层状横观各向同性饱和地基上圆板的非轴对称振动

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．     

横观各向同性饱和地基上刚性圆板的扭转振动

通过解析方法研究了横观各向同性饱和半空间上刚性圆板在简谐扭转荷载作用下的振动问题．运用Hankel变换求解了横观各向同性饱和土的动力控制方程,结合混合边界条件得出了刚性基础的扭转对偶积分方程,并将对偶积分方程转化为第二类Fredholm积分方程求解了基础的扭转振动问题,同时给出了动力柔度系数,基础的角位移幅值和基底接触剪应力的表达式．通过数值算例研究了地基的各向异性程度对基础扭转振动的影响．     

横观各向同性饱和弹性多孔介质非轴对称动力响应

应用Fourier展开和Hankel变换求解了简谐激励下横观各向同性饱和弹性多孔介质的非轴对称Biot波动方程,得到了一般解。用一般解给出了多孔介质总应力分量的表达式。最后对求解横观各向同性饱和弹性多孔介质非轴对称动力响应边值问题的方法作了系统说明,并且给出了数值分析特例。     

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

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C_v随无量纲频率a₀的变化曲线。     

饱和地基上弹性基础的竖向振动特性研究

采用解析的方法研究了饱和地基上受一简谐竖向荷载作用下弹性基础的动力响应．在分析中,首先利用积分变换技术获得了饱和介质基本控制方程的变换解,然后基于基础-半空间完全放松接触、半空间表面完全透水或不透水的假设,建立了该动力混合边值问题的对偶积分方程,并把该对偶积分方程进一步化为易于数值求解的第二类Fredholm积分方程A·D2文末数值算例给出了动力柔度系数、位移和孔隙水压力随振动频域和土-基础体系物理力学参数特性的变化曲线．结果表明:饱和地基上弹性基础的动力响应完全不同于饱和地基上刚性圆板的动力响应．所用方法可用于研究波的传播、土-结构动力相互作用等许多问题．     

功能梯度圆板的轴对称自由振动

基于三维弹性理论,用直接位移法求解了横观各向同性功能梯度圆板的轴对称自由振动,其材料特性沿板厚度方向按指数形式变化,在弹性简支和刚性滑动两种边界条件下得到了三维精确解,即它逐点满足基本方程和边界条件,最后给出了数值算例并与以前的工作进行了对比.该方法也可推广应用于材料特性沿板厚度任意变化情形.     

集中载荷作用下层合厚圆板的轴对称弯曲

从三维弹性力学基本方程出发,建立了横观各向同性层合圆板轴对称弯曲问题的状态方程,并将板面的集中载荷展成付里叶贝塞尔级数,从而给出问题的解析解,此解满足弹性力学全部方程,计及了所有独立的弹性常数,并满足层间连续性条件。     

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

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.     

无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动

在无限介质中,研究了横截面为圆的柱形孔洞表面上瞬时径向力或扭转引起的扰动,讨论了高阶黏弹性和横观各向同性弹性参数的非均匀性对扰动产生的影响．根据高阶黏弹性Voigt模型,将非零应力分量简化为径向位移分量项表示,这对横观各向同性和高阶黏弹性固体介质是合宜的．导出了含有弹性和黏弹性参数以幂律变化时的应力方程．在瞬时力和扭转边界条件下,求解该方程,求得径向位移分量以及和它相关的应力分量,用修正的Bessel函数项来表示．对瞬时径向力作用问题进行了数值分析,并给出了不同阶的黏弹性和非均质性时的位移和应力变化图形．扭转作用时扰动的数值解可以用类似的方法研究,这里不再深入讨论．     

横观各向同性饱和地基的三维动力响应

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．     

Boussinesq indentation of a transversely isotropic half-space reinforced by a buried inextensible membrane

The normal indentation of a rigid circular disk into the surface of a transversely isotropic half-space reinforced by a buried inextensible thin film is addressed. By virtue of a displacement potential function and the Hankel transform, the governing equations of this axisymmetric mixed boundary value problem are represented as a dual integral equation, which is subsequently reduced to a Fredholm integral equation of the second kind. Two important results of the contact stress distribution beneath the disk region as well as the equivalent stiffness of the system are expressed in terms of the solution of the Fredholm integral equation. When the membrane is located on the surface or at the remote boundary, exact closed-form solutions are presented. For the limiting case of an isotropic half-space the results are verified with those available in the literature. As a special case, the elastic fields of a reinforced transversely isotropic half-space under the action of surface axisymmetric patch loads are also given. The effects of anisotropy, embedment depth of the membrane, and material incompressibility on both the contact stress and the normal stiffness factor are depicted in some plots.     

3D dynamic responses of a multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure

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.     

压电压磁复合材料中界面裂纹对弹性波的散射

利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题．经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式．数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同．