移动荷载下粘弹性地基上无限大板的稳态响应

Steady State Response of Infinite Plate on Visco-elastic Foundation Subjected to Moving Load

针对高速交通体系引起的结构与地基振动问题,采用移动荷载作用下Kelvin地基上的无限大板作为力学分析模型,分析了运动车辆荷载作用下路面体系的动力响应。首先采用三维Fourier变换法导出了板在任意匀速运动荷载作用下的稳态挠度的一般解,然后推导了各种移动荷载作用下板挠度的二维积分解析解,包括恒常和简谐移动矩形均布荷载、线均布荷载、集中荷载,最后采用自适应数值积分算法计算了板在移动集中恒载和移动矩形均布恒载作用下的挠度,比较了两种荷载作用下板挠度的异同。结果表明:上述两种荷载作用下板挠度的差异较小,可尝试将运动车辆作用于路面体系的荷载简化为移动集中荷载阵列考虑。

To investigate the dynamic response of freeway pavement system induced by moving vehicles, an infinite plate on Kelvin foundation subjected to moving load was employed to model the pavement system under running vehicles. By means of triple Fourier transform, the general solution for steady state deflection of the plate under constant velocity moving load was derived. The analytical solutions for deflections induced by specific moving load, ie generalized double integrals, were then elaborated respectively, including constant and harmonic moving rectangle load, line load and point load. The integrals were numerically evaluated by self-adaptive numerical integration algorithm. Numerical results for constant moving point load and rectangle load were presented and compared with each othcr. It shows that there are slight differences between deflections induced by these two types of load except that the maximum deflection is a bit larger under point load. In some cases, the load acted on the pavement system by running vehicles can be simplified to array of moving point load.