共查询到20条相似文献，搜索用时 15 毫秒
1.
散射问题中柱面坐标波函数的全域变换公式 总被引：1，自引：0，他引：1
袁晓铭 《地震工程与工程振动》2010,30(4)
为满足偏心源和多体散射理论研究发展的需求,阐明了柱面坐标下波函数变换的基本类型,指出了现有变换公式的局限性,提出了全域变换公式,给出了应用实例并讨论了应用前景。研究表明,不同柱面坐标下波函数变换可以分为内域和外域两种基本类型,现有Graf加法公式仅适用于内域变换问题。提出的新公式突破了现有公式的限制,可完成弹性波散射问题中不同圆柱坐标系下波函数全空间域上的变换。应用新公式,构造了圆形空穴的外线源散射和内线源散射的解答,通过实例与大圆弧近似方法进行了对比,表明了新公式的优势和有效性。波函数变换基本类型的划分、全域变换概念的引入和公式构建的原理具有普适性,可以推广到其它坐标系下波函数的坐标变换公式的建立中。 相似文献
2.
Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution 总被引：2，自引：1，他引：1
This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering. 相似文献
3.
The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating. 相似文献
4.
任意圆弧形凸起地形对平面SH波的散射 总被引：22，自引：10，他引：22
本文采用波函数展开方法提出弹性半空间表面一任意圆弧形凸起边界对平面ＳＨ波二维散射的封闭级数解答，利用引入的辅助函数和推广的外域型Ｇｒａｆ加法公式将解答归结为一代无穷代数方程组的求解，解答的数值结果可由无穷方程的截断计算得出，文中从级数项数增加时计算结果的收敛以及边界条件的收敛满足两方面检验了截断计算的精度，并指出了位移解答的收敛速度与主要参数之间的关系，同时，对凸起角点的应力奇异性及其对解答精度的 相似文献
5.
圆弧状凹陷地形在平面SH波入射下的动力响应：高频解答 总被引：1，自引：0，他引：1
利用波函数的Fourier-Bessel级数展开法和外域型Graf加法公式,推导了圆弧状凹陷地形对平面SH波二维散射问题的解析解。与现有其他解析解不同的是,该解析解的获得无须求解线性方程组,从而避免了高频波入射下方程组系数矩阵可能出现的病态问题。因此,既使在入射波频率很高的情况下,该解析解也能够收敛。利用该解,在一个非常宽的频带范围内讨论了凹陷地形的几何形状对地面运动的影响。 相似文献
6.
Seyyed M. Hasheminejad Reza Avazmohammadi 《Soil Dynamics and Earthquake Engineering》2007,27(1):29-41
This study investigates the dynamic interaction of time harmonic plane waves with a pair of parallel circular cylindrical cavities of infinite length buried in a boundless porous elastic fluid-saturated medium. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two empty cavities are insonified by a fast compressional or a shear wave at end-on incidence. The basic dynamic field quantities such as the hoop stress amplitude and the radial displacement of the elastic frame are evaluated and discussed for representative values of the parameters characterizing the system. The effects of the proximity of the two cavities, the incident wave frequency and type are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. Limiting case involving two empty cylindrical cavities in an elastic solid is considered and excellent agreement with a well-known solution is established. 相似文献
7.
Gin-Show Liou 《地震工程与结构动力学》1991,20(12):1115-1125
Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed. 相似文献
8.
Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves 总被引：2，自引：0，他引：2
A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical hill of circular-arc cross-section in a half-space is presented using the wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations, using the auxiliary functions and the exterior region form of the Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results and by the extent to which the numerical results fit the exact boundary conditions with increasing the truncation order. The numerical results for some typical cases are then presented for checking accuracies of various numerical methods. The effects of the height-to-width ratio of the hill on surface ground motion are finally illustrated. 相似文献
9.
A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth-to-width ratio of the alluvial valley on surface ground motion are finally illustrated. 相似文献
10.
A numerical scheme is developed in the paper for calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme, the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions with unknown coefficients are obtained by solving three-dimensional (3D) wave equations in cylindrical coordinates satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are also obtained by solving the same 3D wave equations satisfying the homogeneous boundary conditions and the prescribed boundary conditions. The prescribed conditions are the interaction tractions at the interfaces between embedded foundation and surrounding soil. The interaction tractions are assumed to be piecewise linear. The piecewise linear tractions at the bottom surface of foundation will be decomposed into a series of Bessel functions which can be easily fitted into the general solutions of wave equations in cylindrical coordinates. After all the analytic solutions with unknown coefficients for both interior and exterior domains are found, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions. 相似文献
11.
Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel 总被引：8，自引：3，他引：5
A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semicylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified. 相似文献
12.
采用复函数、多极坐标法研究了含有可移动圆柱形刚性夹杂的弹性半空间对SH波的散射问题。构造一个能自动满足含可移动刚性圆柱的弹性半空间自由表面上应力为零的边界条件的散射波,应用可移动圆柱形刚性夹杂的运动条件来确定该散射波。最终则可将求解问题归结为求解一个无穷代数方程组,采用截断有限项的方法对其进行求解。给出了地表位移幅值的数值结果,并讨论了各种参数对它的影响。 相似文献
13.
R. Ávila-Carrera F. J. Sánchez-Sesma James H. Spurlin C. Valle-Molina A. Rodríguez-Castellanos 《Pure and Applied Geophysics》2014,171(9):2209-2223
An analytic formulation to understand the scattering, diffraction and attenuation of elastic waves at the neighborhood of fluid filled wells is presented. An important, and not widely exploited, technique to carefully investigate the wave propagation in exploration wells is the logging of sonic waveforms. Fundamental decisions and production planning in petroleum reservoirs are made by interpretation of such recordings. Nowadays, geophysicists and engineers face problems related to the acquisition and interpretation under complex conditions associated with conducting open-hole measurements. A crucial problem that directly affects the response of sonic logs is the eccentricity of the measuring tool with respect to the center of the borehole. Even with the employment of centralizers, this simple variation, dramatically changes the physical conditions on the wave propagation around the well. Recent works in the numerical field reported advanced studies in modeling and simulation of acoustic wave propagation around wells, including complex heterogeneities and anisotropy. However, no analytical efforts have been made to formally understand the wireline sonic logging measurements acquired with borehole-eccentered tools. In this paper, the Graf’s addition theorem was used to describe monopole sources in terms of solutions of the wave equation. The formulation was developed from the three-dimensional discrete wave-number method in the frequency domain. The cylindrical Bessel functions of the third kind and order zero were re-derived to obtain a simplified set of equations projected into a bi-dimensional plane-space for displacements and stresses. This new and condensed analytic formulation allows the straightforward calculation of all converted modes and their visualization in the time domain via Fourier synthesis. The main aim was to obtain spectral surfaces of transfer functions and synthetic seismograms that might be useful to understand the wave motion produced by the eccentricity of the source and explain in detail the new arising borehole propagation modes. Finally, time histories and amplitude spectra for relevant examples are presented and the validation of time traces using the spectral element method is reported. 相似文献
14.
基于Biot饱和多孔介质动力学理论,运用Laplace变换和波函数展开法,根据饱和土体与衬砌结构交界面的连续条件和衬砌结构内边界上的应力自由条件,得到饱和土中深埋圆柱形衬砌洞室对瞬态平面P波和SV波散射问题的解答,该解答可以退化成为饱和土中深埋圆柱形空穴或弹性夹塞物的情形,并很容易转换成为对稳态波散射的解.通过与已有的相关问题的解析解答进行对比,验证了该解答的正确性.同时利用Laplace逆变换的数值方法,给出了饱和土和衬砌中应力和位移场在时域内的数值解,通过算例,分析了衬砌厚度、刚度对衬砌内边界处应力集中因子的影响. 相似文献
15.
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
16.
17.
YANG LIU 《地震学报(英文版)》2000,13(2):143-150
When there exists anisotropy in underground media, elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media, four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed. 相似文献
18.
Three-dimensional time-harmonic Green's functions of saturated soil under buried loading 总被引：3，自引：0，他引：3
Three-dimensional time-harmonic response of a poroelastic half space subjected to an arbitrary buried loading is investigated. The analysis starts with the field equations in cylindrical coordinates based on Biot's general theory of poroelasticity. General solutions for the displacements are first derived using the Fourier expansions and Hankel integral transform with respect to the circumferential and radial coordinates, respectively. The transformed-domain solutions are obtained in explicit form. The physical-domain displacements and stress components are then obtained numerically by inverse integral transform. Comparisons illustrating the accuracy of the developed approach are made with existing solutions for an elastic half space, which is reduced directly from the general solution developed in the paper. Numerical results are presented for the displacements of a saturated soil subjected to a horizontal internal excitation. 相似文献
19.
V. M. Pavlov 《Izvestiya Physics of the Solid Earth》2017,53(4):556-564
The problem of calculating complete synthetic seismograms from a point dipole with an arbitrary seismic moment tensor in a plane parallel medium composed of homogeneous elastic isotropic layers is considered. It is established that the solutions of the system of ordinary differential equations for the motion–stress vector have a reciprocity property, which allows obtaining a compact formula for the derivative of the motion vector with respect to the source depth. The reciprocity theorem for Green’s functions with respect to the interchange of the source and receiver is obtained for a medium with cylindrical boundary. The differentiation of Green’s functions with respect to the coordinates of the source leads to the same calculation formulas as the algorithm developed in the previous work (Pavlov, 2013). A new algorithm appears when the derivatives with respect to the horizontal coordinates of the source is replaced by the derivatives with respect to the horizontal coordinates of the receiver (with the minus sign). This algorithm is more transparent, compact, and economic than the previous one. It requires calculating the wavenumbers associated with Bessel function’s roots of order 0 and order 1, whereas the previous algorithm additionally requires the second order roots. 相似文献
20.
A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases. 相似文献