沉积盆地-山体耦合场地对平面P波、SV波和Rayleigh波的二维散射分析

盆山耦合地形作为一种常见的复杂场地,其对地震动的复合影响目前尚未得到清晰认知。为此,引进一种高精度的有限元-间接边界积分方程耦合方法(FEM-IBIEM),探讨沉积盆地及其邻近山体对地震波(平面P波、SV波和Rayleigh波)的多次散射作用。数值结果表明:沉积盆地及其邻近山体存在显著的动力相互作用,整体位移响应特征依赖于山体、盆地的空间位置和几何特征,入射地震波的频率和角度等因素;整体上看,P波垂直入射下,较高山体的存在对沉积盆地内部位移具有明显的放大效应;SV波入射下,山体的影响相对较小,且盆地内部不同位置可能会表现出完全不同的放大或缩小特征;Rayleigh波从山体一侧入射时,山体对沉积盆地存在明显的"屏障"作用,而从盆地一侧入射时,在低频段山体反而会表现出放大作用;总体上看较高山体对沉积盆地的影响程度更为显著。鉴于山体的存在显著改变了沉积盆地的位移幅值和频谱特性,实际盆地的地震动确定需考虑邻近山体的影响。     

平面弹性波入射下空沟隔振的解析分析EI北大核心CSCD

基于复变函数理论和保角映射方法,采用波函数展开法及多级坐标变换技术,解析求解了半无限空间中空沟对平面SH波和平面P波的隔振问题。首先,通过设虚源法和大圆弧假定法分别给出了平面SH波和平面P波入射半无限空间时的散射场。然后由空沟边界及大圆弧边界处的应力自由边界条件建立无穷阶线性方程组,并通过对该方程组的求解给出了空沟对平面SH波和平面P波散射的解析解答。最后,参数分析了激励频率、空沟深度等因素对隔振效果的影响规律。结果表明,空沟对平面SH波和平面P波的隔振效果随着入射波频率的增大而增大,随着空沟深度增大而增大。     

SH波入射下正交各向异性双相介质界面附近圆孔的动应力集中

基于复变函数和格林函数的方法，探讨了SH波在具有圆孔的正交各向异性两相介质中的散射，分析了圆孔周围的动态响应规律。首先建立问题的二维解析模型，将全空间分为两个部分：均匀各向同性上半空间以及含圆柱形孔洞的正交各向异性下半空间。采用格林函数法推导出了两半空间界面处各点的格林函数表达式，并引入复变量，构造出了SH波入射下求解区域内位移和应力的表达式。考虑界面的连续性条件，将未定反平面力加载到两个半空间的水平界面上，推导出Fredholm定解积分方程组，用弱奇异积分方程的直接离散方法求解。最终通过算例分析，发现介质的正交各向异性参数、入射波波数、角度以及孔洞埋深等对下半空间圆孔周边的动应力集中系数(DSCF)影响显著。     

基于TI介质模型的凸起地形对平面SH波的放大作用

在模拟地震波在介质中传播过程的研究中,正演模拟是一个重要的方面。该文采用间接边界元法（IBEM）对横观各向同性（TI）不同参数介质的凸起场地中入射SH波的散射问题进行了正演模拟,研究了TI凸起场地对SH波的放大效应。放大效应是通过地表位移与基岩露头位移幅值的比值来体现的。该间接边界元法结合了层状TI半空间精确动力刚度矩阵和均布斜线荷载动力格林函数,具有较高的精度。该文分别给出了TI介质凸起中SH波散射问题在频域和时域内的解答。频域内研究分析表明,土体TI介质参数的变化会对场地位移幅值的放大谱和空间分布产生显著的影响,即改变了凸起部分和土层的动力特性,使得两者动力相互作用发生改变。时域内研究表明,SH波在凸起周围的传播同时依赖于TI介质参数的具体取值和传播方向。时域位移幅值云图清晰地展示入射波、透射波、反射波和散射波的传播过程,凸起角点产生的散射波在TI介质中传播呈现"半椭圆"型,而在各向同性介质中呈现"半圆"型。     

层状饱和半空间中沉积谷地对斜入射平面P1波的三维散射

在作者给出层状饱和场地三维精确动力刚度矩阵和层状饱和半空间中移动荷载动力格林函数基础上,采用间接边界元方法在频域内求解了层状流体饱和场地中沉积谷地对斜入射平面P1波的三维散射问题。该方法的特点在于虚拟移动均布荷载和斜线孔隙水压可以直接施加在沉积与层状饱和半空间交界面而不存在奇异性。该文通过与已有结果的比较验证了方法的正确性,并以均匀饱和半空间和弹性基岩上单一饱和土层中沉积谷地为例进行了数值计算分析。研究表明,沉积谷地对平面P1波的三维散射与二维散射之间存在本质差别,入射角度、孔隙率、饱和土层刚度和饱和土层厚度等参数对沉积谷地附近动力响应有着显著影响。     

任意多个沉积谷地对平面SV波的散射

采用间接边界元法研究了入射平面SV波在层状半空间中多个沉积谷地周围的散射问题。该方法将整体模型分解为各个沉积闭合域和开口的层状半空间域。通过在各沉积闭合边界上施加虚拟均布荷载模拟各闭合域内散射波场,通过在层状半空间开口域所有开口边界上施加虚拟荷载模拟开口域内散射波场,通过引入各沉积与层状半空间的连续条件确定所有施加虚拟荷载的密度。验证了该方法的正确性,并对均匀半空间中不同间距和不同数量的半圆沉积为例进行了数值计算分析,数值结果表明,多个沉积与单一沉积对应的位移幅值及其放大谱均显不同,沉积间的动力相互作用,使得多个沉积情况对应位移幅值显著大于单一沉积情况。沉积间距的改变导致了沉积间动力相互作用机制的改变,进而改变了放大谱的峰值及峰值周期。沉积个数影响主要体现在增强或减弱沉积间的动力相互作用上,而对相互作用机制影响较小,因而不同沉积个数对应的放大谱峰值差异明显而峰值周期较为接近。     

基于TI介质模型的沉积谷地对平面SH波的放大效应EI北大核心CSCD

在TI场地平面外动力刚度矩阵的基础上,推导出斜线均布荷载动力格林函数,进而以该格林函数为基本解建立间接边界元方法求解了沉积谷地对平面SH波的散射问题。文中验证了方法的正确性,并分别将沉积内部和外部介质考虑为TI介质,在频域和时域内进行了计算分析。研究表明:沉积TI参数的改变主要导致了沉积自身动力特性的改变,进而使得沉积表面位移幅值放大谱的峰值频率和谱值均发生明显改变;半空间TI参数的改变则导致了各方向上半空间与沉积阻抗比的改变,因而对放大谱的峰值频率影响较小,其影响主要体现在峰值大小上;另外,通过求解Ricker波输入下沉积附近观测点的位移幅值时程发现,沉积和半空间的TI参数亦对弹性波在含沉积半空间中的传播有着显著影响。     

基于TI介质模型的沉积谷地对平面SH波的放大效应

在TI场地平面外动力刚度矩阵的基础上,推导出斜线均布荷载动力格林函数,进而以该格林函数为基本解建立间接边界元方法求解了沉积谷地对平面SH波的散射问题。文中验证了方法的正确性,并分别将沉积内部和外部介质考虑为TI介质,在频域和时域内进行了计算分析。研究表明:沉积TI参数的改变主要导致了沉积自身动力特性的改变,进而使得沉积表面位移幅值放大谱的峰值频率和谱值均发生明显改变;半空间TI参数的改变则导致了各方向上半空间与沉积阻抗比的改变,因而对放大谱的峰值频率影响较小,其影响主要体现在峰值大小上;另外,通过求解Ricker波输入下沉积附近观测点的位移幅值时程发现,沉积和半空间的TI参数亦对弹性波在含沉积半空间中的传播有着显著影响。     

弹性半空间山体裂纹对弹性波的散射

利用间接边界元法(IBEM),求解了弹性半空间山体裂纹对弹性波的二维散射问题。以含裂纹的半圆山体为例,分析了不同频率弹性波入射下裂纹角度、位置、数量等因素对散射的影响规律,计算了山体表面及两侧地表的位移幅值。研究表明:裂纹的存在对山体表面位移有明显的缩放效应,随着频率的增大,裂纹角度的影响逐渐减小,裂纹数量的影响逐渐增大。P波垂直入射下,山腰处的放大效应最明显,与无裂纹山体相比,在3～5这一频段内山腰处水平位移峰值约放大2倍;SV波垂直入射下,山脚处变化最为明显,最大峰值达到1.8,比无裂纹山体增加近27%。     

半空间内孔边界面裂纹对SH波的动力响应

采用"镜像"和"剖分-契合"等方法,对SH波作用下半空间孔边界面裂纹的动应力问题进行了研究。首先,采用"镜像法",将半空间镜像为全空间,构造出满足边界条件的散射波场;其次,借助"剖分-契合"方法和"裂纹切割"技术,将全空间沿界面分割成两个半空间求解后,再由界面应力位移连续"契合"条件组合成全空间,建立起求解该问题的积分方程组;最后,对界面裂纹端点的动应力强度因子(DSIF)进行数值分析。分析结果表明:适当地避开入射波波数、入射角度及裂纹长度等最不利影响因素的组合,可达到降低裂纹尖端点动应力的目的。     

圆弧形层状凹陷地形对平面SH波的散射

利用Fourier—Bessel级数展开法给出了圆弧形层状凹陷地形对平面SH波散射二维问题的一个解析解，分析了层状凹陷地形沉积排列顺序、软夹层刚度和厚度等因素对SH波散射的影响。结果表明，层状凹陷地形对平面SH波的散射和单一凹陷地形差别很大，凹陷地形表面松软沉积的存在，即使厚度很薄，也会大大降低凹陷地形本身对入射波的屏障作用；层状凹陷地形中沉积排列顺序、软夹层刚度和厚度的变化对散射也具有重要影响。     

多排柱腔列对平面P波和SH波的隔离

运用复变函数的保角映射方法和波函数展开法,利用P波和SH波耦合散射的特性,根据土体在柱腔壁处完全自由(即径向应力和切向应力为零)的边界条件,得到了多排柱腔列构成的非连续屏障对平面P波和SH波隔离的二维平面问题的理论解,通过绘制屏障后归一化位移(同一点处由入射和散射波产生的总位移与入射波单独产生的位移之比)的等值线图,分...     

Wave dispersion and attenuation in fiber composites

 This work deals with the dispersion and attenuation of elastic plane waves propagating in a single layer fiber reinforced composite, in a direction which is perpendicular to the fibers. An iterative effective medium model, based on single scattering considerations, for the quantitative estimation of wave dispersion and attenuation is proposed. The single scattering problem is solved numerically by means of a 2-D boundary element methodology. Numerical results concerning the plane velocity and the attenuation coefficient of longitudinal or transverse SH, SV waves propagating in two types of fiber reinforced composite materials, are presented. The obtained results are compared to those taken either experimentaly or numericaly by other investigators.     

An integral equation method for the diffraction of oblique waves by an infinite cylinder

A hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y-direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.     

Transient response of ground surface due to incident SH waves

The amplification of ground motion on the surfaces of two semi-elliptical alluvial valleys due to incident SH waves in homogeneous and layered half-spaces is investigated in time as well as in frequency domains by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the far-field outside a contour enclosing completely the scatterers. First, the response in frequency domain is obtained from solving a set of large sparse unsymmetric complex matrix equations, which are stored in a compacted data structure, by the biconjugate gradient method with good initial guess, and then it is transformed into the time domain by using FFT. An efficient quadrature scheme is adopted to compute the Green's functions in a layered half-space. The study shows that an important role is played by the trapped surface waves (Love waves) that produce much larger amplification than the disturbance associated with the direct incident signal. These Love waves can propagate inside the valley back and forth resulting in a long duration when the impedance contrast is high. In the lower impedance contrast case, the Love waves produce disturbances on the outer sides of the valley. The P and SV cases will be presented in another paper.     

出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射

采用复变函数法和Green函数法,求解出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数,取该位移函数作为Green函数;然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足"公共边界"处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组;最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。     

Scattering of SH-waves by an interface cavity

Summary. The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.     

带形介质内SH型导波对圆柱孔洞的动力分析

弹性板壳的反平面运动中由缺陷引起的应力集中问题可以按照带形介质中圆柱孔洞对SH型导波的散射问题来分析。首先,构造带形介质中相容导波的形式,即其满足上、下边界应力自由条件。之后,由波函数展开法给出圆柱孔洞散射波的级数表示,根据累次镜像叠加的方法构造由上、下边界反射所形成的相容的散射导波。最后,给定入射导波,由圆柱孔洞边界应力自由的条件来定解波函数级数的系数。数值算例求解了特定导波对圆柱孔洞的散射,给出了圆柱孔洞边沿的动应力分布,讨论了导波阶数、频率以及孔洞位置的影响。     

Multiple scattering of electromagnetic waves by an aggregate of uniaxial anisotropic spheres

An exact analytical solution is obtained for the scattering of electromagnetic waves from a plane wave with arbitrary directions of propagation and polarization by an aggregate of interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes. The expansion coefficients of a plane wave with arbitrary directions of propagation and polarization, for both TM and TE modes, are derived in terms of spherical vector wave functions. The effects of the incident angle α and the polarization angle β on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres are numerically analyzed in detail. The characteristics of the forward and backward RCSs in relation to the incident wavelength are also numerically studied. Selected results on the forward and backward RCSs of several types of square arrays of SiO? spheres illuminated by a plane wave with different incident angles are described. The accuracy of the expansion coefficients of the incident fields is verified by comparing them with the results obtained from references when the plane wave is degenerated to a z-propagating and x- or y-polarized plane wave. The validity of the theory is also confirmed by comparing the numerical results with those provided by a CST simulation.