微结构固体中钟型与扭结孤立波的演化

根据Mindlin理论和Murnaghan模型,首先建立了描述耗散、频散及非线性微结构固体中一维纵波传播的一种简单模型.然后利用有限差分方法,数值模拟了微结构效应对钟型与扭结孤立波演化的影响. 结果表明,随着微结构效应的减弱,钟型孤立波的幅度衰减以及非对称特征变得越来越明显;随着微结构效应的增强,扭结孤立波顶部出现的“帽子”状变化以及由此产生的非对称特征变得越来越明显.      

INTERNAL SOLITARY WAVE LOADS EXPERIMENTS AND ITS THEORETICAL MODEL FOR A CYLINDRICAL STRUCTURE

在大型重力式密度分层水槽中, 对内孤立波与圆柱型结构的相互作用特性开展了系列实验. 基于两层流体中 内孤立波的KdV,eKdV和MCC理论, 建立了圆柱型结构内孤立波载荷的理论预报模型, 给出了该载荷理论预报模型中3类内孤立波理论的适用性条件.研究表明, 圆柱型结构内孤立波水平载荷包括水平Froude-Krylov力、附加质量力和拖曳力3个部分, 可以由Morison公式计算, 而内孤立波垂向载荷主要为垂向Froude-Krylov力, 可以由内孤立波诱导动压力计算.系列实验结果表明, 附加质量系数可以取为常数1.0, 拖曳力系数与内孤立波诱导速度场的雷诺数之间为指数函数关系, 而且基于理论预报模型的数值结果与系列实验结果吻合.     

固体介质中球形发散波的实验装置

建立了用于固体介质中球形发散波传播规律研究的实验技术 ,球形波源是当量为 0 .12gTNT和 0 .4 9gTNT的微型炸药球 ,波后粒子速度测计是圆环型电磁粒子速度计。用该实验和测量系统在有机玻璃和花岗岩中进行了大量的实验研究 ,实验的重复性很好。利用微型炸药球可在较小的样品中模拟较大比距离范围内的波传播。利用圆环型电磁粒子速度计可使输出信号幅度不受波强度因几何发散而快速衰减的影响 ,而且信号输出反映了波面上一条圆环线处介质动力学状态的综合平均结果。该技术的这些突出优点对研究固体介质 (特别是非均匀固体介质 )中球形发散波传播规律和相应的材料动力学特性研究具有重要意义。圆环型电磁粒子速度计测量技术同样适用于固体介质中圆柱形发散波的情况。     

无黏流体与固体界面的漏瑞利波

漏瑞利波存在于半无限无黏性流体和半无限固体媒质的界面处. 首先推导流固无限各向同性介质界面处漏瑞利波的特征方程和位移及应力的解析计算公式. 然后结合典型结构通过数值计算研究了漏瑞利波特性以及位移和应力在流体和固体中的分布规律. 数值计算结果表明漏瑞利波的相速度和衰减随流固密度比的增大而增大, 在流固界面上法向位移连续而切向位移不连续. 流固密度比对固体媒质中沿垂直于漏瑞利波的传播方向的位移、正应力和剪应力有比较大的影响,而对沿漏瑞利波的传播方向的正应力几乎没影响. 为利用漏瑞利波的无损检测与评价提供了理论基础.      

三维海洋内孤立波数值水槽造波研究

海洋内孤立波因其分布广泛和携带巨大能量,对于潜艇安全航行影响很大.本文采用有限体积自适应半结构多重网格法求解Navier-Stokes方程,并用VOF方法追踪两层流体界面,应用双推板造波法进行内孤立波数值造波,建立了两层流体中的内孤立波数值水槽.数值模拟结果证实了该数值水槽数值造波的有效性和可靠性,为后续研究打下了基础...     

气体非稳定爆轰波在具有声学吸收壁的直角三通弯管中传播特性研究

本文实验研究了丙烷、氧气和空气的预混气体非稳定爆轰波在具有声学吸收壁的直角三通弯管中传播特性，分析了声学吸收材料厚度对非稳定爆轰波传播特性的影响．实验结果表明，在直角三通弯管中安装声学吸收材料对气体非稳定爆轰波有明显的衰减作用，在弯管前后非稳定爆轰波的传播速度和压力都有很大程度的减小．而且随着声学吸收材料厚度的增加，气体非稳定爆轰波强度衰减幅度增大．这一实验结论对工业安全具有重要的参考价值．     

椭圆柱壳链的波形弥散特性研究

椭圆柱壳链可以引起波形弥散，从而可以调控应力波的传播.本文通过3D打印、冲击测试、细观有限元模拟和理论分析，研究了在质量块冲击加载下，单胞纵横比、冲击质量和速度对椭圆柱壳链中弹性波传播弥散行为的影响.结果表明，冲击过程中，椭圆柱壳链结构中的速度峰值随着波传播逐渐减小，纵横比越大或冲击质量越小，速度峰值衰减越剧烈，而冲击速度对椭圆柱壳链的波形弥散行为几乎无影响.相关研究对新型波形控制器的设计和精确有效地调控弹性波传播具有重要意义.     

爆炸荷载下泡沫铝材料中冲击波衰减特性的实验和数值模拟研究

通过实验和数值模拟对泡沫铝中冲击波传播特性进行了研究,结果表明:冲击波在泡沫铝中传播时显示明显的衰减特性;与此同时波头升时逐渐增加。这种衰减耗散特性主要来源于泡沫铝本身的本构粘性效应,而追赶卸载效应又会进一步促进冲击波的衰减。这为泡沫铝作为新型抗冲击缓冲材料提供设计基础。     

爆轰波拐角传播三维数值模拟

为了研究爆轰波在拐角中的传播特性以及拐角爆轰低压流场现象,用LSDYNA 3D程序对三种常见的拐角装药的爆轰波传播特性进行了数值模拟,清晰显示了爆轰波因拐角处爆轰波传播面积的变化而产生的衰减 增长过程,讨论了侧向三通中爆速的变化情况,并得到了拐角处低压爆轰区的尺寸。     

冲击荷载作用下滤波混凝土的动态响应与层裂损伤数值研究

借鉴局域共振材料的工作机制,通过在混凝土基体中嵌入滤波单元,设计出具有应力波衰减特性的滤波混凝土。通过将滤波混凝土结构简化为质量弹簧力学系统来分析滤波混凝土对应力波的衰减机制。采用数值模拟方法,对比研究了冲击荷载作用下普通混凝土模型和滤波混凝土模型中应力波的传播特性和层裂破坏模式。通过参数分析,研究了滤波单元的材料和几何属性对其储能效果的影响。研究结果表明：滤波单元有效降低了混凝土基体中应力波的传播速度和应力峰值;滤波单元的储能机制有效降低了混凝土基体中的能量;金属球的质量越大,滤波单元的储能效果越好,但弹性层的弹性模量和厚度需要通过适当分析进行设计以实现滤波单元的储能最大化;滤波混凝土基体的局部损伤耗散了荷载中的大量能量,有效降低了结构自由面附近的破坏程度。     

Solitary wave interactions and reshaping in coupled systems

The interaction of the components of composite solitary waves governed by nonlinear coupled equations is studied numerically. It is shown how predictions of the known exact traveling wave solutions may help in understanding and explaining the process of reshaping seen as head-on and take-over collisions of individual solitary waves. The most interesting results concern the switch in the sign or the periodic modulation of the amplitude of the solitary wave and the direction of its propagation due to collisions.     

Finite-amplitude solitary waves in a two-layer fluid

Second-mode nonlinear internal waves at a thin interface between homogeneous layers of immiscible fluids of different densities have been studied theoretically and experimentally. A mathematical model is proposed to describe the generation, interaction, and decay of solitary internal waves which arise during intrusion of a fluid with intermediate density into the interlayer. An exact solution which specifies the shape of solitary waves symmetric about the unperturbed interface is constructed, and the limiting transition for finite-amplitude waves at the interlayer thickness vanishing is substantiated. The fine structure of the flow in the vicinity of a solitary wave and its effect on horizontal mass transfer during propagation of short intrusions have been studied experimentally. It is shown that, with friction at the interfaces taken into account, the mathematical model adequately describes the variation in the phase and amplitude characteristics of solitary waves during their propagation.     

Frontal collision of internal solitary waves of first mode

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.     

Korteweg-de vries-type equations in the theory of surface waves in electrically conducting liquids

Equations are obtained which describe the propagation of long waves of small, but finite amplitude in an ideal weakly conducting liquid and on the basis of these equations the influence of MHD interaction effects on the characteristics of the solitary waves is investigated. The wave equations are derived under less rigorous constraints on the external magnetic field and the MHD interaction parameter than in [1–3]. It is shown that the evolution of the free surface is described by the KdV-Burgers or KdV equations with a dissipative perturbation, and that the propagation velocity of the solitary waves depends on the strength of the external magnetic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 177–180, November–December, 1989.     

Solitary waves in a peridynamic elastic solid

The propagation of large amplitude nonlinear waves in a peridynamic solid is analyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. It is demonstrated by numerical studies that the waves interact only weakly with each other when they collide. Wavetrains composed of many non-interacting solitary waves are found to form and propagate under certain boundary and initial conditions.     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD) wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.     

Solitary waves and conjugate flows in a three-layer fluid

Interfacial symmetric solitary waves propagating horizontally in a three-layer fluid with constant density of each layer are investigated. A fully nonlinear numerical scheme based on integral equations is presented. The method allows for steep and overhanging waves. Equations for three-layer conjugate flows and integral properties like mass, momentum and kinetic energy are derived in parallel. In three-layer fluids the wave amplitude becomes larger than in corresponding two-layer fluids where the thickness of a pycnocline is neglected, while the opposite is true for the propagation velocity. Waves of limiting form are particularly investigated. Extreme overhanging solitary waves of elevation are found in three-layer fluids with large density differences and a thick upper layer. Surprisingly we find that the limiting waves of depression are always broad and flat, satisfying the conjugate flow equations. Mode-two waves, obtained with a periodic version of the numerical method, are accompanied by a train of small mode-one waves. Large amplitude mode-two waves, obtained with the full method, are close to one of the conjugate flow solutions.     

Symmetry and Uniqueness of the Solitary-Wave Solution for the Ostrovsky Equation

We consider herein the Ostrovsky equation which arises in modeling the propagation of the surface and internal solitary waves in shallow water, or the capillary waves in a plasma with the effects of rotation. Using the modified sliding method, we prove that the solitary wave moving to the left to the Ostrovsky equation is symmetric about the origin and unique up to translations. We also establish the regularity and decay properties of solitary waves and obtain some results of the nonexistence of solitary wave solutions depending on the wave speed, weak rotation, and dispersive parameter.