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The pedestrian-bridge dynamic interaction problem in the vertical direction based on a bipedal walking model and damped compliant legs is presented in this work. The classical finite element method, combined with a moving finite element, represents the motion of the pedestrian in the dynamic analysis of a footbridge. A control force is provided by the pedestrian to compensate for the energy loss due to the system damping in walking and to regulate the walking performance of the pedestrian. The effects of leg stiffness, the landing angle of attack, the damping ratio of the leg and the mass ratio of the human and structure are investigated in the numerical studies. Simulation results show that the dynamic interaction will increase with a larger vibration level of the structure. More external energy must be input to maintain steady walkitig and uniform dynamic behavior of the pedestrian in the process. The simple bipedal walking model could well describe the human-structure dynamic interaction.

This paper proposes a vertical crowd-structure interaction (CSI) model, considering the social force interaction effect among pedestrians. Pedestrian, as the basic unit of crowd, is modeled by a dynamic bipedal system with one lump mass and two compliance legs. The CSI model can be applied to self-determining the walking velocities of pedestrians instead of the sensitive passive control force for a stable gait from the original human–structure interaction (HSI) model. The damping compliance legs are responsible for the energy transfer between the pedestrian and the supporting structures during the dynamic walking process. Numerical studies with several pedestrians walking on a simply supported beam show an improvement of the damping property of the structure, but a decrease of the deterioration of natural frequency of the structure. The experiences gained in this study can be adopted for further study on the more complicated social force interaction among pedestrians in a large crowd passing some slender structures such as large-span footbridge.

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