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。     

多孔饱和半空间上弹性圆板垂直振动的积分方程

应用新的方法求解多孔饱和固体的动力基本方程－Ｂｉｏｔ波动方程,首先把Ｂｉｏｔ波动方程化为仅有土骨架位移和孔隙水压力的偏微分方程组,并且逐次解耦方法（不引入位移势函数）求解此偏微分方程组,然后按混合边值条件建立多孔饱和半空间上弹性圆板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。文中考虑两种孔隙流体的表面边界条件：（ａ）半空间表面（包括圆板与半空间的接触面）是     

多孔饱和半空间上刚体垂直振动的轴对称混合边值问题

研究圆柱形刚体在多孔饱和半空间上的垂直振动．首先应用Ｈａｎｋｅｌ变换求解多孔饱和固体的动力基本方程———Ｂｉｏｔ波动方程．然后按混合边值条件建立多孔饱和半空间上刚体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．文末给出了多孔饱和半空间表面动力柔度系数的计算曲线．     

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。     

求解饱和半空间上弹性圆板固结沉降的积分方程

本文采用解析方法分析了弹性圆板在饮和半空间上的固结沉降。考虑弹性圆板与饮和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Ｂｉｏｔ固结理论和积分方程技术,在Ｌａｐｌａｃｅ变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Ｆｒｅｄｈｏｌｍ积分方程。通过对其核函数的有效数值发得到第二类Ｆｒｅｄｈｏｌｍ积分方程的解,再利用Ｌａｐａｃｅ反演技术获得弹性板在时间域中的固结沉     

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。     

上覆单相弹性层的饱和地基上刚性圆板的扭转振动分析

采用解析的方法研究了上覆单相弹层的饱和地基上刚性圆板的扭转振动。首先运用积分变换技术分别求解了单相弹性介质和饱和介质情况时的控制方程，然后按混合边值条件建立了上覆单相弹性层的饱和地基上刚性圆板扭转振动的对偶积分方程，并把对偶积分方程化为易于数值求解的第二类Fredholm积分方程，并给出了数值算例。     

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．     

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。     

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。     

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.     

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.     

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…     

Using fredholm integral equation of the second kind to solve the vertical vibration of elastic plate on an elastic half space

I.IntroductionThedynamicanalysisofelasticplateonanelasticplateisveryimportanttotheresearchandengineering.Article[l]--131studiedtheverticalvibratiollof'rigidplatcl']alldelastic1llatcwitharigidcorely]orarigidedgel'joilallelastichalfspace.BecauseloadillgactatrigidPltltcof'therigidregionofelasticplate,onlytheresultantofh7rcesiscollsidcrcdillldwitll11oI.cliltlolltothedistributionofloading.Thevibrationofplateiscollsidcredastileproblelllof-sillglcdegreeoffi.eedolnsystem..Thepurposeofthepresentpaper…     

Numerical analysis of the isolation of the vibration due to Rayleigh waves by using pile rows in the poroelastic medium

The isolation of the vibration due to harmonic Rayleigh waves using pile rows embedded in a saturated poroelastic half-space is investigated in this study. Based on Biot’s theory and the potential function method, the free field solution for Rayleigh waves along the surface of the poroelastic half-space is derived first. The fundamental solution for a harmonic circular patch load applied in the poroelastic half-space are obtained in terms of Biot’s theory and the integral transform method. Using Muki’s method and the fundamental solution for the circular patch load as well as the Rayleigh waves solution for the poroelastic half-space, the second kind of Fredholm integral equations in the frequency domain for pile rows are derived. Numerical solution of the integral equations yields the dynamic response of the pile–soil system to incident Rayleigh waves. Influences of various parameters on the vibration isolation effect of piles rows are investigated numerically. Numerical results suggest that for the same vibration source, the same pile rows will produce a better vibration isolation effect for the poroelastic medium than for a single phase elastic medium. Also, stiffer piles tend to have better vibration isolation effect than flexible piles. Moreover, the pile length and the spacing between neighboring piles in each pile row have significant influence on the vibration isolation effect of pile rows.