Discussion of “Model for Lateral Excitation of Footbridges by Synchronous Walking” by Shun-ichi Nakamura

This article comments on a research study of a pedestrian footbridge. The researcher (Nakamura, 2004) observed that on a pedestrian cable-stayed bridge that the girder vibrated laterally with a frequency of about 0.9 Hz, the natural frequency of the first lateral mode, when a large number of people crossed the bridge. Once the bridge started to vibrate, some of the pedestrians synchronized with the girder vibration, which further increased the girder response. However, when the vibration reached a certain level, pedestrians modified their walking and the girder response stayed at that level. The researcher proposed a dynamic model to evaluate the pedestrians' synchronized dynamic forces. This commentary author contends that the researcher's equation in the form of a nonlinear, second-order differential equation has no analytical solution; each individual case must be solved by numerical methods. This can be daunting to a design engineer. The commentary author then offers a solution that falls within an "amplitude envelope." The commentary author concludes that both the original model and his proposed equations are correct; the choice of approach should be governed by ease of practical use.