Uncoupled approaches for walking-induced vertical vibration of a lively footbridge

The recent trend towards the design of flexible footbridges, characterized by a low ratio between permanent and variable load, has made them more sensitive to dynamic forces induced by pedestrians. While walking, the pedestrian moves on the flexible structure adapting his gait to the bridge motion and interacting with the footbridge. At contact points, the pedestrian transmits contact forces to the bridge that, in turn, imposes a set of displacements and velocities to the pedestrian’s feet. The pedestrian is here described with an increasing accuracy. Neglecting the interaction with the bridge, the pedestrian is described with a refined force model, that simulates the force pattern transmitted by each foot. The position of the two forces reproduces the sequence of single and double support phases, typical of the human gait. Interaction is accounted for when both systems are described as mechanical systems (having proper mass, stiffness and damping matrices). In this work a newly proposed bipedal pedestrian mass-spring-damper model is adopted, sharing with the force model the same type of locomotion. The mechanical system is excited by an equivalent bio-mechanical force and its equation of motion takes into account the interaction with the bridge. The coupled equations of motion of the bridge-pedestrian system are then derived; with a forced uncoupling of the equations, the two systems can be analyzed separately. The case study concerns a lively footbridge, whose dynamic response is computed with the different modeling approaches.