Resonance and cancellation phenomena in partially clamped simply supported beam bridges under moving trains

Since the development of new railway lines of high speed, the dynamic response of bridges belonging to them constitutes a subject interest for researchers and engineers, in particular at resonance. In the present work, an analytical approach is developed to analyze the dynamic response of a single ballasted track railway bridges supported by identical rotational springs and subjected to the circulation of moving loads at constant speeds. Although the introduction of rotary springs at the ends of the deck enhances the choice of the appropriate analysis model, where most of the contributions reported in this field do not consider this effect. The central idea of the proposed model is based on analyzing the continuity effect of the ballasted track (rails and ballast) on the dynamic response of railway bridges, with taking into account an axial force that models the effect of prestressing, longitudinal ballast-bridge interface, axial displacement, force braking. The equation of motion of the system is derived by using the Hamilton's principle, two dynamic case studies of a simply supported and simply supported partially clamped Euler-Bernoulli beam are presented. The results revealed that the compression force presents an additional stiffness which affects the critical velocity and that the continuity of the track modeled by rotational springs at the beam's end, as it increases the dynamic response decreases. Also, a dynamic analysis for the conditions for maximum response and cancellation in free vibration are derived and interpreted particularly the effect of the geometric scheme of train axles. Equating the condition for resonance of maximum free response and cancellation, cancelled resonance are obtained.