基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

大延伸非均匀介质中地震波全弹性散射理论Ⅰ--弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.     

大延伸非均匀介质中地震波全弹性散射理论I-弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究。应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解。这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础。在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论。该理论可包容小尺度非均匀体,大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论。     

大延伸非均匀介质中地震波全弹性散射理论Ⅱ——弹性波多次散射理论

推出大延伸非均匀连续介质的弹性波能量传输表达式,并以此为基础建立并发展了相应的弹性动力学能量传递理论.构造了一个基于非均匀薄层或非均匀相屏单次散射迭代法的多次散射模型.该模型既适用于弱散射,也适用于强散射;既适用于普通散射,也适用于转换散射;尽管高频情况下只考虑普通散射及前向散射.应用该模型计算了弹性多次散射的能通量,处理了散射衰减问题.数值实验的结果表明,短周期地震图上的尾波主要来源于S波散射.     

非均匀损伤介质中波传播的数值解

对弹性波在非均匀损伤介质中的传播理论进行了研究。通过将非均匀损伤区域离散成分层均匀的区域,结合相邻区域交界面处的连续条件,推导出了以右行波、左行波为状态向量的波动方程和传递矩阵。对几种非均匀损伤介质中波的传播进行了实例数值计算,并和其解析解的结果进行了比较,讨论了弹性波在非均匀损伤介质中传播的一般性质。     

大延伸非均匀介质中地震波全弹性散射理论II-弹性波多次散射理论

推出大延伸非均匀连续介质的弹性波能量传输表达式,并以此为基础建立并发展了相应的弹性动力学能量传递理论.构造了一个基于非均匀薄层或非均匀相屏单次散射迭代法的多次散射模型.该模型既适用于弱散射,也适用于强散驰 既适用于普通散射,也适用于转换散射;尽管高频情况下只考虑普通散射及前向散射.应用该模型计算了弹性多次散射的能通量,处理了散射衰减问题。数值实验的结果表明,短周期地震图上的尾波主要来源于S波散射。     

含非完好界面粒子增强复合材料对弹性波的散射

采用波函数展开的方法研究了非完好界面条件下圆球形夹杂对弹性波的散射。以非完好界面的弹簧模型为基础，通过适当选取弹簧常数，研究了法向和切向界面参数对纵波和横波不同的散射效果。考虑了单个圆球夹杂的散射和颗粒增强复合材料中弹性波的多重散射，研究了复合材料中的有效波速和动态有效弹性常数。并针对金属基颗粒增强复合材料SiC-Al...     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

非均匀介质弹性波动方程的不规则网格有限差分方法

从弹性波动方程出发，提出了一种新的空间不规则网格有限差分方法，并用于求解非均匀各向异性介质中的弹性波正演问题。这种方法简单易行，对于复杂几何结构，例如低速层、套管井和非平面界面等，在较细的不规则网格上进行离散，计算时间和占用内存更少。与多重网格差分方法相比，该方法不需要粗、细网格之间的插值，所有网格差分计算在同一次空间迭代中完成。具有复杂几何交界面的模型计算，包括地下透镜体、套管井眼等，在确定弹性常数和密度后，用不规则网格的差分方法更易实现。该方法使用了Higdon吸收边界条件解决人工边界反射问题，引入了新的稳定性条件和网格频散条件，很好地消除了非物理散射波。理论模型的效值计算表明，该方法具有良好的稳定性和计算精度，在模拟非均匀介质弹性波传播时，比相同精度的规则网格有限差分方法计算速度更快。该方法易于推广到非结构网格和三维问题中。     

层状介质中多个非共面Griffith裂纹的弹性波散射问题研究

本文利用积分变换的方法,研究了层状介质中多个非共面Griffith裂纹的弹性波散射问题,导出了当入射波分别为P(SV)波及SH波时的散射对偶积分方程,并以双覆盖层半空间中的双裂纹为例,对反平面剪切波的散射场进行了求解和较为详尽的分析。最后通过数值计算,得到了许多有关的动力学特性曲线,从而揭示了层状介质中多裂纹弹性波散射问题中的某些内在规律。     

Cloaking of a circular cylindrical elastic inclusion from antiplane elastic waves and resonance effects

Cloaking of a circular cylindrical elastic inclusion embedded in a homogeneous linear isotropic elastic medium from antiplane elastic waves is studied. The transformation or change-of-variables method is used to determine the material properties of the cloak and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The large system of algebraic equations associated with this problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices. Numerical results for cloaking of an elastic inclusion and a rigid inclusion are compared with the case of a cavity. It is found that while the cloaking patterns for the three cases are similar, the major difference is that standing waves are generated in the elastic inclusion and the multilayered cloak cannot prevent the motion inside the elastic inclusion, even though the cloak seems nearly perfect. Waves can penetrate into and cause vibrations inside the elastic inclusion, where the amplitude of standing waves depend on the material properties of the inclusion but are very much reduced when compared to the case when there is no cloak. For a prescribed mass density, the displacements inside the elastic cylinder decrease as the shear modulus increases. Moreover, the cloaking of the elastic inclusion over a range of wavenumbers is also investigated. There is significant low frequency scattering even if the cloak consists of a large number of layers. When the wavenumber increases, the multilayered cloak is not effective if the cloak consists of an insufficient number of layers. Resonance effects that occur in cloaking of elastic inclusions are also discussed.     

Frequency dependence of elastic (SH-) wave velocity and attenuation in anisotropic two phase media

The propagation and attenuation of elastic waves in a random anisotropic two-phase medium is studied using statistical averaging procedures and a self-consistent multiple scattering theory. The specific geometry and orientation of the inhomogeneities (second phase) are incorporated into the formulation via the scattering matrix of each inhomogeneity. The anisotropy of the composite medium is due to the specific orientation of the non-symmetric inclusions. At low frequencies, analytical expressions are derived for the effective wave number in the average medium as a function of the geometry and the material properties and the angle of orientation of the inclusions. The results for the special cases of oriented cracks may find applications in geophysics and material science. The formulation is ideally suited for numerical computation at higher frequencies as evidenced by the results presented for composites reinforced by fibers of elliptical cross section.     

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。     

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.     

平面波对有部分脱胶衬砌的圆形孔洞的散射

将波函数展开法与奇异积分方程技术相结合研究了平面波对有部分脱胶衬砌的圆形孔洞的散射。将脱离区看作弧形裂纹并忽略裂纹表面的相互作用。将衬砌和基体中的波场展开成Fou-rier-Bessel级数,利用混合边界条件得到一组对偶级数方程组并进一步转化成Hilbert奇异积分方程。数值求解给出了脱离区大小和衬砌厚度对动应力强度因子(DSIF)和散射截面(SCS)的影响。结果显示由于脱胶,动应力强度因子和散射截面呈现明显的低频共振特性。     

Dispersion and attenuation in thermoelastic multisize particulate composites

This paper deals with the problem of multiple scattering by a random distribution of spherical solid particles in a solid. The material properties of both media are taken as thermoelastic. The radii of the inclusions may be different. The self-consistent method in its variant of the effective medium is used to find the dispersion and attenuation of quasi-elastic, quasi-thermal and shear waves. The single scattering problem required by this technique is solved approximately by means of the Galerkin method applied to an integral equation using the Green function. Numerical results display a characteristic resonance phenomena which appears in the interval where the results are approximately valid, that is, for very long waves down to wavelengths about twice the largest diameter of the spheres. Examples are shown, for composites with two sets of inclusions, which have either a very similar or dissimilar size. Comparisons are made with the elastic counterpart. Among the material properties, the mass density ratio, inclusion to matrix, seems to play an important and simple role. Frequency intervals are distinguished and shown to depend on that ratio, where the attenuation and dispersion of quasi-elastic and P-waves are either very close to each other or not at all. The same applies to shear waves in either composite. The mass density ratio also displays a simple monotonic decreasing behaviour as a function of the frequency at the first attenuation maximum and velocity minimum. These results may be of interest for the nondestructive testing characterization of particulate composites.     

用二维逆Born近似法对杆中圆形缺陷的反演

在三维弹性波散射问题的Born近似解基础上,进一步分析了在纵波入射条件下二维散射问题的Born近似解,对铝质长杆中的椭圆形空穴缺陷的散射场情况进行了对比分析;最后,提出了在低频下识别缺陷几何特征的二维逆Born近似法,并用此法对铝质长杆中的圆形空穴缺陷作了计算机模拟。