非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内，通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法，给出了一种计算非均匀吸收同中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型，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。     

各向异性层状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质位移位，应力传播矩阵，给出了直角坐标系各向异性层状介质中弹性波的传播矩阵解法，该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题，数值结果表明，计算效率，准确性及稳定性均较好。     

粘弹性垂直向渐变水平复盖层对P-SV波引起的地面运动的影响

本文用幂级数形式的广义传播矩阵计算了粘弹性垂直渐变介质对P-SV波的响应。文中给出了自由表面位移响应表达式,並作了数值计算,还利用超声物理摸型实验作了对比研究,得到一些有价值的结果。     

各向异性展状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质内位移、应力传递矩阵，给出了直角坐标系下各向异性层状介质中弹性波的传播矩阵解法．该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题．数值结果表明，计算效率、准确性及稳定性均较好．     

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。     

分数阶粘弹性地基上薄板波动和振动特性分析

本文研究了粘弹性地基上薄板的波动和振动问题．主要讨论了基于分数导数理论的粘弹性地基模型上 薄板弯曲波的传播特性以及固有频率对地基的依赖特性．推导了三种经典粘弹性地基模型的复模量．并利用分 数导数的性质得到分数阶粘弹性地基上 Kirchhoff板中弯曲波的传播速度、衰减系数以及自由振动的复固有频 率．数值算例表明粘弹性地基对弯曲波传播特性存在显著影响,不同粘弹性模型所对应的色散和衰减特性也存 在较大差别．分数阶导数可以实现相邻整数阶导数之间的光滑过渡．利用分数导数的本构关系可以更加真实地 描述粘弹性地基的历史依赖行为,更准确地表现出粘弹性地基板中弯曲波的色散和衰减特性．     

弹性波混合差分解法的透射边界条件

文中将基于离散应力、速度混合变量弹性波方程的各种数值解法统称为混合差分法，该文研究这类解法中人工边界的透射边界条件。基于波动沿边界法向传播的特征量分析，给出了横观各向同性介质中复杂形状边界的透射条件。该文是一种局部透射条件，所需计算量极小。文中将此方法与交错网格差分解法结合并应用于横观各向同性介质弹性波计算。数值算例及反射系数分析表明，该方法很好地消除了人工边界对来波的反射。     

Laplace变换法及其在粘弹性波中传播的应用

针对波传播分析理论的发展历程进行了简要的综述，详细介绍了几种处理粘弹性波传播问题的分析方法，重点讲解Laplace变换法以及Laplace变换在粘弹性波中的应用，对比分析几种方法在各自应用上的优劣，由于Laplace变换法能准确地描述应力波在任意时刻、任意点的波动情况，在处理大尺寸混凝土类构件中应力波传播问题时具有其独特的优势。     

一维格子结构动力分析的传递矩阵法

本文将传递矩阵法推广应用于分析一维格子结构的波传播和动力响应特性。一个格子结构的元件可分为主元件和次元件,传递矩阵沿主元件形成并考虑次元件的作用。文中通过例子说明形成一个周期单元传递矩阵的方法,指出利用传递矩阵计算无限或半无限长格子结构波传播的传播常数及有限长格子结构固有频率和频率响应函数的方法。作为数例,文中计算了一维平面格子结构的传播常数和频率响应函数。     

各向异性粘弹性多孔截止中平面波的传播

This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.     

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

The Christoffel equation is derived for the propagation of plane harmonic waves in a generalized thermoelastic anisotropic (GTA) medium. Solving this equation for velocities implies the propagation of four attenuating waves in the medium. The same Christoffel equation is solved into a polynomial equation of degree eight. The roots of this equation define the vertical slownesses of the eight attenuating waves existing at a boundary of the medium. Incidence of inhomogeneous waves is considered at the boundary of the medium. A finite non-dimensional parameter defines the inhomogeneity of incident wave and is used to calculate its (complex) slowness vector. The reflected attenuating waves are identified with the values of vertical slowness. Procedure is explained to calculate the slowness vectors of the waves reflected from the boundary of the medium. The slowness vectors are used, further, to calculate the phase velocities, phase directions, directions and amounts of attenuations of the reflected waves. Numerical examples are considered to analyze the variations of these propagation characteristics with the inhomogeneity and propagation direction of incident wave. Incidence of each of the four types of waves is considered. Numerical example is also considered to study the propagation and attenuation of inhomogeneous waves in the unbounded medium.     

The propagation of initially plane waves in nonhomogeneous viscoelastic media

In this study, the propagation of an initially plane wave in a linear isotropic nonhomogeneous viscoelastic medium, where the nonhomogeneity varies transversely to the direction of propagation, is investigated. For this purpose, first the propagation of waves in a linear isotropic viscoelastic medium of arbitrary inhomogeneity is studied by employing the notion of singular surfaces. The characteristic equation governing wave velocities, and the growth and decay equations describing the change of the strength of the discontinuity as the wave front moves are obtained.In the second part of this work, the propagation of initially plane waves is studied for three types of inhomogeneities by employing the findings established in the first part. The first kind of inhomogeneity considered is of axisymmetrical type where the wave propagation velocity depends on the radial coordinate only, increasing linearly up to a certain radial distance and remaining constant thereafter. The second kind is also axisymmetrical with a wave velocity distribution decreasing linearly till a given value of the radial coordinate. In the third one, the wave velocity is assumed to vary linearly over a given interval along a certain coordinate axis only, which is perpendicular to the direction of propagation, and remain constant outside. The ray and wave front analyses are carried out and the decay or growth of stress and velocity discontinuities are studied for each of the three cases.     

黏弹性固体中地下爆炸辐射地震波能量的演化

地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律,分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论,给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法,建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料,计算给出了地震波能量的传播特征,分析了地下爆炸辐射能量的传播衰减规律。结果表明:（1）在黏弹性介质中,某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中,某球面处流入的能量在几倍弹性半径外即可稳定到某一定值;（2）在某一固定的有限观测区域内,当观测时间足够长时,势能和耗散能均趋于某一定值,辐射动能趋于零;（3）当有限的观测区域能容纳一个完整波长的地震波时,地震波辐射动能的稳态值随波传播距离的增大而减小,总体上可以用指数函数和幂函数进行分段拟合。     

流体饱和标准线性粘弹性多孔介质中的平面波

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题．在固相骨架小变形的假定下,得到了粘弹性多孔介质中波动方程的一般解,讨论了弥散关系和波的衰减特性．结果表明：在流体饱和不可压粘弹性多孔介质中,仅存在一个耦合纵波和一个耦合横波,纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性．同时,研究了半空间自由边界上入射波(纵波、横波)的反射问题。得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果．     

Wave propagation through mangrove forests in the presence of a viscoelastic bed

The influence of viscoelastic ocean beds on the characteristics of surface waves passing through mangrove forests is analyzed under the assumption of linearized water wave theory in two dimensions. The trunks of the mangroves are assumed to be in the upper-layer inviscid fluid domain, whilst the roots are inside the viscoelastic bed. The associated equation of motion is obtained by coupling the Voigt’s model for flow within the viscoelastic medium with the equation of motion in the presence of mangroves. The modified dynamic conditions are coupled with the kinematic conditions to obtain the boundary condition at the free surface and the interface of the two fluids consisting of the upper layer inviscid fluid and the viscoelastic fluid bed. To understand the effects of bed viscosity as well as elasticity on energy dissipation, the complex dispersion relation associated with the plane progressive wave is derived and analyzed. Effect of physical parameters associated with mangroves and viscoelastic bed on wave motion in surface and internal modes are computed and analyzed to understand their roles in attenuating wave effects. The present model will be useful in the better understanding of wave propagation through mangroves in the coastal zone having muddy seabed.     

Random wave propagation in a viscoelastic layered half space

An extremely efficient and accurate solution method is presented for the propagation of stationary random waves in a viscoelastic, transversely isotropic and stratified half space. The efficiency and accuracy are obtained by using the pseudo excitation method (PEM) with the precise integration method (PIM). The solid is multi-layered and located above a semi-infinite space. The excitation sources form a random field which is stationary in the time domain. PEM is used to transform the random wave equation into deterministic equations. In the frequency-wavenumber domain, these equations are ordinary differential equations which can be solved precisely by using PIM. The power spectral densities (PSDs) and the variances of the ground responses can then be computed. The paper presents the full theory and gives results for instructive examples. The comparison between the analytical solutions and the numerical results confirms that the algorithm presented in this paper has exceptionally high precision. In addition, the numerical results presented show that: surface waves are very important for the wave propagation problem discussed; the ground displacement PSDs and variances are significant over bigger regions in the spatial domain when surface waves exist; and as the depth of the source increases the ground displacement PSDs decrease and the regions over which they have significant effect become progressively more restricted to low frequencies while becoming more widely distributed in the spatial domain.     

Inhomogeneous wave propagation in partially saturated soils

In the present study, inhomogeneous plane harmonic waves propagation in dissipative partially saturated soils are investigated. The analytical model for the dissipative partially saturated soils is solved in terms of Christoffel equations. These Christoffel equations yields the existence of four wave (three longitudinal and one shear) modes in partially saturated soils. Christoffel equations are further solved to determine the complex velocities and polarizations of four wave modes. Inhomogeneous propagation is considered through a particular specification of complex slowness vector. A finite non-dimensional inhomogeneity parameter is considered to represent the inhomogeneous nature of these four waves. Impact of tortuosity parameter on the movement of pore fluids is considered. Hence, the considered model is capable of describing the wave behavior at high as well as mid and low frequencies. Numerical example is considered to study the effects of inhomogeneity parameter, saturation of water, porosity, permeability, viscosity of fluid phase and wave frequency on the velocity and attenuation of four waves. It is observed that all the waves are dispersive in nature (i.e., frequency dependent).     

Application of asymptotic methods of the theory of nonlinear oscillations to the problem of wave propagation

The problem of the propagation of waves in an inhomogeneous medium is solved on the basis of the equation for a partial wave of the total field. After changing the independent variable x (the geometrical coordinate) to A(x) (the amplitude factor of a direct partial wave of the total field in the inhomogeneous medium) a modification of one of the asymptotic methods of the theory of nonlinear oscillations is applied.     

On wave propagation in inhomogeneous elastic media

Wave propagation in an inhomogeneous elastic rod or slab is considered. The governing equations are written in a matrix form and transformations are sought which reduce the system to a form associated with the wave equation. Integration of the system is then immediate. It is shown that such reduction may be achieved subject to a function involving the density and elastic parameters of the material adopting certain multi-parameter forms. These parameters are available for fitting to the behaviour of a variety of inhomogeneous elastic materials. A specific initial boundary value problem is solved by utilising the present method.