Modelling solitons under the hydrostatic and Boussinesq approximations

An examination of solitary waves in 3D, time‐dependant hydrostatic and Boussinesq numerical models is presented. It is shown that waves in these models will deform and that only the acceleration term in the vertical momentum equation need be included to correct the wave propagation. Modelling of solitary waves propagating near the surface of a small to medium body of water, such as a lake, are used to illustrate the results. The results are also compared with experiments performed by other authors. Then as an improvement, an alternative numerical scheme is used which includes only the vertical acceleration term. Effects of horizontal and vertical diffusion on soliton wave structure is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.      

Elastodynamic analysis of a thin layer bonded on a visco-elastic medium under combined in-plane and lateral pulse loads

An analytic solution of a thin layer bonded on a visco-elastic medium under the action of in-plane and lateral pulse loads is presented. The analysis is based on double integral transforms with respect to space and time. Representative examples are studied and discussed to determine the influence of the (a) damping and elastic coefficients of visco-elastic medium, and (b) in-plane compression and stretching of the thin layer on wave propagation.     

Elastodynamic analysis of a thin layer bonded on a visco-elastic medium under combined in-plane and lateral pulse loads

An analytic solution of a thin layer bonded on a visco-elastic medium under the action of in-plane and lateral pulse loads is presented. The analysis is based on double integral transforms with respect to space and time. Representative examples are studied and discussed to determine the influence of the (a) damping and elastic coefficients of visco-elastic medium, and (b) in-plane compression and stretching of the thin layer on wave propagation.     

固体、流体多相孔隙介质中的波动理论及其数值模拟的进展

简要回顾了两相或三相多孔介质中波动理论和数值模拟的研究历史和现状，着重介绍了用有限元方法对饱水土层中波动进行数值模拟的研究进展，并讨论了有待进一步研究的问题．     

Overall constitutive description of symmetric layered media based on scattering of oblique SH waves

This papers investigates the scattering of oblique shear horizontal (SH) waves off finite periodic media made of elastic and viscoelastic layers. It further considers whether a Willis-type constitutive matrix (in temporal and spatial Fourier domain) may reproduce the scattering matrix (SM) of such a system. In answering this question the procedure to determine the relevant overall constitutive parameters for such a medium is presented. To do this, first the general form of the dispersion relation and impedances for oblique SH propagation in such coupled Willis-type media are developed. The band structure and scattering of layered media are calculated using the transfer matrix (TM) method. The dispersion relation may be derived based on the eigen-solutions of an infinite periodic domain. The wave impedances associated with the exterior surfaces of a finite thickness slab are extracted from the scattering of such a system. Based on reciprocity and available symmetries of the structure and each constituent layer, the general form of the dispersion and impedances may be simplified. The overall quantities may be extracted by equating the scattering data from TM with those expected from a Willis-type medium. It becomes evident that a Willis-type coupled constitutive tensor with components that are assumed independent of wave vector is unable to reproduce all oblique scattering data. Therefore, non-unique wave vector dependent formulations are introduced, whose SM matches that of the layered media exactly. It is further shown that the dependence of the overall constitutive tensors of such systems on the wave vector is not removable even at very small frequencies and incidence angles and that analytical considerations significantly limit the potential forms of the spatially dispersive constitutive tensors.     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

Three-dimensional formulation of time-dependent wave propagation in a gyroanisotropic medium by Bergeron''s method

This paper discusses a numerical vector analysis method for wave propagation and scattering in three-dimensional space and the time domain. The approach is based on both the equivalent-circuit representation of Maxwell's equations and the formulation by Bergeron's method in the time domain. As an example of the application of this technique to a complicated medium, we consider time-dependent electromagnetic wave propagation in a gyroanisotropic medium, specifically the magnetized ferrite and the magnetized plasma. We demonstrate that the numerical approach accurately models relevant physical phenomena, including the Faraday rotation effect.     

Localized strain waves in a nonlinearly elastic conducting medium interacting with a magnetic field

The influence of magnetic field on the generation of a localized wave in a nonlinearly elastic conducting medium is considered. The evolution equation for describing the wave beam propagation in the medium is derived. It is shown that the wave beam parameters depend on the value of the external magnetic field and on the field orientation in space.     

弹性半空间二维出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性半空间自由波场时域计算的一维化有限元方法。首先利用Snell定律确定平面波沿水平方向的传播规律,在用有限元法对弹性半空间进行离散化时,竖向单元尺寸根据波动有限元模拟精度要求确定,而水平向有限元网格尺寸根据水平向波的传播规律和采用的离散时间步长确定,使得有限元离散模型中任意节点的运动可以用水平向相邻节点的运动表示,从而将二维有限元节点运动方程组化为一维的形式。求解此一维方程组,可得到弹性半空间中一列节点的运动,再根据行波的传播规律,可确定全空间自由波场。理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性。     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论１，研究了横观各向同性液体饱和多孔介质中平面波的传播特性。首先导出了波传播的特征方程并给出了其解析解，结果显示：有４种不同波速的平面体波传播；第一准纵波，第二准纵波，准横波和反平面横波。文中给出了波速和衰减的解析表达式，数值计算了频散曲线和衰减曲线，并讨论了各类准体波位移之间的耦合关系。     

Dynamics of shock waves in a liquid containing gas bubbles

Results are presented of a numerical solution of the Korteweg-de Vries-Burgers equation that describes the propagation and establishment process for a stationary structure to a shock wave in a gas-liquid medium. Data are obtained on the time for the establishment of a stationary structure of a shock wave, propagation velocity, and amplitude oscillations in the front of the shock wave. Experiments are discussed on the basis of the results obtained for the study of shock waves in a liquid containing gas bubbles.     

可燃介质中飞行圆球诱导斜爆轰的流场结构

基于带化学反应的二维轴对称Euler方程,利用带有Superbee限制函数的波传播算法,对氢/氧/ 氮预混气中飞行圆球诱导斜爆轰进行了数值模拟。结果表明,在达姆科勒数Da略大于临界情形时,圆球诱导 的驻定爆轰是一个由强过驱斜爆轰、弱过驱斜爆轰、反应激波和惰性激波组合而成的复合结构。波后的圆球 绕流流场内存在2个亚音速区和1个超音速区。在圆球背风表面,还形成了第2道斜激波。     

Propagation of waves in an electro-microstretch generalized thermoelastic semi-space

The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed： （i） reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and （ii） propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case （i）, the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case （ii）, the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plot- ted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.     

成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性.      

Dispersion in oceanic crust during earthquake preparation

Dispersion of Stoneley waves is studied in a sedimentary layer of ocean bottom resting over basaltic solid half space. Sedimentary layer is assumed a transversely isotropic poroelastic medium. Lower-most solid half-space is assumed to be embedded with vertically aligned saturated micro-cracks and behaves transversely isotropic to wave propagation.Frequency equation is obtained in the form of determinantal equation. Role of phase angle is eliminated by expressing slowness of waves in terms of phase velocity and elastic constants. Numerical solutions for phase velocity and group velocity are obtained for a particular model. Calculations are made for different depths of ocean and sediments. Effect of thickness and density of cracks on these velocities are observed.Special cases are discussed which represent the absence of ocean and sediments, in the model considered. Changes in dispersion are discussed during the stress accumulation in an earthquake preparation region.     

Propagation of discontinuities in electromagneto generalized thermoelasticity in cylindrical regions

In this work we study wave propagation for a problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Wave propagation in the elastic medium and in the free space, bounding it, is investigated.     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Nonlinear hyperbolic wave propagation in a one-dimensional random medium

We use an asymptotic expansion introduced by Benilov and Pelinovski to study the propagation of a weakly nonlinear hyperbolic wave pulse through a stationary random medium in one space dimension. We also study the scattering of such a wave by a background scattering wave. The leading-order solution is non-random with respect to a realization-dependent reference frame, as in the linear theory of O’Doherty and Anstey. The wave profile satisfies an inviscid Burgers equation with a nonlocal, lower-order dissipative and dispersive term that describes the effects of double scattering of waves on the pulse. We apply the asymptotic expansion to gas dynamics, nonlinear elasticity, and magnetohydrodynamics.     

Low-frequency axisymmetric waves in blood vessels of constant cross-section: an asymptotic approach

The asymptotic methods of shell theory are used to study the propagation of axisymmetric waves in blood vessels of constant cross-section. The initial equations are simplified using the assumption that the shell radius is small compared with the wave length. We show that the terms corresponding to the shell inertia cannot be omitted if it is required to describe not only the pressure wave but also the longitudinal wave. We study the influence of external fixation on the pressure wave. In this case, we compare the following two models: in the first model, the ambient medium is modelled by elastic and damping elements uniformly distributed over the shell exterior surface and by additional masses; in the second model, the ambient medium is represented by an infinite elastic space with a cylindrical cavity where the vessel is placed. On the interface between the elastic space and the vessel, we pose the full contact conditions. We show that, from the qualitative standpoint, both models lead to the same result: the pressure wave in the first approximation is a wave in the shell whose walls cannot move in the longitudinal direction. We asymptotically integrate the original equations and hence obtain a one-dimensional equation for the bulk blood flow.