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上覆单相弹性层的饱和地基上刚性基础竖向振动的轴对称混合边值问题 总被引:5,自引:1,他引:4
运用作者提出的饱和土弹性波动方程,从理论上研究了上覆单相弹性土层的饱和地基上刚性基础的竖向振动轴对称问题,即采用Hankel积分变换技术并按混合边值条件建立了部分饱和地基上刚性基础竖向振动的对偶积分方程,并将其蜕化为完全饱和地基的情形;该对偶积分方程可化为易于数值计算的第二类Fredholm积分方程。文末的算例给出了地基表面动力柔度系数Cv随无量纲频率a0的变化曲线。 相似文献
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研究了层状横观各向同性饱和地基上弹性圆板的非轴对称振动问题.首先,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三维动力方程转化为一阶常微分方程组,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;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例. 相似文献
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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,即首先利用Fourier展开和Hankel变换技术,求解了简谐激励下横观各向同性饱和土地基的非轴对称Biot波动方程,然后按混合边值问题建立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,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程.文末给出了算例.数值结果表明,在一定频率范围内,地基表面的位移幅值随激振频率增加而增大,随距离的增大以振荡形式衰减变化. 相似文献
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用第二类Fredholm积分方程求解弹性半空间上弹性板的垂直振动 总被引:4,自引:0,他引:4
根据混合边值条件,建立均布简谐荷载作用下弹性半空间上弹性板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,并进行了数值计算. 相似文献
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横观各向同性饱和地基的三维动力响应 总被引:5,自引:1,他引:4
首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式.在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例. 相似文献
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基于直角坐标系下Biot固结的基本控制方程,并考虑软土土骨架的黏弹性特性,通过Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论,推导了黏弹性地基Biot固结三维空间问题和平面应变问题在积分变换域的解析解,进而得到对应问题的单元刚度矩阵.然后根据对号入座原则组装得到层状黏弹性地基Biot固结对应问题的总体刚度矩阵.通过求解总体刚度矩阵形成的线性代数方程,得到层状黏弹性地基Biot固结对应问题在积分变换域内的解答.最后应用Fourier-Laplace逆变换得到其物理域内的解.对比求解黏弹性Biot固结问题退化的弹性Biot固结问题与已有解答,验证了刚度矩阵计算方法的正确性,为层状黏弹性地基Biot固结问题提供了理论基础. 相似文献
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Dynamic Green's function plays an important role in the study of various wave radiation, scattering and soil-structure interaction problems. However, little research has been done on the response of transversely isotropic saturated layered media. In this paper, the 3D dynamic responses of a multi-layered transversely isotropic saturated half-space subjected to concentrated forces and pore pressure are investigated. First, utilizing Fourier expansion in circumferential direction accompanied by Hankel integral transform in radial direction, the wave equations for transversely isotropic saturated medium in cylindrical coordinate system are solved. Next, with the aid of the exact dynamic stiffness matrix for in-plane and out-of-plane motions, the solutions for multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure are obtained by direct stiffness method. A FORTRAN computer code is developed to achieve numerical evaluation of the proposed method, and its accuracy is validated through comparison with existing solutions that are special cases of the more general problems addressed. In addition, selected numerical results for a homogeneous and a layered material model are performed to illustrate the effects of material anisotropy, load frequency, drainage condition and layering on the dynamic responses. The presented solutions form a complete set of Green's functions for concentrated forces (including horizontal load in x(y)-direction, vertical load in z-direction) as well as pore pressure, which lays the foundation for further exploring wave propagation of complex local site in a layered transversely isotropic saturated half-space by using the BEMs. 相似文献
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In this paper, an effective numerical algorithm for 2.5D seismic and acoustic-gravitational wave propagation is applied to a combined “Earth-Atmosphere” model in the presence of wind in the air. Seismic wave propagation in an elastic half-space is described by a system of first-order dynamic equations of elasticity theory. The propagation of acoustic-gravitational waves in the atmosphere in the presence of wind is described by the linearized Navier-Stokes equations. The algorithm is based on the integral Laguerre transform with respect to time, the finite integral Fourier transform with respect to a spatial coordinate combined with a finite difference method for the reduced problem. 相似文献
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The complete 3D dynamic Green’s functions in the multilayered poroelastic media are presented in this study. A method of potentials in cylindrical coordinate system is applied first to decouple the Biot’s wave equations into four scalar Helmholtz equations, and then, general solutions to 3D wave propagation problems are obtained. After that, a three vector base and the propagator matrix method are introduced to treat 3D wave propagation problems in the stratified poroelastic half-space disturbed by buried sources. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. At last, the validity of the present approach for accurate and efficient calculating 3D dynamic Green’s functions of a multilayered poroelastic half-space is confirmed by comparing the numerical results with the known exact analytical solutions of a uniform poroelastic half-space. 相似文献
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The problem of an elastic half-space with stress-free surface and a crack of arbitrary shape with prescribed displacements or tractions is reduced to an equivalent system of integral equations on the crack. For a pressurized crack in a plane perpendicular to the free surface, a scalar integral equation is derived. In properly chosen function spaces, unique solvability of the integral equation and regularity of solutions for regular data are proven. 相似文献
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变温度荷载作用下半无限成层饱和介质的热固结分析 总被引:1,自引:0,他引:1
对半无限成层饱和多孔介质作用随时间变化的温度荷载的热固结问题进行解析求解.其中,热-水-力耦合线性弹性控制方程考虑了热渗效应和等温热流效应的影响.先采用Laplace变换求其在变换域上的解,然后用数值方法求逆变换.对半无限体表面作用呈指数衰减热荷载的双层体系进行研究,分析了两层介质热固结系数、弹性模量等的差异性对热固结特征的影响.研究表明:位移场和应力场对温度场的耦合作用可以忽略,而热渗效应对温度和孔压有显著影响. 相似文献
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Michihiro Kitahara Yoshiji Niwa Sohichi Hirose Mikio Yamazaki 《Applied Mathematical Modelling》1984,8(6):397-407
A coupled system of integral equations (of the domain and boundary types) is formulated for the elastodynamic response analysis of a locally inhomogeneous body on a homogeneous elastic half-space. The method uses the fundamental solution for homogeneous elastostatics in the inhomogeneous domain owing to the lack of a fundamental solution in inhomogeneous elastodynamics.
The integral representation of displacements in the inhomogeneous domain is formulated with the help of this elastostatic fundamental solution by considering the term induced by the inhomogeneity of materials and the acceleration term as the body force term. Then the Green's matrix is obtained numerically from this integral representation and combined with the ordinary boundary integral equations, which are valid in the exterior homogeneous half-space.
Some numerical examples show the efficiency and the versatility of this coupled method. 相似文献