任意排列的弹性实心桩屏障对平面SH波的多重散射

为了弥补以往假设单重散射的计算方法中不考虑桩列作为整体屏障从而忽略桩间互相干涉关系的不足,提出了一种新的理论计算方法以求解任意直径、任意排列的弹性桩对入射平面SH波的多重散射。通过桩土界面的位移、应力连续条件可以求得待定的多重散射系数。多重散射中,每根桩的第一重散射即为通常的单重散射;第二重散射可表示为该桩被其余桩的第一重散射波之和所激发的散射波;以此类推至无穷多重散射。将无限重散射叠加即任意直径、任意排列弹性桩对平面SH波的多重散射的精确解。随后数值算例分析讨论了不同散射重数、剪切模量、桩间距以及桩数等对单排弹性桩屏障隔离效果的影响,绘制了屏障后的无量纲位移曲线,并引入透射系数来评价非连续弹性桩屏障的隔振效果,对实际工程中的振动污染治理和屏障隔振设计提出了有意义的结论和建议。     

饱和土体中多排桩屏障对压缩快波的隔离

假定桩的长度远大于直径, 将多排弹性桩组成的非连续屏障对平面压缩快波(简称P₁波)的隔离简化为弹性波多重散射的二维平面问题, 运用复变函数的保角映射方法和波场势函数展开法, 根据桩-土界面处应力和位移连续的边界条件, 得到散射波场势函数展开式中待定复系数的理论解。通过分析屏障后的位移比值(某点由入射和散射弹性波产生的总位移与入射弹性波单独产生的位移之比)的变化规律, 对比了单排、双排和三排桩屏障的隔离效果, 研究结果表明：1) 多排桩屏障对高频入射P₁波的隔离效果好于低频入射P₁波;2) 随着桩排数的增多, 多排桩屏障的隔离效果明显提高, 有效隔离区域明显增大;3) 当桩排数达到三排时, 屏障后一定范围内的隔离效果提高到了70%, 隔离效果比较理想。     

非连续弹性圆柱实心桩屏障对弹性波的隔离

采用波函数展开法和Graf加法定理,根据桩土界面处位移和应力连续的边界条件,得到了非连续弹性圆柱实心桩屏障对入射平面P波和SH波散射系数的理论解,通过引入无量纲位移,即屏障后某处土体内由入射波和散射波引起的总的纵向位移和水平位移与未设屏障时由入射平面P波和SH波在该处土体内单独引起的位移幅值的比值,根据求得的散射系数的理论解,绘制了平面P波和SH波单独入射情况下,弹性圆柱实心桩屏障后不同位置的无量纲位移、不同剪切模量的弹性圆柱实心桩屏障后的无量纲位移等值线和透射系数随桩间距的变化曲线,通过研究这些图件进而分析了屏障后不同位置、剪切模量、桩间距和入射频率对非连续弹性圆柱实心桩屏障的隔离效果的影响,为非连续弹性屏障的隔振设计提供了理论依据.     

单排非连续刚性桩屏障对弹性波的隔离

对于人工振动产生的弹性波,如果刚性桩屏障埋置足够深,在分析其对弹性波的隔离效果时,可以简化为固定的刚性桩屏障对弹性波的多重散射问题。采用波函数展开法将入射波和散射波的势函数展开成Fourier-Bessel函数的级数形式,根据Graf加法定理和固定刚性桩周边土体的边界条件得到散射系数的理论解,引入了无量纲位移(屏障后土体中由入射波和散射波产生的总的位移幅值与入射波在该处单独产生的位移幅值之间的比值)和透射系数(屏障后屏障宽度范围内的无量纲位移的几何平均值)的概念,绘制了屏障后一定范围内的无量纲位移等值线,及屏障后某处的透射系数随桩净距(相邻两桩之间的空隙)的变化曲线,通过分析这些曲线得出,对于三种入射体波(SV波、P波和SH波):屏障后越靠近屏障,隔离效果越好;当桩净距接近一倍桩半径时,屏障的整体隔离效果达到最好。     

弹性波多重散射的改进算法及双排刚性桩隔振研究

同Aviles等学者传统的多重散射隔振理论相比较,采用更为完整的Fourier-Bessel函数系的级数展开式来研究波的散射问题,同时,结合更具一般意义上的Graf加法定理,并引入连续性边界条件,得到了任意分布的多个刚性圆柱体关于平面SV波入射下散射系数的理论解析解。随后,取所有的圆柱体位于两条相平行的直线上,该问题演变成为双排非连续刚性屏障对于弹性SV波的隔离问题。引入无量纲位移和屏障后透射系数的概念,重点讨论了屏障双排桩之间间距h的影响以及屏障其他一些隔振性状。特别地,当h=0时,该问题退化为单排非连续刚性屏障的隔振问题。     

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...     

空沟对弹性波散射的时域分析：平面SV波入射

基于土-结构相互作用理论,利用比例边界有限元法,将含有空沟地形条件的场地分解为近场系统和无穷远场系统。利用四叉树对近场计算区域进行网格精细化离散,并利用位移单位-脉冲响应矩阵来表示近场和远场交界面上的相互作用力,从而将斜入射的平面SV波转化为作用在近场系统边界上的等效节点力来模拟入射波对近场系统的激励作用,建立了时域-空间域弹性波传播问题的数值模型,通过数值算例验证了方法的有效性,分析了入射角和空沟深度等参数对隔振效果的影响。结果表明：隔振效果随着入射角的增大而增大;当入射角较大时,通过进一步增大空沟深度,可使得空沟发挥出更优的隔振效果。     

多排柱腔构成的非连续屏障对SV波的隔离

运用复变函数的保角映射方法和波函数展开法,根据柱腔壁处土体完全自由,即应力为零的边界条件,得到了多排柱腔构成的屏障对入射平面SV波的多重散射的理论解,根据屏障后归一化位移(入射和散射SV波产生的总位移与入射SV波在同一点产生的位移之比)的变化规律,着重分析了多排(双排和三排)和单排柱腔对平面SV波的隔离效果,结果表明：(1) 双排和三排柱腔屏障的隔离效果明显好于单排柱腔屏障;(2) 当入射SV波的频率较低时,双排并列正对的柱腔屏障的隔离效果较好,而当频率较高时,双排交错的柱腔屏障的隔离效果较好;(3) 三排梅花桩布置的柱腔屏障的隔离效果好于双排柱腔,当入射SV波的频率较高时,屏障后有近3/4的面积的隔离效果都超过了60%;(4) 无论是单排还是多排柱腔屏障,当入射SV波频率较高时,靠近屏障边缘区域的隔离效果要好于中心区域。     

SH波入射下多重散射的改进算法及任意桩布置形式的隔振研究

引入位移连续的边界条件并结合Graf加法定理,得到了任意分布的多个圆柱体对于弹性波入射时散射系数的理论解析解。随后,将此任意分布的多个圆柱体重新分布在相平行的两条直线上,该问题演变成为双排非连续屏障对于弹性波的隔离问题。引入无量纲位移概念来研究屏障的隔振效果,即屏障后某处土体由入射波和散射波引起的总的位移幅值与未设置屏障时由入射波在该处土体单独引起的位移幅值的比值。重点讨论了屏障的排间距h和桩间净距Sp对整体隔振效果的影响。特别地,当h=0时,该问题退化为常见的单排非连续屏障的隔振问题。     

SV波入射下多重散射问题的改进算法以及双排非连续刚性屏障的隔振研究

摘 要：相比起Aviles等学者的单排非连续刚性屏障隔振理论,采用更为完整的Fourier-Bessel函数系的级数展开表达式来研究弹性波的多重散射问题,结合位移连续的边界条件,并引入更具一般意义上的Graf加法定理,推导了无限均匀介质中任意分布的多个刚性圆柱体对于平面SV波入射时散射系数的理论解析解。随后,取所有的圆柱体位于相平行的两条直线上,则问题演变成为双排刚性桩屏障对于平面SV波的隔离问题。重点讨论了两排桩之间的间距h对屏障整体隔振效果的影响及其他的一些隔振性状。特别地,当h=0时,该问题退化为常见的单排非连续屏障的隔振问题。     

饱和土中管桩对倾斜入射弹性波的隔离

在Biot饱和土波动方程的基础上,分析了全空间均质饱和土体中单排空心管桩对倾斜入射弹性波的隔离效果。将倾斜入射波和散射波的势函数展开成Fourier-Bessel函数的无穷级数的形式,利用一组圆柱坐标系统和Graff加法转换定理,通过施加桩土界面处的应力和位移连续的边界条件,求解出散射波势函数的待定系数,进而得到饱和土体中任意点的位移和应力。数值算例分析了饱和土体的渗透性和管桩的壁厚等参数对管桩隔离效果的影响。结果表明：空心管桩的隔离效果要好于实心排桩;随着饱和土体渗透性的降低,管桩的隔离效果越好,但当渗透性降低到一定程度后,再减小土体渗透性对管桩的隔离效果影响不大。     

Coupled P and SV waves propagating in spherical elastic layers: Exact solution and interpretation

We study the propagation of coupled P and SV waves emitted by a source point placed outside a given finite set of concentric elastic spherical layers. We show that the system of boundary conditions of this pattern is a linear combination of the boundary conditions of the simpler problem of reflectionrefraction phenomenon of a wave at a spherical surface. From this result the exact solution follows for all regions of the multilayered structure without using Cramer's technique. This solution is written as a series of which each element is interpreted directly in terms of multiple reflection-refraction. It gives a simple explanation for triggering of resonance phenomena. The solution contains many particular bases of which several are investigated.     

On the theory of elastic scattering of electromagnetic waves by atoms

A Hamiltonian describing the elastic interaction of electromagnetic radiation (EMR) with an atom is obtained using the invariant theory of perturbations in the limit of EMR wavelengths λ significantly exceeding the atom size a₀. An exact expression for the interaction amplitude is obtained, and the probability of EMR scattering on the atom is calculated. It is established that the scattering probability at large λ is proportional to the squared frequency of monochromatic EMR. It is shown that, in the limit of large wavelengths, the formula h∼(ω/c)⁴ v ₀ for the extinction coefficient is inapplicable and the relation h=Aω² becomes valid, where A is a definite coefficient.     

Transient scattering of elastic waves by three dimensional non-axisymmetric dipping layers

Scattering of elastic plane waves by three dimensional non-axisymmetric multiple dipping layers embedded in an elastic half-space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square sense at points on the layer interfaces and on the surface of the half-space. The transient response is constructed from the steady state solution by using Fourier synthesis. Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non-axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.     

Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers

Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.     

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.     

Effects of sinusoidal crack-face perturbations on scattering of elastic waves

The scattering of a plane longitudinal wave from a two-dimensional crack, with a sinusoidal surface perturbation whose amplitude and wavelength are much smaller than the length of the crack, is investigated. The amplitude of the cylindrical body waves in the far field are calculated from a Kirchhoff approximation that utilizes the solution to the reflection from the sinusoidal surface profile of a semiinfinite solid. The results are compared to those for a flat crack, and conditions for significant differences of the amplitude as a function of the angle of observation are discussed. Characteristic changes in the scattered field produced by profiles with different amplitudes and periods are explained.