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.