简支梁移动质量响应分析

随着行车速度与交通量不断增加,荷载不断加重,桥梁的移动荷载响应越来越得到人们的重视.考虑移动车辆的惯性效应与桥梁的阻尼效应时,需要把车辆荷载简化为移动质量进行研究,这时得到的控制方程是变系数偏微分方程,在数学上通常难以精确求解.经分离变量与模态叠加后,化为变系数常微分方程组.本文利用WKB法,得到了近似的动力学响应,并与数值解、移动常力、Inglis解进行了比较.

Analysis of the dynamic response of a simple supported beam under a moving mass

With the increasing of the vehicle speed, traffic volume and moving loads, the dynamic response of bridges under moving loads attracts more and more attentions. If one considers the inertia effect of moving vehicle and the damping effect of bridges, the moving vehicle could be modeled as a moving mass. Its govern equation is a partial differential equation with variable coefficients. The equation is usually difficult to solve exactly in mathematics. Using the variable separation and modal superposition method, the partial differential equation is reduced as an ordinary equation with variable equation set. Using the method of WKB method, an approximate solution of the problem is obtained, which is compared with the results of numerical simulation, the solutions of moving constant forces and Inglis.