共查询到20条相似文献，搜索用时 234 毫秒
1.
In this paper, the dynamic stress concentration and scattering of SH-waves by bi-naterial structures that possess an interface elliptic cavity are investigated. First, by using the complex function method, the Green‘s function is constructed. This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface. Then, the problem is divided into an upper and lower half space along the horizontal interface, regarded as a harmony model. In order to satisfythe integral continuity condition,the unknown anti-plane forces are applied to the interface. The integral equations with unknown forces can be established through the continuity condition, and after transformation, the algebraic equations are solved numerically. Finally, the distribution of the dynamic stress concentration factor (DSCF) around the elliptic cavity is given and the effect of different parameters on DSCF is discussed. 相似文献
2.
V. N. Krizskii 《Izvestiya Physics of the Solid Earth》2009,45(10):861-873
Recurrent algorithms for solving 3D direct problems on the distribution of geophysical fields in the piecewise-homogeneous
media are built, based on methods of integral transforms, integral representations, and integral equations. The algorithms
allow the recalculation of Green’s functions of one medium into Green’s function of another medium. The computational procedure
is applicable to problems with equations of elliptic, parabolic, hyperbolic, and mixed types. The algorithms can be split
and implemented on computing clusters and multiprocessor complexes. Inverse problems and algorithms of searching for boundaries
of piecewise-homogeneous media as extremals of the Tikhonov regulating functional, approximated by the spline functions, are
formulated. 相似文献
3.
在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件. 相似文献
4.
本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式. 相似文献
5.
In this work, a hybrid boundary integral equation method (BIEM) is developed, based on both displacement and hypersingular traction formulations, for the analysis of time-harmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography and under plane strain conditions. Specifically, the displacement-based BIEM is used for a multi-layered deposit with interface cracks, while the regularized, traction-based BIEM is used when internal cracks are present within the layers. The standard uni-dimensional boundary element with parabolic shape functions is employed for discretizing the free surface and the layer interfaces, while special discontinuous boundary elements are placed near the crack tips to model the asymptotic behaviour of both displacements and tractions. This formulation yields displacement amplitudes and phase angles on the free surface of a geological deposit, as well as stress intensity factors near the tips of the cracks. Finally, in the companion paper, numerical results are presented which show that both scattered wave and stress concentration fields are sensitive to the incidence seismic wave parameters and to specific site conditions such as surface topography, layering, the presence of cracks and crack interaction. 相似文献
6.
Summary Three dimensional magneto-elastic equations pertaining to the problem of propagation of axial Rayleigh waves on the surface of elastic cylinder of isotropic material have been solved. Two cases have been considered — first, when the density varies linearly and second, when it varies inversely as the radius vector and frequency equations for both the cases have been obtained. 相似文献
7.
确认旋转中心是工业CT系统必然遇到的问题。本文提出对薄圆筒模体的切片图像自动识别,通过随机Hough变换识别薄圆筒模体的圆心位置和半径,从而计算出当前圆心与实际圆心的差别,据此可以计算出需要矫正的尺寸,减少确认旋转中心的复杂度并增加可靠性。 相似文献
8.
用布希涅斯克定义的弹性半空间内的垂直位移包括两项积分,除了积分号前面系数的差别之外,第一项积分是单层位势而第二项积分为双层位势。若扁壳基础是正高斯曲率的几何曲面,则壳底与半空间表面间的挤压强度就是半空间表面作用的分布垂直荷载。当越过边界时,双层势位的函数值和单层势位的法向导数值发生跳跃。利用这些性质,本文得出布希涅斯克积分的反演公式,从而避开要求解偏微分—积分方程组的巨大数学困难而易于得出解析解。以椭园抛物面扁壳为例说明本文方法的应用。 相似文献
9.
Boris Gurevich Miroslav Brajanovski Robert J. Galvin Tobias M. Müller Julianna Toms-Stewart 《Geophysical Prospecting》2009,57(2):225-237
Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models. 相似文献
10.
O. V. Mingalev I. V. Mingalev V. S. Mingalev M. L. Khodachenko 《Geomagnetism and Aeronomy》2009,49(5):574-581
The problem of a smooth field configuration, which should be an initial configuration in modeling (using the method of coarse particles) the problem of a stationary solar wind flow around a magnetic cloud in the case of a spatially two-dimensional statement (when a magnetic cloud is considered as a force-free magnetic cylinder with a finite radius) is considered. It has been indicated that such a statement is possible only when the magnetic field in the solar wind is parallel to the cylinder axis. The method for finding the magnetic field of a force-free cylinder with a finite radius, when some field component is specified and another component is determined based on this one (which makes it possible to construct fields with preassigned properties), has been proposed. The variant for constructing the initial field configuration in the transition region around a cylinder has been proposed. This variant makes it possible to gradually pass from homogeneous crossed fields in the solar wind to a force-free magnetic and zero electric fields within a cylinder, an electric field being potential and orthogonal to a magnetic field (in the reference system related to a magnetic cloud). 相似文献
11.
We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270–8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range. 相似文献
12.
ＳｔａｔｉｃｓｏｌｕｔｉｏｎｏｆａｃｒａｃｋｄｅｇｅｎｅｒａｔｅｄｆｒｏｍｄｙｎａｍｉｃｓｏｌｕｔｉｏｎｏｆａｐｒｏｐａｇａｔｉｎｇｃｒａｃｋＳｈｉ－ＹｕＬＩ（李世愚）ａｎｄＹｕｎ－ＴａｉＣＨＥＮ（陈运泰）（ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｐｈｙｓｉｃｓ... 相似文献
13.
E.H. ELORANTA 《Geophysical Prospecting》1986,34(6):856-872
An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the ‘second kind’ developed for the potential of the electric field. In this method the discontinuity-surfaces of electrical conductivity are divided into ‘sub-areas’ that are so small that the value of their potential can be regarded as constant. The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-a-la-masse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite. 相似文献
14.
Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation 总被引：1，自引：0，他引：1
A. Rodríguez-Castellanos F. Luzn F.J. Snchez-Sesma 《Soil Dynamics and Earthquake Engineering》2005,25(11):827-837
The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks. 相似文献
15.
16.
Yang-De Feng Yue-Sheng Wang Zi-Mao Zhang 《Soil Dynamics and Earthquake Engineering》2003,23(4):303-311
A 2D time domain boundary element method (BEM) is developed to study the dynamic response of a cylinder embedded in soil. The interface is assumed in contact with Coulomb friction. For the incident wave strong enough, local slip may occur along the interface. We suppose a pressure enough high is applied on the interface so that separation is impossible. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The nonlinear nature of the system is discussed. 相似文献
17.
G. S. Murty 《Pure and Applied Geophysics》1971,90(1):96-108
Summary An infinite cylinder with a small ridge on the surface parallel to the axis is assumed to be excited by an embedded periodic line source radiating compressional waves. The line source is also assumed to lie parallel to the axis, and the frequency of radiation is small enough so that the corresponding wavelength is large compared to the dimension of the ridge on the surface of the cylinder. Considering the effect of the ridge as a small perturbation, the wave equations are solved and the amplitudes of the potential fields are expressed in terms of a set of inhomogeneous algebraic equations in which the solution of the problem without the ridge supplies the source term for the first order perturbation in potential fields. 相似文献
18.
在隧道的施工和运营中,隧道衬砌不可避免会产生裂纹。裂纹和地震荷载的相互作用将加剧隧道的破坏,因此研究带裂纹隧道衬砌地震荷载作用下的破坏具有重要的意义。为了证明本文二维有限元数值模拟计算结果的正确性,首先用相互作用积分的方法计算动载作用下的静态裂纹,并与解析解进行比对,发现二者的吻合性很好。计算结果表明相互作用积分法可以用来精确地计算动载作用下带裂纹结构的动应力强度因子。用这种经过验证的方法来计算带裂纹重载铁路隧道衬砌的动应力强度因子和动承载力安全系数,可以看出在地震荷载作用下,I型裂纹的动应力强度因子在隧道结构的安全中起控制作用。当裂纹的长度大于某特定值时,隧道处于很危险的状态。 相似文献
19.
Ursula Iturrarn-Viveros Francisco J. Snchez-Sesma Francisco Luzn 《Journal of Applied Geophysics》2008,64(3-4):70-82
Numerical modelling techniques are now becoming common for understanding the complicated nature of seismic wave propagation in fractured rock. Here the Indirect Boundary Element Method (IBEM) is applied to study scattering of elastic waves by cracks. The problem addressed in this paper is the diffraction of P and S waves by open 3-D cracks of arbitrary shape embedded in a homogeneous isotropic medium. The IBEM yields the value of the jump of displacements between opposite surfaces of the crack, often called Crack Opening Displacement (COD). This is used to evaluate the solution away from the crack. We use a multi-regional approach which consists of splitting a surface S into two identical surfaces S+ and S− chosen such that the crack lies at the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain open cracks can be rigorously solved. In order to validate the method, we compare results of displacements of a penny-shaped crack for a vertical incident P-wave with the classic results by Mal (1970) obtaining excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P or S waves upon cracks with various shapes are depicted and the salient aspects of the method are also discussed. Both frequency and time-domain results are included. 相似文献
20.
A half-space containing horizontally multilayered regions of different transversely isotropic elastic materials as well as a homogeneous half-space as the lowest layer is considered such that the axes of material symmetries of different layers and the lowest half-space to be as depth-wise. A rigid circular disc rested on the free surface of the whole half-space is considered to be under a forced either vertical or horizontal vibration of constant amplitudes. Because of the involved integral transforms, the mixed boundary value problems due to mixed condition at the surface of the half-space are changed to some dual integral equations, which are reduced to Fredholm integral equations of second kind. With the help of contour integration, the governing Fredholm integral equations are numerically solved. Some numerical evaluations are given for different combinations of transversely isotropic layers to show the effect of degree of anisotropy of different layers on the response of the inhomogeneous half-space. 相似文献