缺陷岩体中弹性波传播的多次散射效应分析

弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响,建立了双椭圆缺陷模型,基于Green函数基本解,采用边界积分的计算方法,得到了反映缺陷界面条件的刚度矩阵,分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明：与单椭圆缺陷模型相比,双缺陷的相互作用使得弹性波频散和衰减效应增强,定量给出了缺陷的影响区域,从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应,结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关,存在明确的定量关系。相应的数值模拟结果表明,弹性波和缺陷相互作用在缺陷界面上诱发界面波,该界面波也存在频率相关性,影响了弹性波宏观传播的频散和衰减特征。     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Simple waves in general elastic materials

The general theory of simple waves in Green-elastic and Cauchy-elastic materials is given. Such waves generate three-dimensional unsteady deformations. Boundary conditions producing such waves are derived together with conditions under which shocks occur. The theory is used to illustrate conditions behind acceleration fronts moving into homogeneously deformed regions and also the modes of propagation of fronts moving into a simple wave. The steady flow of an elastic material past a rigid developable surface is discussed. Simple waves which are principal waves are also discussed.     

Energy propagation in a deformed elastic material

Resultant material and spatial energy propagation vectors are defined for waves of small amplitude superposed on large static deformations in elastic materials of arbitrary symmetry. It is shown that the resultant material energy propagation vector is in the direction of the normal to the slowness surface and hence in that of the bicharacteristics.     

EFFECT OF FRACTIONAL ORDER PARAMETER ON THERMOELASTIC BEHAVIORS IN INFINITE ELASTIC MEDIUM WITH A CYLINDRICAL CAVITY

The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement,temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

On SH waves in a pre-stressed layered half-space for an incompressible elastic material

The propagation of Love waves along the boundary between a half-space and a layer of different pre-stressed material is examined for incompressible isotropic elastic materials. The secular equation is obtained for a general strain-energy function and analysed for particular deformations and materials. For the neo-Hookean strain-energy function, numerical results are obtained to illustrate the dependence of the wavespeed on the wave number and on the deformation.     

On diffraction of normally incident SH-waves by a line crack in micropolar elastic medium

The problem of diffraction of waves due to plane harmonic SH-waves incident normally on a line crack situated in an infinite micropolar elastic medium has been considered. The solution of the problem is obtained for both low and high frequencies for small coupling parameter. The stress-intensity factors in micropolar elastic medium have been derived. The stress-intensity factor for such problem in an elastic medium can be deduced from results obtained in this paper. It is also found that the effect of micropolarity in the propagation of waves is more significant in high frequencies than low frequencies.     

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.      

单向纤维增强复合材料中剪切波多重散射问题的复变函数法

基于弹性波的多体散射理论和复变函数方法,利用波函数展开法和保角映射方法,研究了任意形纤维增强复合材料中剪切波的传播。根据相应的边界条件确定弹性波模式系数。给出了复合材料中基体区和纤维核区的波场。作为算例,分析了相同入射频率,不同纤维核的尺寸和形状的情况下,弹性波的传播特性。通过分析发现,低频长波区,弹性波以近似正弦函数的形式传播,纤维核的尺寸和形状对波场影响不明显;随着频率的增加,影响变得明显,大于一定的频率,纤维核的形状可明显地辨别出。最后对结果进行了分析讨论。     

The coupling between ocean waves and rectangular ice sheets

This paper describes a semi-analytic approach to problems involving rectangular elastic plates of shallow draft floating on water. Specifically, two problems are considered: the scattering of plane monochromatic incident waves by a single elastic plate and the propagation/attenuation of waves through a periodic rectangular arrangement of plates. The approach combines Fourier methods with Rayleigh–Ritz methods for free modes of rectangular plates which reduces each problem to an algebraic system of equations which are numerically accurate and efficient to compute. A selection of results are given to illustrate the work. The approach can be applied to many problems in hydroelasticity including the seakeeping of large flat-bottomed marine vessels, deflections in very large floating structures such as offshore airports and wave propagation through areas of broken sea ice.     

Investigations on flexural wave propagation of a periodic beam using multi-reflection method

The flexural wave propagation in a periodic beam with a propagating disturbance is studied by the use of the multi-reflection method. A propagating wave is incident upon a discontinuity and gives rise to transmitted and reflected waves. Here all of the transmitted and reflected waves of given flexural wave incident upon the beam at some specified location are found and superposed, and the method is extended to the case of incident evanescent wave. The results of incident waves at some location between discontinuities in a periodic beam are concerned. The relation between the wave-field of incident waves and the wave-field of resulting waves on any segments is expressed. As an example, the application of the results to the analysis of a finite periodic beam with a propagating disturbance is then demonstrated. The influences of the number of cells on the energy associated with propagating waves are considered.     

The integral operator representation of propagation invariants for elastic waves in irregularly layered media

The reflection and transmission of elastic waves in irregularly layered media can be represented in terms of a set of propagation invariants for elastic wavefields. There are a number of such invariants depending on different integral operators acting on the displacement and traction fields. By exploiting different classes of invariants, representations for reflection and transmission operators at an irregular interface can be derived which are easier to compute than previous forms.

In a similar way, a simplified representation for the surface amplification factor for incident waves on a free surface can be constructed. This is particularly useful for calculating theoretical seismograms on the surface of a body.     

Propagation,reflection, and transmission of SH-waves in slightly compressible,finitely deformed elastic media

The propagation, reflection, and transmission of SH waves in slightly compressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer overlying a slightly compressible, finitely deformed half-space is derived. The present paper also deals with the reflection and refraction (transmission) phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suitable boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.     

Wave propagation at the boundary surface of elastic and initially stressed viscothermoelastic diffusion with voids media

The present investigation is concerned with the wave propagation at the boundary surface of elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. The longitudinal and transverse waves are incident obliquely at the plane interface between uniform elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. It is found that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency of incident wave and are influenced by the initial stress, diffusion, voids, elastic and viscoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form and computed numerically for a specific model. The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy at the interface is verified.     

Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation

This paper presents an analysis of wave propagation in a microstretch elastic medium in the context of the Green–Naghdi (GN) theory. Moreover, the dissipation and the influence of gravity on reflected waves have also been investigated. In the present article, five reflected waves propagate into the medium for any incident wave. The problem is solved numerically, and the amplitude ratios are graphically represented allowing for a comparison between the simple GN theory and the case in which one considers the effect of gravity on waves.     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.     

Linear water wave propagation through multiple floating elastic plates of variable properties

We investigate the problem of linear water wave propagation under a set of elastic plates of variable properties. The problem is two-dimensional, but we allow the waves to be incident from an angle. Since the properties of the elastic plates can be set arbitrarily, the solution method can also be applied to model regions of open water as well as elastic plates. We assume that the boundary conditions at the plate edges are the free boundary conditions, although the method could be extended straightforwardly to cover other possible boundary conditions. The solution method is based on an eigenfunction expansion under each elastic plate and on matching these expansions at each plate boundary. We choose the number of matching conditions so that we have fewer equations than unknowns. The extra equations are found by applying the free-edge boundary conditions. We show that our results agree with previous work and that they satisfy the energy balance condition. We also compare our results with a series of experiments using floating elastic plates, which were performed in a two-dimensional wave tank.     

Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Many composite materials, including biological tissues, are modeled as non-linear elastic materials reinforced with elastic fibers. In the current paper, the full set of dynamic equations for finite deformations of incompressible hyperelastic solids containing a single fiber family are considered. Finite-amplitude wave propagation ansätze compatible with the incompressibility condition are employed for a generic fiber family orientation. Corresponding non-linear and linear wave equations are derived. It is shown that for a certain class of constitutive relations, the fiber contribution vanishes when the displacement is independent of the fiber direction.Point symmetries of the derived wave models are classified with respect to the material parameters and the angle between the fibers and the wave propagation direction. For planar shear waves in materials with a strong fiber contribution, a special wave propagation direction is found for which the non-linear wave equations admit an additional symmetry group. Examples of exact time-dependent solutions are provided in several physical situations, including the evolution of pre-strained configurations and traveling waves.