各向异性体内多个夹杂对反平面波的散射

本文导出了各向异性介质反平面剪切运动的基本解。在此基础上引用等效体力及二维亥维赛函数建立了内含多个任意形状夹杂(空洞)时散射位移场的积分方程。针对两个异质物情形运用Born近似理论讨论了散射远场。同时定义和推导了微分横截线,并给出了计算实例。     

非均匀介质体中的缺陷响应研究

由于粗颗粒界面的散射作用,所以在考虑了超声波在非均匀介质体中传播时的衰减以及相速度的频散特性的基础上,用MGB模型表示了入射超声波波束,对非均匀介质固体中的缺陷响应进行了研究。分析了不同尺寸的方形孔缺陷由于压电超声传感器距离其位置的不同对接收到回波信号的影响,同时研究了由于粗颗粒平均尺寸的变化对接收回波信号的影响;并给出了不同颗粒直径尺寸的变化对回波信号影响的实验研究结果。研究结果表明:Born近似方法对弱散射体的散射作用下的预测效果较好,但在强散射体作用下不能使用这种方法预测;实验的结果和理论的预测结果基本一致。     

用电网模型研究二相二维非定常渗流的一种近似方法

二相非定常渗流理论近年来得到了很大的发展。在忽略毛细管压力情况下的一维问题,原则上都已能解决。对二维问题,由于在数学上存在困难,目前还没有得到分析解。文献[3]作了在数字电子计算机上直接求二相二维问题的数值解的尝试。文献[4]在渗流过程中流管形状不变化的假设下提出了一个解决二相二维非定常渗流的近似方法,但是,这个假设只是在特定的条件下才适用,在一般情况下,流管的形状却可能随时间显著地变化。本文把已有的二相一维渗流理论和电模拟方法结合起来,提出了一个在理论上较严格、在实用上也可行的研究二相非定常渗流二维问题的近似方法。     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法，对无限大含孔曲板弹性波散射及动应力问题进行了分析研究，将经典薄板弯曲波动问题的分析解作为本问题的主项，给出了在稳态波下孔洞附近散射波的零阶渐近解。建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法，利用积分方程法可获得问题的近似分析解。并给出了无限大曲板圆孔附近动应力集中系数的数值结果，且对计算结果进行了分析与讨论。     

预扭转钨合金杆弹侵彻钢靶的数值模拟

在实验的基础上 ,对预扭转钨合金长杆弹提出了一个唯象的本构模型和破坏准则 ,并针对预扭转钨合金长杆弹侵彻厚钢靶进行二维有限元计算 ,得到了侵彻过程中的主要物理图象和曲线 ,进而对计算结果进行了分析讨论。计算结果表明 ,侵彻过程中的主要物理数据与实验测量结果基本一致。     

有限散射信号下二维缺陷形状识别的罚函数方法

研究在有限照射角度和频带宽度下二维缺陷的形状识别问题。首先,通过引进介质参数扰动函数,建立介质参数扰动函数和弹性波散射场之间的非线性关系,并将所关心的缺陷的形状识别问题转化为关于扰动函数的反演;然后,利用变分技术和优化方法求解,为了弥补散射数据的不足,在总的目标函数中,采用附加度量函数作为罚函数;最后,对后场散射远场测量时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别,表明了;表明了罚函数法的有效性。     

复数矢径虚拟边界谱方法在二维空穴声辐射和散射问题中的应用

基于复数矢径虚拟边界积分法,通过将虚拟积分曲线上的未知源强密度函数用Fourier级数展开,同时借助快速数值Fourier变换计算程序,提出了一种求解二维任意形状空穴声辐射和散射问题的复数矢径虚拟边界谱方法．该方法具有以下特点：(1)不存在奇异积分处理;(2)采用复数矢径虚拟边界积分方法,不仅保证了解的唯一性,而且由于虚拟源强密度函数采用Fourier级数展开,克服了用单元离散方法不能用于较高频率范围的缺点;(3)采用快速数值Fourier变换技术使计算效率大幅度提高．文中给出的计算结果表明：在求解任意形状二维空穴声辐射和散射问题上较通常采用的FEM、BEM和VBEM更为有效．     

“具有轴对称几何缺陷圆柱壳的静力分析”中的疑问

<正> 1.文献[1]中的可疑结论文献[1]利用小参数展开的方法,对具有轴对称几何缺陷圆柱壳进行了静力分析.这个想法很好.但是,该文却得出了一个奇怪的结论:“通过对零阶近似方程的讨论发现:缺陷壳形状函数的性态对零阶近似方程的性态影响很大.缺陷壳的零阶解不一定只反映完善壳的解.”,“按通常的想象,只要缺陷的幅度很小,那么缺陷的作用就应该只反映在一阶近似中,零阶近似解应该是完善柱壳的解,然而,这里却出现了违反直觉     

长杆高速侵彻的特征控制参量分析

针对理想长杆侵彻,通过对长杆侵彻Alekseevskii-Tate模型近似解进行分析,指出单一的无量纲速度衰减系数α（deceleration index）不足以完全表征长杆高速侵彻的准定常阶段。在此基础上,重新定义了2个无量纲特征参量:Johnson破坏数Φ_Jp和特征时间系数β,2个参量之间的关系为α=β/Φ_Jp。分析表明,Φ_Jp和β（或α和β）可实现对长杆高速侵彻准定常阶段的弹尾速度的完全表征;若再引入长杆弹相对临界速度v_c*,则可完全表征长杆侵彻的准定常阶段。此外,还证明了α能够判定侵彻过程偏离定常状态的程度,并指出通过确定Φ_Jp和β（或α和β）,可针对攻防需求对长杆弹侵彻设计进行指导。     

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.     

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals.

The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.     

Exterior reconstruction of a three dimensional scatterer

An explicit algorithm is constructed for the exterior Radon transform in three dimensions. An immediate consequence is the development of an exterior form for the inverse Born approximation. From this we discuss reconstruction from the time domain elastic wave scattering of a defect which is partly strongly scattering and partly weakly scattering.     

Elastodynamic inversion for shape reconstruction and type classification of flaws

Two linearized inverse scattering methods are investigated to reconstruct the shape of flaws in the elastic solid. One is based on the Born approximation and the other is based on the Kirchhoff approximation. The Born inversion is sensitive to the volumetric flaw but not to a crack-like flaw. On the other hand, the Kirchhoff inversion reacts to both boundaries of volumetric and crack-like flaws. The combined use of Born and Kirchhoff inversions leads to the classification method of flaw type. The performance of the proposed classification procedure is demonstrated by the numerical simulations and then by the experimental measurements for the two-dimensional models of flaws. An example for the three-dimensional shape reconstruction is also shown by using the numerically calculated backscattering amplitudes.     

A method of interface inversion in inhomogeneous media

First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of acoustic wave, are given. The project supported by the National Natural Science Foundation of China (No.19232031) and Chinese Education Commission Science Foundation     

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.     

Scattering attenuation of elastic waves due to low-contrast inclusions

Seismic scattering attenuation due to random lithospheric heterogeneity has been theoretically modeled using two approaches. One approach is the Born approximation theory (BAT), which is primarily used to treat weak continuous heterogeneity, and the other approach is the Foldy approximation theory (FAT), which deals with sparsely distributed discrete inclusions. We apply the BAT to elastic wave scattering due to inclusions having low contrast with the matrix, and compare the results with those predicted by the FAT. We thus investigate the valid wavenumber range of the BAT based on a reasonable assumption that the inclusions are distributed so sparsely that the FAT is effectively correct for any wavenumber. For simplicity, we consider a specific type of round inclusion, which is either two- or three-dimensional and has a two-valued wave velocity and/or mass density. Both theories are confirmed to yield essentially equivalent results below a certain wavenumber limit, depending on the contrast. This is known as the Rayleigh-Gans scattering regime. Beyond the wavenumber limit, the BAT overestimates the attenuation for common-mode scattering due to wave-velocity contrast, but remains valid with respect to the attenuation for scattering due to mass-density contrast and/or conversion scattering. These conclusions are independent of the spatial dimensions of the media as well as the modes of the elastic waves (P or S). Some advantages of the BAT over the FAT for application to low-contrast inclusions are discussed.     

The multi-parameter inversion of elastic wave in half-space

The multi-parameter inverse scattering problem of elastic wave equation with single frequency is investigated within Born approximation. By use of a wideband measuring scheme in which both transmitters and receivers scan over the half-space surface, the formula of the scattering field of elastic wave is derived. Four types of mode conversion of elastic wave (P→P,P→S,S→P,S→S) are separated from the scattering field. These components contain sufficient information for us to reconstruct the configurations of the density and Lamé parameters of the medium. The inverse formulas have the form of filtered back-propagation as in the acoustic diffraction tomography. Computer simulations are also obtained. Supported by Foundation of Ph.D Program of the State Education Commission of China.     

Determnation of elasticity constants for microheterogeneous media

The foundations of the theory of stochastically heterogeneous solids were laid a long time ago by Voigt [1J, who developed a method for determining the macroscopic parameters of polycrystalline materials by averaging the appropriate crystallite parameters with respect to orientations. Lifshits and Rozentzveig [2] showed that it was necessary to consider the correlation properties of the field in computations of macroscopic parameters. They calculated the first corrections for the averaged elastic constants of polycrystallites for the case of cubic and hexagonal crystallites. Assuming a low degree of heterogeneity, these authors used an approximation which corresponds to the Born approximation in the theory of scattering [3]. This method and its modifications were subsequently used by several authors for the computation of macroscopic parameters of polycrystallites [4– 6] and of other microheterogeneous materials [8].Moreover, the assumption of a low degree of heterogeneity of the properties is very restrictive. It precludes use of the method in the case of macroscopically isotropic polycrystallites formed from essentially anisotropic crystallite stochastically glass reinforced plastics, and similar microheterogeneous materials. This rises the problem of developing procedures that could be applied in cases of a high degree of heterogeneity. This problem presents serious analytical difficulties, however. It is sufficient to point out that even computation of the second approximation (i.e., the one following the Born approximation) has not yet been completed. Analogous problems in the classical and quantum theories of scattering are also, as a rule, considered only in the Born approximation. More complicated methods (e.g., Feyman's method) make possible only partial summation of infinite sequences in which the result is obtained. A method analogous to that of a selfconsistent field in quantum mechanics [9,10] is promising; however, this method is approximate and the magnitude of its error has not yet been estimated.The possibility of accurate determination of mascroscopic parameters for certain classes of microheterogeneous media was demostrated in [11], in which a detailed analysis was presented of parameters forming a second order tensor and characterizing the distribution in the medium of a certain scalar value obeying an equation similar to the steady-state heat-conduction equation. Accurate formulas for macroscopic coefficients of thermal conductivity (diffusion) were derived for the case of a strongly anisotropic medium and for that of a medium with a high degree of transverse isotropy. We made a comparison with various approximate methods and evaluated their degree of error. This article describes an accurate method of computing macroscopic elastic constants for polycrystalline media with a high degree of anisotropy; for the case of polycrystals with a cubic structure [12] the error margin and range of application of approximate methods are estimated.     

二维介质参数的大扰动反演方法

对非均匀介质参数反演问题进行了研究，并提出了用于反演二维介质参数的广义射线近似方法．利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Ｇｒｅｅｎ函数理论得到扰动参数比的积分方程．基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Ｆｒｅｄｈｏｌｍ积分方程．利用积分变换方法得到二维介质的介质参数函数，从而得到介质参数，在Ｂｏｒｎ近似方法中，反演的介质参数扰动不能超过２０％，但是在本文中介绍的方法能够有效地反演其扰动比不超过５０％的变化情况