正交各向异性地基平面问题动力响应研究

以位移分量为基本未知量，在直角坐标系下建立正交各向异性地基的平面应变问题动力偏微分方程．采用Laplace-Fourier变换和逆变换方法，引入初始条件和边界条件，推导了任意形式表面动荷载作用下正交各向异性地基平面问题在时域内动力反应的积分形式解．基于理论解，编制了相应的计算程序，并对正交各向异性土
体表面作用线性移动谐振荷载进行了算例分析，研究了土体参数、荷载移动速度、荷载频率不同而导致的土体表面各点竖向位移幅值的变化规律，以及荷载速度对竖向应力分量的影响规律．数值分析结果表明：土体的各向异性、荷载频率和移动速度对表面位移幅值有较大影响，土体阻尼比对于荷载中心点附近的位移幅值影响较小；荷载移动速度对于竖向应力分量有较大影响，这对工程实践具有重要指导意义．

Research on Two-Dimensional Dynamic Response of Orthotropic Medium

With displacement as the basic unknown quantity, the dynamic partial differential equations of plane strain problem were established for orthotropic medium in Cartesian coordinate system. The initial and boundary conditions were introduced. The integral forms of the dynamic responses of orthotropic half-space medium under arbitrary dynamic loads were derived by using the technique of Laplace-Fourier integral transforms and reverse transforms. Based on the theoretical solutions, a computational program was developed to calculate the numerical examples of orthotropic soil medium under the moving harmonic vibrating strip load applied on the surface. The effects of soil parameters, load speeds, load frequencies and different depth on the amplitude of the surface vertical displacement were studied. The effect of the load moving speed on the vertical stress component was also investigated. The numerical results show that the soil orthotropy, the loading frequencies and moving speeds have significant influences on the surface vertical displacement amplitude. The damping ratio of soil has little impact on displacement amplitude near the load center. The load moving speed has a great influence on vertical stress component. The results could have an instructional significance to the engineering practice.