行动载荷作用下的连续梁的横向振动问题

本文在考虑行动载荷质量、惯性力及阻尼影响的情况下,研究了机车通过连续梁时横向振动问题的整个过程,并得出了在任意行动载荷PF(t)作用下的连续梁的动力方程的一般解.我们具体计算了单个行动载荷为P_i+Q_isin(a_it+ε_i)时的情形并建立了行动载荷作用下的连续梁横向振动问题的动力理论.最后,做为例子,我们求解了两跨梁的横向振动问题,跨中点的挠度如图2和图3所示.

Vibration Theory of Continuous Beam under the Action of Moving Load

This paper uses the small parameter method to investigate the dynamic calculation of the whole vibration process of trains passing through a continuous beam, considering the effects of the mass and the damping as well as the masses of the moving loads. By solving a set of integral equation, we find out the general solution of continuous beam under the action of arbitrary moving load PF(t) and calculate the case of single moving load being Q_#em/em#+P_#em/em#sin(a_#em/em#t + b_#em/em#). By concluding our results, we establish the dynamic theory of vibration of continuous beam acted by the moving load.Finally, as an example, we calculate the vibration question of two-span continuous beam. The deflections of two midspan are shown in Fig. 2 and Fig. 3.