截面框架-剪力墙-薄壁筒结构弯扭耦连振动的常微分方程求解器解法

本文用沿高度方向分段连续化的方法,对沿高度方向为阶形变截面,在平面内为任意斜向布置的框架-剪力墙-薄壁筒协同工作体系,建立了弯扭耦连的振动方程,用常微分方程求解器(COLSYS)求解了自振频率及相应的振型。     

骑行波的非线性演化方程

从能量的角度出发,采用Ｈａｍｉｌｔｏｎ描述交结合变分原理和摄动分析,并借助于符号运算导出了骑行在大波上的小波的Ｈａｍｉｔｏｎ密度函数和非线性动力学方程。这里的大流和小波是对波高而言的。在Ｈａｍｉｌｔｏｎ描述中,正则变量取为波高和速度势。本文导出了描述小波演化的二阶方程,在一阶近下的方程与Ｈｅｎｙｅｙ等人（１９８８）的结果一致。     

叶轮机械沿任意曲线的运动方程及其应用

本文推导了叶轮机械内理想气体沿任意曲线方向的运动方程,方程表示为流面上气体速度沿任意曲线方向变化率的一阶微分方程,适于求解。详细讨论了方程在S_1和S_2两类流面上的求解方法,包括电子计算机解和手算近似解。将计算实例与其它文献或实验结果作了比较,表明本文提供的方法适合在叶轮机械气动设计中应用。     

一般非完整系统的Kane方程

本文从理想约束条件出发,不依赖任何形式的变分原理,将Kane方程推广到任意阶非完整系统。而且任何阶非完整系统的Kane方程都可以由对应完整系统(包括简单非完整系统)的Kane方程组合而成。本文结果表明,将Mangeron方程用于k阶非完整系统时,其阶数不必与约束的阶数相同。     

移动载荷作用下浮冰的非线性动力学响应

本文考虑非线性、惯性和阻尼的影响, 研究了任意深度二维理想流体顶部浮冰的振动. 对相关的拟微分算子进行展开并将非线性项保留至三阶后, 完全非线性问题被简化为仅与自由面上的变量相关的三阶截断模型. 为了验证简化模型的准确性, 重点关注了自由孤立波解. 在不考虑阻尼的情况下, 采用多重尺度方法推导了三阶非线性薛定谔方程(NLS), 利用该方程预测了任意水深下原始欧拉方程中自由波包型孤立波解的存在性及三阶截断模型的准确性. 相比于Dinvay等所提出的二阶模型, 三阶截断模型的优势在于其对应的三阶NLS具有准确的非线性项系数, 能够在最小相速度附近更好地模拟冰层的动力学响应. 进一步地对自由孤立波解进行数值计算, 数值结果表明三阶截断模型在分岔曲线和孤立波波形上均与完全欧拉方程吻合良好, 准确性高于二阶截断模型. 基于三阶截断模型, 探究了匀速局域化载荷作用下的浮冰非线性动力学响应并将时间依赖解与实验测量数据进行比较, 数值计算结果与实验记录吻合良好.      

On the Resonant Generation of Weakly Nonlinear Stokes Waves in Regions with Fast Varying Topography and Free Surface Current

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｔｅｒａｃｔｉｏｎｏｆｓｕｒｆａｃｅｗａｔｅｒｗａｖｅｓｗｉｔｈａｍｂｉｅｎｔｃｕｒｒｅｎｔｓａｎｄｕｎｄｕｌａｔｉｎｇｓｅａｂｅｄｔｏｐｏｇｒａｐｈｙｉｓｏｆｆｕｎｄａｍｅｎｔａｌｉｍｐｏｒｔａｎｃｅｔｏｃｏａｓｔａｌｅｎｇｉｎｅｅｒｓａｎｄｓｅｄｉｍｅｎｔｏｌｏｇｉｓｔｓ.Ｆｏｒｅｘａｍｐｌｅ,ｔｈｅｒｅｓｏｎａｎｔｇｅｎｅｒａｔｉｏｎｏｆｓｕｒｆａｃｅｗａｖｅｓｉｎａｃｕｒｒｅｎｔｏｖｅｒｏｔｈｅｒｔｉｄａｌｌｙｏｒｗａｖｅｉｎｄｕｃｅｄｂｅｄｆｏｒｍｓ,ｓ…     

Quasi-periodic waves and quasi-solitary waves in stratified fluid of slowly varying depth

The nonlinear waves in a stratified fluid of slowly varying depth are investigated in this paper. The model considered here consists of a two-layer incompressible constantdensity inviscid fluid confined by a slightly uneven bottom and a horizontal rigid wall. The Korteweg-de Vries (KdV) equation with varying coefficients is derived with the aid of the reductive perturbation method. By using the method of multiple scales, the approximate solutions of this equation are obtained. It is found that the unevenness of bottom may lead to the generation of so-called quasi-periodic waves and quasisolitary waves, whose periods, propagation velocities and wave profiles vary slowly. The relations of the period of quasiperiodic waves and of the amplitude, propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented. The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.Project Supported by National Natural Science Foundation of China.     

Extended Mild-Slope Equation

ＩｎｔｒｏｄｕｃｔｉｏｎＡｃｃｕｒａｔｅｍｏｄｅｌｌｉｎｇｏｆｓｕｒｆａｃｅｗａｖｅｄｙｎａｍｉｃｓｉｎｃｏａｓｔａｌｒｅｇｉｏｎｓｈａｓｂｅｅｎｔｈｅｇｏａｌｏｆｍｕｃｈｒｅｃｅｎｔｒｅｓｅａｒｃｈ ,ｗｈｉｃｈｈａｓｂｅｅｎｓｕｍｍａｒｉｚｅｄｉｎｓｕｒｖｅｙｓｂｙＤｉｎｇｅｍａｎｓ( 1 997) [1]ａｎｄＫｉｒｂｙ( 1 997) [2 ].Ｔｈｅｒｉｃｈｎｅｓｓｏｆｃｏａｓｔａｌｗａｖｅｄｙｎａｍｉｃｓａｒｉｓｅｓｆｒｏｍｔｈｅｓｔｒｏｎｇａｍｂｉｅｎｔｃｕｒｒｅｎｔｓａｎｄｔｈｅｗｉｄｅｖａｒｉａｔｉｏｎｓ…     

平板单面剥层X射线应力测定中的幂级数校正

在具有矩形截面的平板或棒材的单面剥层 X 射线应力测定中,可以用幂级数来分段近似沿层深变化的剥离面的实测应力曲线,从而计算剥层所产生的附加应力,求得原始真实应力沿厚度方向的分布。文中给出了计算应力校正量的公式,并且用两个实测例说明,用项数不多的幂级数来近似实测曲线,就能得到足够高的近似程度.这种近似对计算结果的影响远小于 X 射线应力测量误差的影响.     

Stability analysis of the whirl motion of a breathing cracked rotor with asymmetric rotational damping

The stability of the whirl motion of a breathing cracked rotor with the distinction of stationary damping and the asymmetric rotational damping is studied. By Lagrange’s principal, the motion equations are formed in rotational frame such that the multi-asymmetric system, i.e., asymmetric rotational damping and asymmetric time-periodic varying stiffness, is simplified to be a system with anisotropic damping and anisotropic time-periodical varying stiffness in rotational operation. Based on the multiple scales solution of the simplified whirling equation in moving frame, root locus method for stability analysis is proposed. Different from the former stability estimation method, the corresponding Campbell diagram, decay rate plot, and root locus plot of the fifth-order approach are derived to prove the effects of both crack depth and damping effects. The numerical results of the instabilizing effects of the crack depth are well agreeing with the previous studies. In addition, the destabilizing influence of the rotational damping on the breathing cracked rotor is presented for the first time.     

Nonlinear surface waves on a ferromagnetic fluid of variable depth

A nonlinear ray method is used to study surface waves on a ferromagnetic fluid of variable depth subject to a horizontal magnetic field, and an equation of the KdV type with variable coefficients is derived. An approximate solution of the equation representing a three-dimensional soliton with varying amplitude and phase is constructed and numerical results are presented.     

Fracture analysis of functionally graded coatings: plane deformation

A new multi-layered model for fracture analysis of functionally graded materials (FGMs) with arbitrarily varying elastic moduli under plane deformation has been developed. In this model, the FGM is divided into several sub-layers and in each sub-layer the shear modulus is assumed to be a linear function of the depth while the Poisson's ratio is assumed to be a constant. With this new model, an interface crack problem of a functionally graded coating bonded to a homogeneous half-plane under normal and shear loading is investigated. Employment of transfer matrix method and Fourier integral transform technique reduces the problem to a system of Cauchy singular integral equations which are solved numerically. Stress intensity factors of an interface crack are obtained for the cases of the shear modulus varying in an exponential manner and in a sinusoidal manner. Comparison of the present new model to other existing models shows that the new one is more efficient.     

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅰ)——GENERAL THEORY

In the present paper a finite layer method is studied for the elastodynamics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half.space into a series of layers in the direction of depth the material fimetioms in each layer are simulated by exponential fumctions Consequently, the fundamental equations to be solved can be simplified if the fouricr transform with repsect to coordinates is used. We have obtained the relationship between the "layer forces" and "layer displacements". This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.