P波对具有不等深度凹陷地形的散射

采用曲线坐标的分析方法研究稳态Ｐ波对凹陷地形散射的边值问题。利用曲线坐标描述整个凹陷半空间，应用复变函数方法给出凹陷地形中波场解答的函数逼近序列。进一步将待解的问题转化成无穷代数方程组，利用正交展开得到问题的解答。研究表明：应用曲线坐标的方法研究Ｐ波对凹陷地形的散射是一个可行的新方法。     

位移阶跃SH波对半圆形凹陷地形的散射

本文利用积分变换和波函数展开方法求解位移阶跃的平面ＳＨ波对半圆形凹陷地形的散射问题，导出了散射位移场的解析表达式，，并给出了在凹陷地形表面上各点位移时程反应的数值结果。本文的结果可做为Ｄｕｈａｍｅｌ积分的影响系数求解一个随时间任意变化的平面ＳＨ波被半圆形凹陷地形散射的问题。     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分,基于土-结构相互作用SSI原理,建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度,解析求解各向异性介质自由场qP波波动,将两者代入控制方程,可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比,验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示,介质的各向异性改变了半圆形河谷散射位移的空间分布,增大了水平向位移的峰值;同时,介质的各向异性加剧了入射角对散射波场位移分布的影响。     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分，基于土-结构相互作用SSI原理，建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度，解析求解各向异性介质自由场qP波波动，将两者代入控制方程，可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比，验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示，介质的各向异性改变了半圆形河谷散射位移的空间分布，增大了水平向位移的峰值；同时，介质的各向异性加剧了入射角对散射波场位移分布的影响。     

SH波对浅埋圆形弹性夹杂附近任意三角形凸起地形的散射

利用"契合"的思想,给出了地下弹性夹杂与地面任意三角形凸起地形对SH波散射问题的解析解答。将整个求解区域分割成三部分,区域Ⅰ为带有半圆形弧底的三角形凸起,区域Ⅱ为含半圆形凹陷和浅埋孔洞的弹性半空间,区域Ⅲ为一圆柱形弹性体。在区域Ⅰ中构造满足三角形两斜边应力自由的驻波函数,在区域Ⅱ中构造出半圆形凹陷和浅埋孔洞的散射波,在区域Ⅲ内构造一驻波函数,使得圆柱边界应力不受约束;利用复平面下坐标移动,通过区域Ⅰ和区域Ⅱ以及区域Ⅱ和区域Ⅲ的两个"公共边界"位移应力连续条件,建立起求解该问题的无穷代数方程组,并截断有限项进行求解,最后通过具体算例及结果分析得出相应结论。     

浅埋圆形孔洞附近的半圆形凸起对SH波的散射

采用"契合"的思想，给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的 解答. 将整个求解区域分割成两部分来处理. 其一为包括半圆形凸起地形在内的一个圆形区 域I，其余为区域II. 在区域I和II中分别构造位移解，并在两个区域的"公共边界"上 实施"契合". 在区域I中构造一个上半部边界应力为零，而其余部分位移、应力任意的驻 波解，在区域II中构造出半圆形凹陷和浅埋圆孔的散射波，且要求它满足水平界面上应力 为零的约束条件. 然后再通过移动坐标，满足"公共边界"的"契合"条件和地下孔洞的边 界条件，建立起求解该问题的无穷代数方程组. 最后，给出了分析例题和数值结果，并 对其进行了讨论.     

SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动

利用“契合”思想,给出SH波作用下浅埋圆孔附近等腰三角形凸起地形表面地震动的解析解答.首先将整个求解区域分割成两部分,其一为半圆形弧底和等腰三角形组成的区域Ⅰ,其余部分为区域Ⅱ.在区域Ⅰ中构造一个满足等腰三角形两斜边上应力自由的驻波函数,在区域Ⅱ中构造出半圆形凹陷和浅埋圆孔的散射波,且要求其预先满足水平界面上应力为零的边界条件.利用复平面下坐标移动,利用“公共边界”的位移应力连续条件和浅埋孔洞内边界应力自由条件,建立起求解该问题的无穷代数方程组,并截断有限项进行求解.最后给出算例及结果,并进行了分析.     

圆弧形凹陷地形表面覆盖层对入射平面P波的影响

利用Fourier-Bessel级数展开法给出了表面具有覆盖层的圆弧形凹陷地形对入射平面P波散射问题的一个解析解，并利用该解分析了不同形状凹陷地形表面覆盖层刚度和厚度对入射P波的影响。结果表明，凹陷地形表面覆盖层的存在，即使厚度很薄，对入射P波的散射也具有很大覆盖，覆盖层刚度和厚度的变化可显著改善凹陷地形场地的动力特性。     

各向异性介质中SH波引起圆孔周围的能量散射

本文利用复变函数方法求解无限的各向异性介质中入射SH波对圆孔的散射问题.并指出能量的散射与入射波波长和圆孔半径有关.最后给出了圆孔周围能量散射的数值结果.     

各向异性介质中SH波引起的圆孔附近的动应力集中

本文利用复变函数方法求解无限的各向异性介质中入射的SH波对圆形孔洞的散射问题,指出动应力集中系数与入射波波数K_σ和圆孔半径r有关,最后给出了圆孔附近动应力集中系数的数值结果。     

Scattering of plane SH-waves on cylindrical canyon of arbitrary shape in anisotropic media

The complex function method is used to solve problems of scattering of plane SH-waves on cylindrical canyon topography of arbitrary shape in anisotropic media. This paper gives the complete function series and general expressions with boundary condition to approach the solution of steady state scattering of plane SH-waves on two-dimensional canyon topography in anisotropic media. The problem to be solved can be reduced to a solution of infinite algebraic equation series by using Hermite function and it's orthogonal conditions. The solution can be obtained directly by using computers. Finally, as an example, computational results of scattering of plane SH-waves on a semi-cylindrical canyon topography are presented. The projects sponsored by The Joint Seismological Science Foundation.     

SH波与界面多圆孔的散射及动应力集中

研究了平面SH波对相邻多个界面圆孔的散射及其动应力集中,为了求解,首先利用复变函数和多极坐标方法构造了在含有多个半圆形缺口的弹性半空间,水平面上任一点随时间谐和出平面线源载荷作用时失主移,邓Green函数,且采用“契合”模型,推导了SH波对相邻多个界面圆孔散射的定解积分方程组,进而求得圆孔附近的动应力系数,作为算例,讨论了具有两个界面圆孔对SH波的散射及其相互影响,给出了孔附近的动应力分布曲线。     

Scattering of plane SH-waves on semi-canyon topography of arbitrary shape with linging in anisotropic media

I.IntroductionItisofgreattheoreticalandpracticalimportancetostudytheproblemofscatteringofSH-wavesonsemi-canyontopographyofarbitraryshapewithlining.Especiallyinengineeringpractice,itisofgrePthelptotechnicians'analysisanddesignoftheanti-seismicstructureoftu…     

The interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media

In this paper, we use the complex function method for solving the problem of interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media. Anisotropic media can be used to simulate the conditions of the geology. This problem can be handled by using the method similar to that incorporated in Ref. [5] to define the scattering waves in media, added with the given boundary condition of the circular cavity. In this paper, as illustrated in the examples, the results and discussions of numerical studies have been done for the interaction of plane SH-waves and two kinds of circular cavities, surfaced with lining made up of different materials, in anisotropic media.     

Derivatives of the three-dimensional Green’s functions for anisotropic materials

A concise formulation is presented for the derivatives of Green’s functions of three-dimensional generally anisotropic elastic materials. Direct calculation for derivatives of the Green’s function on the Cartesian coordinate system is a common practice, which, however, usually leads to a complicated course. In this paper the Green’s function derived by Ting and Lee [Ting, T.C.T., Lee, V.G., 1997. The three-dimensional elastostatic Green’s function for general anisotropic linear elastic solids. The Quarterly Journal of Mechanics and Applied Mathematics 50 (3) 407–426] is extended to obtain the derivatives. Using a spherical coordinate system, the Green’s function can be shown as the composition of two independent functions, one depends only on the radial distance of the field point to the origin and the other is in spherical angles. The method of derivation is based on the total differential scheme and then takes its partial differentiation accordingly. With the application of Cauchy residue theorem, the contour integral can be evaluated in terms of the Stroh eigenvalues of a sextic equation. For the degenerate case, evaluation of residues at multiple poles is also given. Applications of the present result are made to examine the Green’s functions and stress components for isotropic and transversely isotropic materials. The results are in exact agreement with existing solutions.     

Rapoport-leas two-phase flow model for anisotropic porous media

The Rapoport-Leas mathematical model of two-phase flow is generalized to include the case of anisotropic porous media. The formula for the capillary pressure, which specifies the relationship between the phase pressures, contains a scalar function of a vector argument. In order to determine the scalar function, the capillary pressure tensor and the tensor inverse to the tensor of characteristic linear dimensions are introduced. The capillary pressure is determined by the contraction of the second-rank tensors with a unit vector collinear to the phase pressure gradients, also assumed to be collinear. It is shown that the saturation function introduced for isotropic porous media (Leverett function) can be generalized to include anisotropic media and is now determined by a fourth-rank tensor. Generalized expressions for the Leverett and relative phase permeability functions are given for orthotropic and transversely isotropic media with account for the hysteresis of the phase permeabilities and capillary pressure.     

多水平成层的非均匀介质圆弧形峡谷地下多点地震动模拟

开发了考虑圆弧场地水平多分层效应的地下多点地震动模拟可视化程序,验证其可靠性。首先,描述了给出的圆弧场地多分层效应的SH波动散射频域解,其本质是突破了传统均匀介质和分层不穿越峡谷前提的局限性;其次,利用从水平地表到峡谷表面再到地下土层的传递函数,通过两次传递得到了圆弧峡谷地下的目标功率谱和反应谱;进而,具体描述所导出的圆弧场地平-凹相关性的相干函数及其推导过程;最后,基于上述理论,开发了多层状的非均匀圆弧场地的多点地震动模拟程序,给出了模拟结果与目标功率谱、反应谱和相干函数的拟合对比,验证了该理论和程序的合理性和可靠性,便于所发展理论和方法的实用化和推广。     

SERIES SOLUTION FOR SCATTERING OF PLANE SH－WAVES BY MULTIPLE SHALLOW CIRCULAR－ARC CANYONS

ＳＥＲＩＥＳＳＯＬＵＴＩＯＮＦＯＲＳＣＡＴＴＥＲＩＮＧＯＦＰＬＡＮＥＳＨ－ＷＡＶＥＳＢＹＭＵＬＴＩＰＬＥＳＨＡＬＬＯＷＣＩＲＣＵＬＡＲ－ＡＲＣＣＡＮＹＯＮＳＦａｎｇＹｉｎｇｇｕａｎｇ（房营光）（Ｇｕａｎｇｄｏｎｇ｀ＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌ...     

Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphases

We obtain a limit model for a thin curved anisotropic interphase adherent to two elastic media. Our method is based on asymptotic expansions and energy minimization procedures. The model of perfect interface is obtained at the first order, while an imperfect interface model is obtained at the next order. The conditions of imperfect contact, given in a parallel orthogonal curvilinear coordinate system, involve the interphase material properties, the first order displacement and traction vectors, and their derivatives. An example of implementation of the imperfect interface condition is given for a composite sphere assemblage.     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.