层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程;求解状态方程后,得到传递矩阵. 进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

横观各向同性饱和土中柱面载荷的动力Green函数

基于饱和介质的三维波动理论的Biot模型,利用Fourier展开和Hankel变换,并借助算子理论,给出了圆柱坐标系下横观各向同性饱和土波动方程的非轴对称通解;利用通解,建立了饱和土层及饱和半空间的精确动力刚度矩阵;借助刚度矩阵,给出层状横观各向同性饱和地基中,作用沿土层深度方向分布的竖向和水平柱面载荷时的动力Green函数,进而解决了利用间接边界元法分析桩-饱和土动力相互作用的关键问题.     

上覆单相弹性层饱和地基上弹性基础的竖向振动分析

基于Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上弹性基础竖向振动的对偶积分方程.利用正交多项式将对偶积分方程化简,得到了动力柔度系数随无量纲频率b0的变化关系曲线,从而得到了上覆单相弹性层饱和地基上弹性基础的竖向振动规律.数值分析结果表明,对于弹性基础,当弹性基础的挠曲刚度较大时,发现弹性基础的竖向振动特性与刚性基础的类同,可忽略挠曲刚度对竖向振动的影响,且当无量纲频率较小的时候,动力柔度系数Cv随着无量纲频率b0的变化而发生显著的变化,但当无量纲频率b0较大的时候,动力柔度系数Cv受无量纲频率的影响较小,甚至基本上不受影响.当弹性基础的挠曲刚度较小时,随着挠曲刚度的减小,弹性基础的竖向振动将发生显著的变化,动力柔度系数Cv的实部和虚部的绝对值均变大.     

饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程，应用Fourier级数展开和Hankel积分变换，得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解．考虑地基表面透水情形，由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答．给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解．该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础．     

受移动简谐力作用的多孔弹性半平面问题

研究了匀速移动的振动荷载作用下半无限多孔饱和固体中产生的应力和孔隙水压力．应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答进行了比较．结果显示多孔饱和半平面中应力和孔隙水压力随荷载的移动速度与振动频率的增加而增大,多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体的动力响应有较大的差别。     

饱和地基上含刚核弹性圆板的竖向振动分析

基于作者提出的饱和土弹性波动方程，研究了饱和地基上含刚核弹性圆板在竖向集中谐和力作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程，然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程，并将其化为第二类Fredholm积分方程进行数值求解。文末给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率a0的变化曲线，并考察了土的渗透系数，弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响，得出了一些有意义的结论。     

上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动分析

基于弹性层和饱和土半空间轴对称弹性波动方程，运用Hankel积分变换方法，得到它们在变换空间内的解．进而由层间完全接触条件及圆板底面的混合边值条件，构造一组描述上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动的对偶积分方程．将该对偶积分方程化为易于数值计算的第二类Fredholm积分方程，求得地基表面动力柔度系数随无量纲频率的变化曲线及弹性圆板的相对位移幅值．     

横观各向同性饱和地基上无限板的稳态振动

研究了横观各向同性饱和土地基上无限板的稳态振动问题. 基于直角坐标系下横观各向同性饱和介质Biot波动方程的一般解，采用双重Fourier积分变换技术，建立了饱和地基与无限矩形板相互作用的动力方程，利用数值方法求解该方程，得到任意谐振荷载作用下饱和半空间体上无限板稳态响应的一般解. 数值结果表明，横观各向同性饱和地基上无限板的振动与各向同性饱和地基上的无限板的振动特性存在明显差异.     

具有弹性层的两圆管间夹入弹性薄膜时的回转接触

应用弹性接触理论及Fourier变换,考虑接触域的粘着及微小滑状态,对具有弹性层的两圆筒间夹入弹性薄膜的非对称回转接触问题进行了0研究,讨论了接触宽度,弹性层厚度及摩擦系数等对弹性薄膜传送速度和圆筒公称圆周速度之比的影响。     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

Dynamic interaction between elastic thick circular plate and transversely isotropic saturated soil ground

IntroductionThe vibration of the plate on the porous saturated building foundation is a complicateddynamic contact problem.Its consideration is very important in both earthquake and geo-technical engineering.Lots of research works have been done in recent…     

THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATIONON SATURATED LAYERED SOIL SUBGRADE

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The axisymmetric mixed boundary-value problem of the vertical vibration of a rigid foundation on saturated layered soil subgrade

Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient C_v versus the dimensionless frequency a₀ are presented. Foundation item: the National Natural Science Foundation of China (59579018) Biography: CHEN Sheng-li (1974-)     

Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space

Transient scattering of elastic waves by inclusions in a half space is investigated by the boundary integral equation (BIE) method. The formulation of BIE presented here is based on the Fourier transform method, and involves the analysis of transformed problems and the reconstitution of transient solutions by Fourier inversion. After the BIE has been solved numerically in the transformed domain, the transient wave fields are obtained with the help of the fast Fourier transform (FFT) algorithm. After confirmation of the accuracy of the present method, some numerical examples are shown for various inclusions in a half space, such as a cavity, an elastic inclusion, and a fluid inclusion.     

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foun- dation of finite height bounded to the surface of a saturated half-space.The foundation is subjected to time-harmonic vertical loadings.First,the transform solutions for the governing equations of the saturated media are obtained.Then,based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half- space is completely pervious or impervious,this dynamic mixed boundary-value problem can lead to dual integral equations,which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures.In the numerical exam- ples,the dynamic compliances,displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system.In most of the cases,the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.     

ANALYSIS OF GROUND VIBRATION CONTROL BY GRADED WAVE IMPEDING BLOCK

波阻板（wave impeding block,WIB）隔振体系是一种有效的振动污染治理措施,虽逐渐被应用在工程实际中,但以往的研究多集中于单相固体均质材料的情形,而对材料特性沿空间连续变化的非均匀固体材料的波阻板隔振性能的研究相对较少.基于功能梯度材料（functionally graded material,FGM）特点,本文提出了以功能梯度波阻板作为隔振屏障的一类新型的地基振动控制体系.考虑在弹性地基内部设置梯度波阻板,基于线弹性理论,利用傅里叶积分变换,根据Helmholtz矢量分解原理,建立了弹性地基在动载荷作用下的回传射线矩阵法（reverberation ray matrix method,RRMM）计算列式.假设梯度波阻板的物理力学性质沿深度方向按幂函数连续变化,采用数值傅里叶逆变换获得了弹性地基的位移和应力等物理量的数值解.通过数值算例,与单相固体均质波阻板进行了对比,并分析讨论了梯度波阻板的材料梯度因子、埋深以及梯度波阻板厚度等物理力学参数对地基隔振性能的影响规律.结果表明,梯度波阻板能有效降低振动的振幅,与单相固体均质波阻板相比,梯度波阻板具有更好的减振隔振效果.地基的位移幅值和应力幅值随着梯度因子的增大而减小.梯度波阻板的隔振效果随着波阻板厚度的增大而提高,而随着梯度波阻板埋深的增大而降低.     

Dynamic Analysis of an Infinite Cylindrical Hole in a Saturated Poroelastic Medium

In this paper, the dynamic response of an infinite cylindrical hole embedded in a porous medium and subjected to an axisymmetric ring load is investigated. Two scalar potentials and two vector potentials are introduced to decouple the governing equations of Biot’s theory. By taking a Fourier transform with respect to time and the axial coordinate, we derive general solutions for the potentials, displacements, stresses and pore pressures in the frequency-wave-number domain. Using the general solutions and a set of boundary conditions applied at the hole surface, the frequency-wave-number domain solutions for the proposed problem are determined. Numerical inversion of the Fourier transform with respect to the axial wave number yields the frequency domain solutions, while a double inverse Fourier transform with respect to frequency as well as the axial wave number generates the time-space domain solution. The numerical results of this paper indicate that the dynamic response of a porous medium surrounding an infinite hole is dependant upon many factors including the parameters of the porous media, the location of receivers, the boundary conditions along the hole surface as well as the load characteristics.     

Generalized Fourier transform and its application to the volume integral equation for elastic wave propagation in a half space

In the present study, a generalized Fourier transform for time harmonic elastic wave propagation in a half space is developed. The generalized Fourier transform is obtained from the spectral representation of the operator derived from the elastic wave equation. By means of the generalized Fourier transform, a volume integral equation method for the analysis of scattered elastic waves is presented. The proposed method is based on the Krylov subspace iteration technique. During the iterative process, the discrete generalized Fourier transform is used, where the derivation of a huge and dense matrix from the volume integral equation is not necessary.