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     

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     

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。     

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。     

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.     

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．     

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…     

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.     

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…     

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。     

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。     

成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性.      

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．     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｌａｓｔｉｃｈａｌｆ＿ｓｐａｃｅｔｈｅｏｒｙｏｆｆｏｕｎｄａｔｉｏｎｖｉｂｒａｔｉｏｎａｎｄｔｈｅｓｔｕｄｙｏｆｓｏｉｌ＿ｓｔｒｕｃｔｕｒｅｉｎｔｅｒａｃｔｉｏｎｐｒｏｂｌｅｍｈａｖｅｂｅｅｎｔｈｅｓｕｂｊｅｃｔｏｆｉｎｔｅｎｓｉｖｅｒｅｓｅａｒｃｈｉｎｔｈｅｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ .ＳｉｎｃｅＬｕｃｏｅｔａｌ.[1]ｓｕｍｍａｒｉｚｅｄｔｈｅｖｉｂｒａｔｉｏｎｏｆａｃｉｒｃｕｌａｒｒｉｇｉｄｆｏｕｎｄａｔｉｏｎｒｅｓｔｉｎｇｏｎａｎｅｌａｓｔｉｃｈａｌｆ＿ｓ…     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

加层半空间硬币形(Penny—Shaped)交界裂纹的弹性波散射——远场散射波导分析

本文研究了加层半空间硬币形交界裂纹的弹性波散射。文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组.应用积分变换,围道积分技术和渐近分析方法,得到了弹性层中散射位移场的远场模式,理论分析表明弹性层中的散射位移场主要由RayLeigh-Like-Mode波组成,该波是弹性层中的散射波导.最后,给出两组弹性常数组合情形下的数值结果及讨论.     

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.     

高速荷载下多孔饱和地基的动力响应

研究高速荷载作用下梁与多孔饱和半空间的动力响应。由Fourier变换求解多孔饱和固体的动力基本方程，根据梁与半空间的接触条件得出多孔饱和半空间上梁的垂直位移的表达式。文中的数值算例考虑了荷载移动速度对梁的动力位移的影响，并与相应的弹性半空间问题作了对比。从算例中可以发现荷载移动速度对动力位移有很大的影响，当移动速度与半空间的表面波速相近时，地面会当产生很大的振动，同时还发现当速度大于介质的剪切波速时，多孔饱和半空间上梁的动力响应与弹性半空间上梁的动力响应有很大的差别。     

NON-AXISYMMETRIC MIXED BOUNDARY VALUE PROBLEM FOR DYNAMIC INTERACTION BETWEEN SATURATED POROUS FOUNDATION AND RECTANGULAR PLATE$^{\bf 1)}$

在同一界面的不同区域具有多种边界条件, 称之为混合边界, 这是一个熟知的力学问题. 对这类问题进行精确分析时, 必须要进行混合边值问题的求解. 而对于一般的三维非轴对称情形, 混合边值问题的求解往往存在数学困难. 本文利用Hilbert定理和双重Fourier变换, 给出了一种求解三维非轴对称混合边值问题的解析方法, 利用该方法对具有混合透水边界的饱和多孔地基上矩形板的振动弯曲进行了解析研究(板与地基接触面为不透水边界, 其余为透水边界). 首先, 基于Kirchhoff理论和Biot多孔介质理论建立矩形板与饱和多孔地基的动力控制方程, 进行耦合求解. 针对板土接触面和非接触面的混合边值问题, 采用双重Fourier变换构造出两对二维对偶积分方程, 以接触应力和接触面孔隙压力为基本未知量, 用Jacobi正交多项式将未知量展开, 再利用Schmidt法对二维对偶积分方程完成求解, 最终推导出板土系统在动力作用下的位移和应力解析式. 通过将本文计算模型退化为单一弹性地基, 与已有研究结果进行对比, 验证了本文方法的正确性和有效性. 最后, 通过数值算例, 对饱和多孔地基上矩形板的动力响应及参数影响做出分析和讨论. 此外, 本文提出的解析法具有一般性, 可广泛应用于复杂接触问题和多场耦合问题的求解.