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.     

细观结构固体层中孤立波的传播及相互作用特性

利用直接微扰方法.确定了孤立波的放大或衰减与孤立波的初始幅度以及介质的结构参数之间的关系.然后利用线性化技术构造出一种二阶精度的稳定差分格式,并对孤立波在细观结构固体层中传播特性进行了数值模拟,特别对细观结构固体层中传播的不同幅度的孤立波的相互作用进行了详细的数值模拟,从而得到在适当条件下细观结构固体层中孤立波传播时即可以衰减、放大又可以稳定传播,且相互作用不影响这种传播特性.     

正交各向异性含液饱和多孔介质中应力波的传播

基于Biot的孔隙介质理论，研究了正交各向异性含液饱和多孔介质中应力波的传播特性．本文引入动态渗透率，导出了整个实频域内应力波传播的复特征方程及其解析解，给出了各种应力波成分的波速和衰减的解析表达武，计算了频散曲线和衰减曲线，并讨论了各类应力波之间的耦合关系及介质的各向异性对应力波传播的影响．     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

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。     

海洋地震工程流固耦合问题统一计算框架

海底地震动的模拟以及海洋工程结构的地震反应分析中,涉及到海水、饱和海床、弹性基岩、结构之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩和结构,分别考虑相互之间的耦合,十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后,以饱和多孔介质方程为基础,经集中质量有限元离散,考虑不同孔隙率的饱和多孔介质之间耦合的一般情形,建立了该耦合情形的求解方法.进一步论证了该一般情形的耦合计算方法可分别退化到流体与固体、流体与饱和多孔介质、固体与饱和多孔介质之间的耦合计算,从而将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.以P-SV波垂直入射时,半无限层状海水-饱和海床、海水-弹性基岩、海水-饱和海床-弹性基岩三种情形的动力分析为例,采用统一计算框架结合透射边界条件进行求解,并与传递矩阵方法得到的解进行对比,验证了该统一计算框架的有效性以及并行计算的可行性.      

水平成层介质中粘弹性波的计算

本文提出了一种水平成层介质中弹性波粘弹性波计算的新方法，分别研究了线源和点源作用情况。该方法适用于各种粘弹性模型，数值计算简单，可模拟任意震源及所产生的各种体波，面波，数值结果表明具有很高的计算精度和计算效率。     

水平成层介质中粘弹性波的计算

本文提出了一种水平成层介质中弹性波粘弹性波计算的新方法，分别研究了线源和点源作用情况。该方法适用于各种粘弹性模型，数值计算简单，可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度和计算效率。     

液固半无限空间低频点声源的地震波动

将舰船地震波简化为液固半无限空间低频点声源引起的地震波动,基于简正波理论,通过计算围道内的留数得到了位移势函数的表达式.分析了液体层内声传播损失和固体层表面的位移、加速度的频率特性曲线,为分析舰船地震波的形成机理以及波动特征提供了一定的理论基础.     

波在双孔隙与单孔隙介质界面上的反射与透射

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质 界面的反射和透射问题，在界面上假定裂缝孔隙流体相对于固体骨架的位移为零，推导了反 射系数和透射系数的计算公式，数值讨论了反射系数和透射系数随入射角和频率的变化关 系. 同时，讨论了双重孔隙介质中3种压缩波(P-1, P-2和P-3波)和一种剪切波(S波) 的频散和衰减特性.     

Uniqueness of Stoneley waves in pre-stressed incompressible elastic media

The main aim of this paper is to prove, for the general case, the uniqueness of Stoneley waves propagating along the bonded interface of two pre-stressed incompressible elastic half-spaces. In order to do that the authors have used the complex function method. By this approach, it is shown that the secular equation of Stoneley waves in pre-stressed incompressible elastic half-spaces has at most one solution in the complex plane. This says that if a Stoneley wave exists, then it is unique.     

Secular Equations for Rayleigh and Stoneley Waves in?Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

The Stroh formalism is employed to study Rayleigh and Stoneley waves in exponentially graded elastic materials of general anisotropy under the influence of gravity. The 6×6 fundamental matrix N is no longer real. Nevertheless the coefficients of the sextic equation for the Stroh eigenvalue p are real. The orthogonality and closure relations are derived. Also derived are three Barnett-Lothe tensors. They are not necessarily real. Secular equations for Rayleigh and Stoneley wave speeds are presented. Explicit secular equations are obtained when the materials are orthotropic. In the literature, the secular equations for Stoneley waves in orthotropic materials are obtained without using the Stroh formalism. As a result, it requires computation of a 4×4 determinant. The secular equation presented here requires computation of a 2×2 determinant, and hence is fully explicit. A Rayleigh or Stoneley wave exists in the exponentially graded material under the influence of gravity if the wave can propagate in the homogeneous material without the influence of gravity. As the wave number k????, the Rayleigh or Stoneley wave speed approaches the speed for the homogeneous material.     

On formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two elastic half-spaces

Formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two isotropic elastic half-spaces are derived using the complex function method. The derivation also shows that if a Stoneley wave exists, then it is unique. By using the obtained formulas, we can easily reproduce the numerical results previously obtained by Murty [G. S. Murty, Phys. Earth Planet. Interiors 11 (1975), 65–79.] by directly solving the secular equation.     

Surface waves at the interface between an inviscid fluid and a dipolar gradient solid

This paper is about the dispersion analysis of surface waves propagating at the interface between an inviscid fluid and a higher gradient homogeneous elastic solid modelled as a dipolar gradient continuum. In order to compare the results, a second gradient model is also evaluated. The analysis is carried out by finding the roots of the secular equation, and by carefully studying their physical meaning. As it is well known, higher gradient continua are dispersive, i.e. phase and group velocities are frequency dependent. As a consequence, the existence of surface waves will indeed depend on frequency. In order to investigate the behaviour of surface waves in this specific fluid–solid configuration, a complete dispersion analysis is performed, with a particular focus on the frequency range in which the phase velocity of shear waves is lower than the speed of waves of the fluid. Surface waves of the type Leaky Rayleigh and Scholte–Stoneley are observed in this frequency range. This work extends the knowledge on surface waves in the case of higher gradient solids and applications of these results can be found in the field of non-destructive damage evaluation in micro structured materials, composites, metamaterials and biological tissues.     

Elastic interface acoustic waves in twinned crystals

A new type of interface acoustic waves (IAW) is presented, for single-crystal orthotropic twins bonded symmetrically along a plane containing only one common crystallographic axis. The effective boundary conditions show that the waves are linearly polarized at the interface, either transversally or longitudinally. Then the secular equation is obtained in full analytical form using new relationships for the displacement–traction quadrivector at the interface. For gallium arsenide and for silicon, it is found that the IAWs with transverse (resp. longitudinal) polarization at the interface are of the Stoneley (resp. leaky) type.     

Rayleigh waves in orthotropic fluid-saturated porous media

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation.     

Computation of interface wave motions by reciprocity considerations

The current theoretical study deals with computation of Stoneley waves along a solid–solid interface and Scholte waves (also called Scholte-Gogoladze) along a solid–liquid interface by reciprocity considerations. Closed-form solutions of the wave motions generated by a time-harmonic line load applied in two bonded elastic half-spaces of different material properties are derived in a simple manner. In order to perform direct applications of reciprocity theorems, we introduce in this article new expressions for the displacements of free interface waves. Reciprocity relations between an actual state, interface wave motion generated by a time-harmonic line load, and a virtual state, an appropriately chosen free wave traveling along the interface, are derived. Scattered amplitudes of Stoneley waves and Scholte waves due to the load are thus computed. To show application of the obtained results, scattering of Stoneley wave by a delamination at the interface is then studied.     

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.     

On the existence of the low-frequency surface waves in a porous mediumSur l'existence des ondes de surface basse fréquence en milieux poreux

The existence and propagation of the surface waves at a vacuum/porous medium interface are investigated in the low frequency range. Two types of surface waves are shown to be possible: the generalized Rayleigh wave, which always exists, and the Stoneley wave, which exists for a limited range of wave numbers. Moreover, within the k-domain of existence the Stoneley wave cannot appear for certain values of elastic parameters of the solid phase. The bifurcation behavior of both the Stoneley wave and the Biot (P2) bulk wave, depending on the wave number, is revealed. The asymptotic formulas for the phase velocities of the surface waves are derived. To cite this article: I. Edelman, C. R. Mecanique 332 (2004).