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由于路面不平整,车辆会以一定的频率和振幅在路面上运动,研究简谐移动荷载作用下单相弹性地基的动态响应具有更加现实的意义。将移动单元法引入到单相弹性介质的半解析方法中,构造了随荷载以相同速度运动的移动层单元。基于移动坐标下单相弹性介质的动力控制方程和边界条件,应用加权残数法建立了简谐移动荷载下单相弹性介质的三维动态响应半解析方程;将固定坐标下的动力问题转化为移动坐标下的拟静力问题,数值分析了简谐移动荷载作用下单相弹性地基的动态响应及其参数的影响。计算结果表明:在简谐移动荷载作用下,当无阻尼或小阻尼时,位移幅值随着速度变化不是单调递增或递减。当速度在瑞利波波速附近时,会出现各位移幅值的极大值(或第一极大值);当阻尼较大时,位移随着速度增加变化缓慢。这说明阻尼和频率的共同作用会有效地抑制位移幅值响应。研究结果表明本文所提供半解析移动单元法是研究简谐移动荷载下介质动态响应的一种简单有效的方法。
Due to the uneven road surface, the vehicle will move on the road with a certain frequency and amplitude. It is more realistic to study the dynamic response of single-phase elastic foundation under simple harmonic load. The moving element method is introduced into the semi-analytical method of single-phase elastic medium, and the moving layer element moving at the same speed with load is constructed. Based on the dynamic governing equations and the boundary conditions of single-phase elastic medium under moving coordinates, the semi-analytical solution of three-dimensional dynamic response of single-phase elastic medium under simple harmonic loading is established by using the weighted residual method. The dynamic problems under fixed coordinates are transformed into moving Under the simple quasi-static problem, the dynamic response of single-phase elastic foundation under simple harmonic load and the influence of its parameters are analyzed numerically. The calculated results show that the amplitude of the displacement does not increase or decrease monotonically with the change of velocity under no-damping or small-damping under simple harmonic load. When the velocity is near the Rayleigh wave velocity, the maximum value (or the first maximum value) of each displacement amplitude appears. When the damping is large, the displacement changes slowly with the increase of velocity. This shows that the combination of damping and frequency will effectively suppress the displacement amplitude response. The results show that the semi-analytical moving element method provided in this paper is a simple and effective method to study the dynamic response of the medium under simple harmonic moving loads.