移动荷载作用下周期支撑无限长梁动力响应

摘要

A study is presented of the oscillation of an infinite beam which rests on identical periodic sim-ple elastic supports. The beam transverse defection is caused by a harmonic concentrated force,moving steadily along the beam. It is supposed that the beam had been at rest before the force approached and re-turned to rest after the force had moved away. It is further supposed that the beam defections at any pair of points,separated on the periodic support spacing,obey the special condition. The beam defection is gov-erned within the segment by the Euler-Bernoulli partial differential equation,four boundary conditions and the above mentioned suppositions. The Fourier transformation is used to solve the problem. Some numeri-cal examples and corresponding analysis are presented. If the angular velocity of the moving load is small, then the beam inertia forces are small in comparison with its elastic ones. In this case,the beam defection has to be near the quasi static defection of the beam without inertia. Also,the value of beam defection in-creases as the oscillation frequency and the velocity of the movin load grow.%基于解析法，分析了具有周期等间距弹性支撑的无限长梁在移动荷载作用下的动力响应。当荷载进入考察梁段之前与离开后，梁不会产生振动。而且对于梁在空间距离上呈周期对的观测点，动力响应相同。无限长梁的振动方程采用Euler-Bernoulli梁微分方程，同时满足4个空间边界条件，利用Fourier变换求解微分方程。数值计算表明，当荷载移动速度较小时，梁的振动为准静态；同时，随荷载速度与激励频率增大，梁的振动变形也较大。