玄武岩中裂隙分布形式对声波传播的影响

复杂岩体含有大量的裂隙,这些裂隙尺寸及其分布形式等对弹性波传播都有很大的影响.本文加工了含单个裂隙、双裂隙和三个裂隙的玄武岩岩样单元对其进行组合,进行了25kHz、 50kHz、 400kHz、 600kHz和1000kHz 等5种频率的声波测试.通过考虑垂直或平行波传播方向的裂隙长度,来探索裂隙分布形式和不同裂隙长度对弹性波传播的影响,研究玄武岩的频散效应和波的衰减.结果表明:裂隙方向与波传播方向夹角对弹性波传播有很大的影响.当裂隙方向与波传播方向垂直时,散射效应最大;而当裂隙方向与波传播方向平行时,影响最小.上述结果可为理论模型和数值分析提供依据.     

Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

The work is devoted to the problem of plane monochromatic longitudinal wave propagation through a homogeneous elastic medium with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the calculation of the phase velocity and attenuation factor of the mean (coherent) wave field in the composite. The hypotheses of the method reduce the diffraction problem for many inclusions to a diffraction problem for one inclusion and, finally, allow for the derivation of the dispersion equation for the wave vector of the mean wave field in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. The long and short wave asymptotics of the solution of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies of the incident field that covers long, middle, and short wave regions of propagating waves. The phase velocities and attenuation factors of the mean wave field are calculated for various elastic properties, density, and volume concentrations of the inclusions. Comparisons of the predictions of the method with some experimental data are presented; possible errors of the method are indicated and discussed.     

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。     

Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach)

The work is dedicated to the problem of plane monochromatic shear wave propagation through elastic matrix composite materials with a homogeneous random set of spherical inclusions. The effective field method (EFM) and quasi-crystalline approximation are used for the calculation of phase velocity and attenuation factor of the mean wave field propagating through the composite. The version of the method developed in the work allows us to obtain the dispersion equation for the wave vector of the mean wave field that serves for all frequencies of the incident field, properties and volume concentrations of the inclusions. The long- and short-wave asymptotic solutions of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies that covers the long-, middle- and short-wave regions of the propagating waves. The phase velocities and attenuation factors of the mean wave field in the composites are analyzed for various elastic properties, density and volume concentrations of the inclusions. Comparisons of the predictions of the method with some numerical computation of the effective parameters of matrix composites are presented; possible errors in predictions of the velocities and attenuation factors of the mean wave field in the composites are indicated and discussed.     

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated. A part of this work has been performed in the Laboratoire Matériaux Endommagement Fiabilité of the Ecole Nationale Supérieure des Arts et Métiers de Bordeaux.     

Effective medium method in the problem of axial elastic shear wave propagation through fiber composites

The effective medium method (EMM) is applied to the solution of the problem of monochromatic elastic shear wave propagation through matrix composite materials reinforced with cylindrical unidirected fibers. The dispersion equations for the wave numbers of the mean wave field in such composites are derived using two different versions of the EMM. Asymptotic solutions of these equations in the long and short wave regions are found in closed analytical forms. Numerical solutions of the dispersion equations are constructed in a wide region of frequencies of the incident field that covers long, middle and short wave regions of the mean wave field. Velocities and attenuation factors of the mean wave fields in the composites obtained by different versions of the EMM are compared for various volume concentrations and properties of the inclusions. The main discrepancies in the predictions of different versions of the EMM are indicated, analyzed and discussed.     

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．     

高频纵向导波在钢杆中传播特性的研究

计算了钢杆中纵向轴对称导波模态的衰减频散曲线和群 速度频散曲线. 分析了1~3MHz范围内高频纵向轴对称超声导波在钢杆中的传播特 性. 理论分析表明，各高阶纵向模态都存在一个衰减最小值，在此衰减最小值所对应频率下 的高阶模态能传播较远距离，可用于钢杆导波检测. 建立实验系统，采用轴对称同端激 励接收的方法，根据第1次端面回波做出群速度和端面回波幅值随频率变化曲线，实验结 果与理论分析基本吻合. 表明考虑材料衰减特性的钢杆频散曲线可以作为实验指导依据.     

岩石对冲击波的非线性动态响应

对干燥、饱水、饱泵油大理岩和饱和砂岩进行了SHPB冲击压缩实验,得到了干燥岩石和饱和岩石的应力波衰减规律。在应力波传播过程中,其幅值有较大的衰减,干燥岩石的衰减最大,且孔隙度越大衰减越大,饱和岩石还存在较强的波弥散效应。在小于岩石屈服强度时,多次冲击加载下获得随冲击加载次数的增加,加载模量增大,残余应变减小的压实效应。这一结果可用于大型地震工程和防护工程的设计和建造。     

Ultrasonic attenuation in polycrystals using a self-consistent approach

The self-consistent method of averaging elastic moduli to define the effective medium of a polycrystal is used to investigate the dynamic problem of wave propagation. An alternative covariance tensor describing the elastic moduli fluctuations of the polycrystal containing self-consistent elastic properties is derived and found to be significantly smaller than the covariance tensor formed through traditional Voigt averaging. Attenuation curves are generated using the self-consistent elastic moduli and covariance tensors and these results are compared with previous Voigt-averaged estimates. The second-order polycrystalline dispersion relation for the self-consistent scheme is found for cases of low and high crystallite anisotropy. The attenuation coefficients and dispersion relations derived through the self-consistent scheme are considerably different than previous estimates. Experimentally measured longitudinal attenuation coefficients support the use of the self-consistent scheme for estimation of attenuation.     

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。     

Effect of a viscous liquid loading on Love wave propagation

This paper describes a theory of surface Love waves propagating in a layered elastic waveguide loaded on its surface by a viscous (Newtonian) liquid. An analytical expression for the complex dispersion equation of Love waves has been established. The real and imaginary parts of the complex dispersion equation were separated and resulting system of nonlinear algebraic equations was solved numerically. The influence of the viscosity of liquid on the dispersion curves of phase velocity, the wave attenuation and the distribution of the Love wave amplitude is analyzed numerically. The propagation loss is produced only by the viscosity of liquids. Elastic layered waveguide is assumed to be loss-less. The numerical solutions show the dependence of the phase velocity change, the wave attenuation and the wave amplitude distribution in terms of the liquid viscosity and the wave frequency. The results of the investigations are fundamental and can be applied in the design and development of liquid viscosity sensors and biosensors, in Non-Destructive Testing (NDT) of materials, in geophysics and seismology.     

粘弹性Hopkinson压杆中波的衰减和弥散

研究了线性粘弹性Hopkinson压杆中由于粘性效应和横向惯性效应引起的就力波衰减和弥散。导出计及横向惯性效应的线性粘弹性杆中纵波控制方程和应力解应变解，进而导出表征波衰竭和弥散性质的纵波传播系数的修正公式。这一修正公式计入粘性效应和几何效应，与Bacon公式相比，其形式简单，更便于在实验数据处理中应用。最后利用实验方法测定了有机玻璃杆的传播系数。     

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．     

G-type seismic waves in fibre reinforced media

This paper investigates the possibility of shear wave propagation along the plane surface in the interface of two different types of fibre reinforced media. The upper layer is fibre reinforced and the lower half-space is taken inhomogeneous fibre reinforced. Dispersion equation and condition for maximum energy flow near the surface are obtained in compact form. The dispersion equation coincides with that of Love wave for uniform media. Effect of reinforcement and inhomogeneity on phase and group velocity has been depicted by means of graphs. It is observed that inhomogeneity and reinforcement decreases the phase velocity and presence of reinforcement deviate the group velocity.     

Analysis of damped guided waves using the method of multiple scales

We analytically investigate the influence of damping on Lamb waves, which are a specific type of guided wave in two-dimensional plates. Considering material attenuation, we suppose that Lamé constants are complex numbers. This leads to the associated wavenumbers being complex, with the imaginary part of the wavenumber being associated with effect of attenuation of the guided wave. In this paper, we show how dispersion curves and attenuation coefficients can be obtained using the self-adjointness and the method of multiple scales (MMS), which is a type of perturbation method. Using the self-adjointness and the MMS, we can calculate the frequency- and wavenumber-dependent attenuation coefficients from the integral values and boundary values of a corresponding eigenfunction with respect to each propagation mode. This analytical method can yield not only dispersion curves but also mode-by-mode attenuation coefficients regardless of the numerical initial values, unlike numerical approaches using the Newton method. Thus, the proposed method can more easily calculate the attenuation coefficients with respect to a particular mode than conventional methods. Furthermore, the results obtained by proposed method were in good agreement with those obtained by the semi-analytical finite element (SAFE) method, which validates the proposed method.     

Wave dispersion in randomly layered materials

Wave scattering in materials composed of two kinds of alternating layers with different elastic properties and randomly distributed thicknesses has been modeled. The general form of the dispersion equation is derived for the unbounded layered medium. It defines two basic macroscopic characteristics of the scattered wave: phase velocity and attenuation, which are explicit functions of wave frequency and microscopic parameters of the system: acoustic properties of the layers and stochastic characteristics of their thickness distributions. The analytical expressions are derived for three special cases: for long waves; for a periodic medium composed of layers with constant thicknesses and for random medium with uniform distribution of layer thicknesses. Special attention is paid to the analysis of the frequency dependence of the wave parameters. It was shown that the predictions of the model for long waves and for periodic medium are compatible with the results obtained in the literature.Moreover, comparison of theoretical results for frequency dependent wave parameters with numerical simulations of pulse transmission through the slab of the randomly layered medium shows good qualitative and quantitative agreement in wide frequency range.     

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal(SH)wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder.The interface of the two media is assumed mechanically imperfect.For obtaining the dispersion relation,the mathematical formulation has been developed and solved by an analytical treatment.The effects of various parameters,i.e.,the thickness ratio,the imperfect interface,the initial stress,the reinforcement,and the piezoelectric and dielectric constants,on the dispersion curve are observed prominently.The dispersion curves for different modes have been also plotted.The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.     

梯度密度黏弹性材料的波传播研究

梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征,基于控制方程的Euler形式,利用Laplace变换,得到了这种材料中的波传播规律的一个理论公式;并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛（Ti-TiB₂）材料和碳纤维树脂材料,采用不同的叠合方向和方式,利用分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）加载装置进行了动态冲击实验,并用三波法对得到的实验结果进行处理。同时,采用数值Laplace逆变换方法,结合SHPB测得的入射波与透射波数据,使用推导的理论公式计算出理论解,并与实验结果进行了比较。结果表明:（1）梯度钛-硼化钛材料由于内界面和叠层界面的存在,表现出一定的黏性特性;单层Ti-TiB₂材料的计算结果和三波法分析得到的结果基本一致,双层Ti-TiB₂材料叠合后的计算结果与三波法分析结果存在一定的差异。（2）双层碳纤维树脂材料表现出较强的黏弹性特征,应力波的衰减幅度较大,三波法分析结果与该材料的冲击性能有较大的差异。由此可知,无论是细微观结构特征产生的黏性,还是材料本身的黏性,对材料动力学行为的影响都不可忽略。。     

Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein–Gulyaev wave is a shear-type surface acoustic wave and has the advantage of not radiating energy into the adjacent liquid. These features make the B–G wave sensitive to changes in both mechanical and electrical properties of the surrounding environment. The Bleustein–Gulyaev wave has been reported to be a good candidate for liquid sensing application. In this paper, we investigate the potential application of B–G wave in 6 mm crystals for liquid sensing. The explicit dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.