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．     

饱和地基上弹性圆板的动力响应

研究弹性圆板在饱和地基上的垂直振动特性,即首先应用Hankel变换方法求解饱和土波动方程,然后按混合边值条件建立饱和地基上圆板垂直振动的对偶积分方程,用一种简便的方法,对偶积分方程可化为易于数值计算的第二类Fredholm积分方程。文末的数值分析得出了板振动的一些规律性,由此表明当板的挠曲刚度D趋于无穷大且不计板的质量时,其结果和无质量刚性圆盘在饱和地基上的振动特性完全一致。     

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。     

横观各向同性饱和地基上中厚圆板的非轴对称振动

研究横观各向同性饱和土地基上中厚弹性圆板的非轴对称振动问题。基于横观各向同性饱和介质Biot波动方程的一般解,按混合边值问题建立了饱和地基与弹性中厚圆板非轴对称动力相互作用的对偶积分方程,并将对偶积分方程转化为易于计算的第二类Fredholm积分方程;采用数值方法求解该积分方程。数值算例结果表明,当h/a>0.05时,饱和半空间体上中厚度圆板在不同频率下的振动特性与相应频率下的刚性板的振动特性基本相同,当h/a<0.05时,板中心的位移将随h/a的减小而增大。     

具有混合边界透水条件的多孔饱和半空间上刚性圆板的垂直振动

用积分变换和积分方程研究多孔饱和半空间上刚性圆板的垂直振动问题。首先应用逐次解耦方法求解多孔饱和固体的动力基本方程－Ｂｉｏｔ波动方程。然后考虑混合边界透水条件（半空间表面与圆板的接触面是不透水的,而其余表面是透水的）,建立子多孔饱和半空间上刚性圆板垂直振动的对偶积分方程,并化对偶积分方程为第二类Ｆｒｄｄｈｏｌｍ积分方程。     

多孔饱和半空间上弹性圆板的动力分析

用解析方法研究多孔饱和半空间上弹性圆板的低垂直振动，首先用Ｈａｎｋｅｌ变换求解多孔饱和介质动力问题控制方程，然后按混合边值条件建立多孔饱和半空间上弹性板的垂直振动的对偶积分方程，用Ａｂｅｌ变换化对偶积分方程为第二类Ｆｒｅｄｈｏｌｍ积分方程，并给出了数值算例。     

多层地基上轴对称受荷刚性圆板问题

利用刚性圆板表面各点位移相等,并结合刚性圆板与地基表面的位移相容条件与光滑接触条件,经由Hankel变换,推导出了刚性圆板与分层地基表面接触应力的对偶积分方程;求解该对偶积分方程,再由多层地基应力与位移的传递矩阵解,并经Hankel逆变换,得到了多层地基上轴对称受荷刚性圆板问题的解.编制了计算程序,并进行了数值分析与计算.计算结果表明:对均匀地基而言,实际工程的计算分析可只考虑4倍刚性圆板直径以内深度范围内的应力与位移;而地基的分层性对地基的位移和应力有着较大的影响,简单地将均匀地基的结论推广到分层和非均匀地基是不恰当的.     

下卧刚性基岩的饱和地基上基础的动力分析

采用积分变换与积分方程研究了单层饱和地基上刚性基础的竖向振动问题，首先从饱和土的动力控制方程出发，考虑混合边值条件，获得了一组描述基础振动的对偶积分方程，进而给出了单层饱和地基表面的动力柔度系数。该文的工作可视为对饱和半空间地基上基础振动解答的推广。     

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.     

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.     

TORSIONAL VIBRATIONS OF RIGID CIRCULAR PLATE ON TRANSVERSELY ISOTROPIC SATURATED SOIL

An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil's anisotropy on the foundation's vibrations.     

TORSIONAL VIBRATIONS OF A RIGID CIRCULAR PLATE ON SATURATED STRATUM OVERLAYING BEDROCK

The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.     

A dynamic analysis of elastic circular plate on saturated poroelastic half space

In this paper the low frequency vibrations of an elastic circular plate on a saturated poroelastic half space are studied by the analytical method. First the governing equations of the dynamic problem for a saturated poroelastic medium are solved by means of Hankel transform. Then the dual integral equations of vertical forced vibration of an elastic plate on saturated poroelastic half space are established according to the mixed boundary-valued condition. By applying Abel transform the dual integral equations are reduced to a Fredholm integral equation of the second kind. Numerical examples are given at the end of the paper.     

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-)     

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.