Abstract: 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_i+ P_isin(a_it + b_i). 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.

Key words: nonlinear, reaction diffusion, singular perturbation