组分连续变化梯度材料中位移波和速度波的研究

建立了线弹性组分连续变化梯度材料的位移波动方程和速度波动方程，这2个方程的特征方程及特征线上质点应力、质点应变与质点速度在位移波阵面上的相容关系和质点应变变化率、质点应力变化率与质点加速度在速度波阵面上的相容关系。     

具任意次非线性项的非线性Klein-Gordon方程孤波解的轨道稳定性

具任意次非线性项的非线性Klein-Gordon方程是一类非常重要的物理模型,它的孤波解的轨道稳定性有着很好的物理意义.本文利用抽象的Grillakis轨道稳定性理论和谱分析,讨论具任意次非线性项的非线性Klein-Gordon方程的孤波解的轨道稳定性.当非线性项的系数以及波速满足一定的条件时,得出了其钟状孤波解总是不...     

非线性弦振动的Kdv方程及其速度孤波解

文中用递减微扰法导出了非线性弦振动的 Kdv 方程。文中分析了无色散和无非线性(线性色散)两种特殊情况下的解。然后,详细地讨论了 Kdv 方程的速度孤波解的性态,并指出了非线性弦振动中孤波的主要特征。     

脉冲源反演介质参数的近似波前法

在时域内对弹性波动方程退化的非均匀介质声波方程，引入背景场参数与扰动参数，并化为积分方程形式；针对脉冲源情况，根据射线理论中的传递方程和程函方程，对非均匀介质中的波场形式引入一种波前近似形式，得到波散射点满足散射关系曲线及散射波幅值与介质参数扰动比的代数关系方程式；为求解非均匀介质中散射波场及反演介质参数提供了一种方法，通过对一个完整算例全部过程的模拟，验证了此方法的正确性。     

纤维增强复合板中声弹Lamb波的波结构分析

基于线性三维弹性理论和“增量变形力学”理论,采用勒让德正交多项式展开法,推导了在水平和垂直方向施加初应力时,沿纤维增强复合板的非主对称轴方向传播的声弹Lamb波的波动方程,并对波动方程进行数值求解。为了验证方法的准确性,将该文方法求解的各向同性材料的相速度频散曲线与Disperse?软件的计算结果进行比较,两者吻合良好。以单层单向纤维增强复合材料板为例,计算了无初应力状态下的波结构应力曲线,并与应力自由边界初始条件的一致性进行了比较。研究了水平和垂直方向初应力效应对Lamb波频散曲线的影响。针对声弹效应较为敏感的Lamb波A₀模态,着重分析了初应力效应对波结构位移分布曲线的影响。     

快速重载作用下浮桥位移波传播特性研究

为研究快速重载作用下柔性浮桥位移波的传播特性,利用弹性基础梁理论,建立了浮桥的运动控制方程,并用振型叠加法进行求解。计算了浮桥位移波的传播速度、不同荷载速度下位移波最大振幅与浮桥最大位移的比值以及荷载处坡度随速度的变化曲线。结果表明:在重载快速通过时,柔性浮桥会激发位移波向两端传播,当荷载运动速度与位移波传播速度相当时,会有位移波堆积和荷载爬坡等新的现象出现,而且荷载运动速度越大,这种现象越明显。     

(1+1)维KdV型方程的变速孤波解

利用齐次平衡原则,导出了一(1 1)维KdV型方程的Baecklund变换,借助于该变换．获得了该方程的孤波解：且由孤波解的形式可以看出,变系数影响孤波的振幅及波速。     

正交各向异性空心圆柱体的周向SH波

基于线性三维弹性理论,得到了正交各向异性管道中位移表示的周向波控制方程.波动方程中的轴向位移独立于其它两个方向.即波的传播可以分解为SH波和类Lamb波.通过贝塞尔函数求得了这个周向SH波频散方程.方程中决定周向SH波特性的弹性常数有两个,一个决定了波的频率,另一个决定了波速.最后分别讨论了两个弹性常数和波数变化对周向SH波位移模式的影响.     

覆盖层为功能梯度材料弹性半平面中的Love波

对均匀各向同性弹性半平面上覆盖一层功能梯度材料中存在的Love波的频散问题进行了研究,给出了Love波频散方程的一般形式。利用WKBJ近似理论,给出了功能梯度材料层的位移、应力近似解析解,导出了Love波WKBJ近似频散方程的一般形式。该文以功能梯度材料层的剪切弹性模量和质量密度沿厚度方向均为指数函数变化为例,进行了实例计算和分析,给出了频散曲线,讨论了Love波在功能梯度材料覆盖层弹性半平面中传播的一般性质。这些结论对无损检测和反问题分析方法的改进提供理论依据。     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

On a simple wave approximation

Summary An approximation (the linear version of Burgers' equation with appropriate initial data) to a simple wave initial value problem for a set of two linear coupled dissipative partial differential equations is discussed. It has been shown that for the class of square integrable initial functions of which the spectra (Fourier-transforms) have bounded support 2 the approximation is valid for some finite interval of time [0, T()]. For some finite timeT ₁ > T() the approximation may fail. However, fort, it is asymptotically valid again. For the class of initial conditions mentioned above expansions in series of the two solutions, which for every finite interval of time [0, ] are convergent, may be constructed.Detached by Philips Research Laboratories.     

Measurement of evanescent wave properties of a bulk acoustic wave resonator

Acoustic wave fields in a thin-film bulk acoustic wave resonator are studied using a heterodyne laser interferometer. The measurement area is extended outside the active electrode region of the resonator, so that wave fields in both the active and surrounding regions can be characterized. At frequencies at which the region surrounding the resonator does not support laterally propagating acoustic waves, the analysis of the measurement data shows exponentially decaying amplitude fields outside the active resonator area, as suggested by theory. The magnitude of the imaginary wave vectors is determined by fitting an exponential function to the measured amplitude data, and thereby the experimentally determined dispersion diagram is extended into the region of imaginary wave numbers.     

Longitudinal wave propagation in a micropolar wave guide of circular cross section

The problem of longitudinal vibrations of a long circular cylinder of linear micropolar elastic material was studied by Smith, Nowacki and Nowacki, and independtly by Willson [8]. Willson has studied only one aspect of the problem in the case of a thin long cylinder. In the following paper the frequency equation gets factorised. The frequency equation is studied in detail. The phase and group velocities are given in graphs.     

Break-through wave over a deformable bottom

A mathematical model of liquid flow over a bottom being washed out is suggested and investigated.     

Numerical simulation of a wave channel

The application of the Mixed Eulerian-Lagrangrian method to the simulation of transient free surface flows in the vicinity of a free surface piercing structure is considered. Particular attention is given to the validation of the numerical procedure.

Several applications are studied. Comparisons between the results of the numerical scheme and those of approximate theories or experiments are shown. They demonstrate the accuracy and versatility of the simulation that can be used as a “standard” to check the applicability of approximate theories.

The main limitation of the method is that it cannot account for viscous effects, in particular in the vicinity of the free surface. Approximate ways to simulate dissipative phenomena associated to breaking would be most useful.     

Fracture generated by a dilatational wave

A Griffith crack in a brittle elastic material is struck by a plane longitudinal stress wave whose wavefront is parallel to the crack. The paper investigates the conditions for crack propagation at an instantaneous velocity upon diffraction of the incident wave by the crack. The investigation consists of two parts. In the first part, the particle velocity and the normal stress are determined in the vicinity of the crack tip for diffraction of a transient wave of arbitrary shape by a crack which extends at a constant speed once the wavefront has impinged on the crack. In the second part of the investigation a balance of rate of energy is employed to determine that shape of the incident pulse which is compatible with instantaneous crack propagation. If energy is dissipated only as fracture energy, and if the specific fracture energy is a constant, crack propagation at an instantaneous velocity occurs only if the stress has a square-root singularity at the wavefront of the incident wave.

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Résumé Une fissure de Griffith dans un matériau élastique et fragile est entrainée par une onde de contrainte longitudinale plane, dont le front est parallèle au plan de la fissure.Le mèmoire analyse les conditions pour lesquelles la propagation d'une fissure peut s'effectuer à une vitesse instantanée sous l'effet de la diffraction, par la fissure, d'une onde incidente.La recherche comporte deux parties. Dans la première, on determine les conditions de vitesse et de contraintes normales au voisinage de l'extrémité d'une fissure, qui permettent la diffraction d'une onde transitoire, de forme arbitraire, par la fissure en extension à une vitesse constante, dès lots que le front d'onde incidente s'est heurté au plan de la fissure.Dans la seconde partie de la recherche, on recourt à une équation d'equilibre énergetique pour déterminer la forme de l'impulsion initiale qui est la plus compatible avec une propagation instantanée de la fissure. Si l'énergie se dissipe exclusivement sous forme d'energie de rupture, et si l'énergie spécifique de rupture est une constante, la propagation de la fissure à une vitesse instantanée ne se produit que pour autant que l'onde incidente ait un front correspondant à une singularité d'ordre 1/2 pour la contrainte.

     

High-power pumping wave influence on the volume spin wave propagation in a ferrite film

The influence of a high-power pumping wave on the propagation of backward volume spin waves in a longitudinally magnetized ferrite film was experimentally studied. Narrowing of the frequency band of propagation and the subsequent complete suppression of the volume spin waves with an increase of the pumping power were observed for the magnetic fields and frequencies allowing three-wave processes of the volume wave splitting.     

On a simple wave approximation to a non-linear problem

Summary The range of validity of a simple wave approximation to a non-linear set of two dissipative wave equations has been studied. The non-linear set is, when the dissipative terms are omitted, totally exceptional. It describes the propagation of longitudinal waves in an ideal elastic bar with some viscous stress. Upon a non-linear transformation, the equations become linear. These linear equations have been studied first. The results for the non-linear equations are then easily obtained by transforming backwards. It turns out that, if the non-linearity is small enough, they are similar to those obtained for the linear equations.Detached by Philips Research Laboratories     

On the range of validity of a simple wave approximation of a non-linear set of diffusive wave equations

Summary The set of wave equations considered is an intermediate approximation of the Navier-Stokes equations. A further approximation leads to Burgers' equation. The range of validity of this simple wave approximation has been studied. The method used is especially useful for small nonlinearity.