饱和地基上含刚核弹性圆板的摇摆振动分析

基于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摇摆谐和力矩作用下的振动特性。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。此外,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。     

基于Boer多孔介质理论的饱和半空间上刚性圆板基础竖向振动特性研究

针对饱和黏弹性半空间地基上刚性圆板基础竖向振动问题,基于Boer多孔介质动力控制方程组,应用Hankel积分变换技术并结合基础与地基土接触面混合边值条件,推导求解相关方程得到了饱和黏弹性半空间地基上刚性圆板基础的竖向动力阻抗以及振幅放大系数公式。在此基础上进一步通过数值算例对比分析探讨了液固耦合系数、基础质量比、地基土黏滞阻尼系数对所得基础竖向动力阻抗及振幅放大系数的影响规律。解析推导得出的对应竖向动力阻抗三维精确解不但丰富了基础振动理论,还可为相关工程实践提供参考和理论支持。     

粘弹性层状半空间上刚体的垂直振动

本文较深入地研究了层状粘弹性半空间上刚性圆形基础的垂直振动问题。首先作者采用独创的方法求解弹性动力学基本方程，并借助于Ｔｈｏｍｓｏｎ Ｈａｓｋｅｌ的传递矩阵方法得出层状地基表面位移的Ｈａｎｋｅｌ变换式。然后按弹性力学混合边值问题建立层状粘弹性地基上刚体垂直振动的对偶积分方程，并化为第二类Ｆｒｅｄｈｏｌｍ积分方程。文末给出了数值算例。     

层状横观各向同性地基性质对刚性条基摇摆振动的影响

分析了土体的横观各向同性及层状性质对刚性条形基础摇摆振动的影响。首先利用解析层元法得出层状横观各向同性地基的总刚度矩阵。再根据刚性条形基础与地基相互作用的混合边值条件,建立了一组对偶积分方程,并借助Jacobi正交多项式求解了该对偶积分方程,从而得到地基动力柔度系数。计算结果与已有文献的结果吻合较好。同时,算例结果表明:土的水平向与竖向弹性模量比的减小、竖向的剪切模量与弹性模量比的增大,以及水平向泊松比与竖向泊松比比值的增大,都将导致地基动力柔度系数增大;而且,层状地基中上层土的弹性模量的减小使得地基动力柔度系数也增大。     

埋置移动荷载作用下成层饱和地基的动力响应

利用Fourier变换和传递反射矩阵法（TRM法）研究了成层饱和地基在埋置移动荷载作用下的动力响应。土体被假设为完全饱和的多孔弹性介质并且服从Biot多孔弹性波动方程,用修正粘滞阻尼模型来描述土体的粘弹性行为,采用TRM法来考虑饱和地基的成层性,利用Fourier变换和Fourier逆变换得到了埋置移动荷载作用下饱和地基动力响应积分形式解答。当饱和成层地基退化单层饱和地基时,该文解与已有解能很好的吻合。最后,通过数值计算分析了埋置荷载深度﹑荷载速度、荷载频率及软硬夹层对动力响应的影响。     

饱和弹性半空间地基与中厚圆板的动力相互作用

利用Fourier-Bessel级数,对横观各向同性饱和弹性半空间地基与中厚圆板的动力相互作用问题进行了系统地分析。板的位移函数、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数由板的边界条件、板的控制方程及板-地基的相容条件加以确定,从而将饱和弹性半空间地基与中厚圆板的动力相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解答具有较快的收敛速度。可以将该方法推广到弹性半空间与梁、矩形板相互作用问题的分析。     

饱和地基上弹性圆板的固结位移

 采用Laplace变换及Hankel变换研究弹性圆板在饱和地基上的固结位移．在Laplace变换域上建立了求解弹性圆板固结位移的第二类Fredholm积分方程，由数值反变换获得时域解，给出了对工程实践有参考价值的计算结果．计算结果表明，弹性板的固结位移随饱和土的排水泊松比的减少而增加，而弹性板的初始位移随饱和土的不排水泊松比的减少而增加．     

饱和层状地基条形基础动刚度的精细积分算法

采用基于积分变换、对偶方程和精细积分的算法求解饱和多层地基条形基础的动刚度问题。利用Fourier积分变换得到Biot多孔饱和介质波动方程在频域-波数域内的常微分方程,引入广义对偶变量,对二阶常微分波动方程进行降阶处理;针对地表自由排水和封闭排水边界条件,给出了适于精细积分算法的矩阵表达;对控制方程采用精细积分解答,得到波数域内的格林函数,对结果进行逆Fourier积分变换,得到空间域的力和位移关系;施加边界条件,最终得到刚性条形基础的动刚度的解答。通过与文献已有结果进行对比,验证了精细积分算法的准确性。最后计算两组算例,分别分析了表面薄层的孔隙率、渗透力阻尼系数对条形基础动刚度的影响。     

饱和地基上列车运行引起的地面振动特性分析

从饱和土Biot波动方程出发,基于二次形函数薄层法,将圆柱坐标系下饱和土的Biot轴对称波动方程在竖向进行离散,沿切向及轴向坐标分别进行Fourier级数分解和Hankel变换,得到饱和地基频域-波数域中的位移基本解,再利用Hankel逆变换和Fourier综合,求得频域柱坐标系下的位移表达。结合移动列车-轨道-地基的振动模型,对饱和地基上列车运行引起的地面振动进行了分析,讨论了动力渗透系数、孔隙率和动力流体粘滞系数等参数对地面振动传播与衰减的影响规律,并与弹性地基的振动衰减进行了比较。结果表明:在不同列车运行速度下,饱和地基和弹性地基的竖向位移振动响应差异较大;饱和土体的动力渗透系数、孔隙率和孔隙流体动力粘滞系数是影响地面振动的主要参数。     

饱和土中管桩的扭转振动特性研究

基于Biot提出的饱和多孔介质的波动方程,研究了均质各向同性饱和土中端承管桩的扭转振动问题。首先对土层动力平衡方程进行求解并得到土体扭转振动位移形式解,然后对管桩的动力平衡方程进行求解,得到了管桩桩顶转角解析解,进一步通过数值算例分析了桩周土与桩芯土的物理力学参数对管桩桩顶复刚度和桩身转角的影响。数值分析结果表明,在动力基础设计所关注的低频段,桩周土与桩芯土的剪切模量比、壁厚以及桩的长径比对管桩的动力响应有较大的影响,而液固耦合系数的影响很小。     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程并得到传递矩阵。进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题。数值算例表明采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的动力特性。     

Investigation of vertical vibrations of rigid disk on saturated poroelastic stratum under high-frequency excitation

The forced high-frequency vertical vibrations of a rigid circular disk on a saturated poroelastic stratum supported by a rigid rock foundation are studied. An exact formulation is developed for the dual integral equations governing the mixed boundary-value problem of the vertical vibration. By finding an approximate solution to the exact governing dual integral equations, an evaluation of the amplitude response of the rigid disk is presented for the case of a frictionless contact both between the disk and the stratum and between the stratum and the foundation. The influences of parameters regarding the disk and the elastic stratum on the amplitude response of the disk are discussed. It is concluded that the amplitude response of the disk is dependent on the exciting frequency, the depth of the stratum, the Poison’s ratio of the solid skeleton, the porosity of the medium and the radius and mass of the disk.     

Slow torsional oscillations: The reissner-sagoci and crack problems at low frequencies

The axisymmetric elastic field produced by slowly forced torsional oscillations of a finite circular fiaw in a certain inhomogeneous medium is sought. The problem is reduced to a system of integral equations, which system is shown to cover intrinsically, the two separate cases of the flaw in the form of a penny-shaped crack and the flaw in the form of a rigid disc. The solutions are given in series of the frequency factor. Estimates of the radius of convergence are given as functions of the inhomogeneity parameter. For the flaw in the form of a rigid disc, the solution of the integral equations gives the normal displacement gradient just above the disc, from which simple integration gives the moment of the applied forces necessary to oscillate the disc. In the case of the flaw in the form of a penny-shaped crack, the solution gives the normal displacement over the crack region. This is then used to obtain the surface shear stress just outside the crack rim, from which is obtained the stress intensity factor. These physical results are all given as functions of the frequency factor and inhomogeneity parameter.     

Coupled horizontal and rocking vibrations of a rigid circular plate on a transversely isotropic bi-material interface

This paper investigates the coupled rocking and horizontal vibratory response of a rigid circular plate embedded in viscoelastic, transversely isotropic, three-dimensional unbounded media. The boundary-value problem corresponding to the case of distributed horizontal and rocking ring loads at a bi-material interface is solved to obtain the required influence functions for the solution of the present problem. The case of an embedded rigid plate is formulated in terms of a discretized integral equation, which couples the rigid body displacements of the plate with the tractions acting over its contact surface through a set of displacement influence functions. The system of resulting discretized integral equations is solved numerically. The solution results in the tractions over each disc element. This paper carefully takes into account the coupling of the rocking and horizontal responses of the plates that is typical of non-homogeneous interfaces, i.e., their horizontal displacements due to rocking moments and their rotations due to horizontal loads. The dynamic direct and cross compliances of the embedded plate are shown for different governing parameters such as frequency of excitation and bi-material configuration. The present results are useful to the study of dynamic response of deeply buried foundations and anchors in non-homogeneous soils.     

Torsional impact of a layer or a cylinder bonded to an elastic half-space

In this paper two torsional impact problems are considered. The first problem deals with the solution of a layer bonded to an elastic half-space when the layer is driven by the torsional impact over a bonded rigid circular disc. In the second problem sudden torsion by a rigid disc attached over the plane face of a circular cylinder is considered and the rest of the plane surface of the cylinder is stress free. The cylinder is bonded to the half-space, making use of Laplace and Hankel transforms the solution of each problem is reduced into Fredholm integral equations of the second kind. A numerical Laplace inversion technique is then used to recover the time depencence of the solution. The numerical values for the applied torque at the surface of rigid disc are calculated for each problem and then are displayed graphically.     

Vibration analysis of a poroelastic composite hollow sphere

Vibrations in a poroelastic composite hollow sphere are investigated employing Biot’s theory of wave propagation in poroelastic media. A composite hollow poroelastic sphere consists of two concentric poroelastic spherical layers both of which are made of different poroelastic materials with each poroelastic material being homogeneous and isotropic. The boundaries of the composite hollow poroelastic sphere are free from stress. The frequency equations of both radial and rotatory vibrations are obtained each for pervious and impervious surfaces. The frequency equation of vibrations of a poroelastic composite hollow sphere with rigid core is derived as a particular case. The non-dimensional frequency for propagating modes is computed as a function of ratio of thickness to inner radius of core. The results are presented graphically for two types of poroelastic composite spheres and then discussed.     

Hybrid-Trefftz displacement element for poroelastic media

The elastodynamic response of saturated poroelastic media is modelled approximating independently the solid and seepage displacements in the domain and the force and pressure components on the boundary of the element. The domain and boundary approximation bases are used to enforce on average the dynamic equilibrium and the displacement continuity conditions, respectively. The resulting solving system is Hermitian, except for the damping term, and its coefficients are defined by boundary integral expressions as a Trefftz basis is used to set up the domain approximation. This basis is taken from the solution set of the governing differential equation and models the free-field elastodynamic response of the medium. This option justifies the relatively high levels of performance that are illustrated with the time domain analysis of unbounded domains.     

Dynamic responses of a pile embedded in a layered poroelastic half-space to a harmonic axial loading

The dynamic response of a single pile embedded in a layered poroelastic half-space to an axial harmonic load is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile subjected to a harmonic axial load is constructed. The proposed model is validated by comparing a special case of our model with an existing result. Based on numerical results of this paper, it is concluded that the presence of a stiffer or a softer middle layer in the layered half-space will affect the impedance of the pile considerably and the inhomogeneity of the half-space will enhance the pore pressure significantly.