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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.
Taking the displacement component as the basic unknowns, the dynamic partial differential equation of plane strain problem in orthotropic anisotropic foundation is established in Cartesian coordinates.The initial conditions and boundary conditions are introduced by using Laplace-Fourier transform and inverse transformation method, and the arbitrary form Integral formal solution to the dynamical response of plane problem of orthotropic foundation under the action of surface dynamic load. Based on the theoretical solution, the corresponding calculation program is compiled and the linearly moving resonance load of the surface of orthotropic soils The case study was carried out to study the variation law of vertical displacement amplitude of each point on the soil surface caused by different parameters of soil, load moving speed and load frequency, as well as the influence law of load velocity on vertical stress component.Results of numerical analysis The results show that: the anisotropy of soil, load frequency and moving speed have great influence on the amplitude of surface displacement, and the damping ratio of soil has less influence on the amplitude of displacement near the center of load. For load on vertical load, A greater impact, which has important guiding significance for engineering practice.