Swaying of Pedestrian Bridges

The paper considers nonlinear (autoparametric) resonance in footbridges as a reason for excessive lateral vibrations induced by walking pedestrians. To describe the above-mentioned phenomenon, a physical model (an elastic pendulum) is proposed. Under the special frequency conditions (the ratio between frequencies of vertical and lateral beam modes is about 2, or 2:1), nonlinear resonance becomes possible if a vertically excited mode is near a primary resonance and a load parameter (a static displacement caused by pedestrians) is equal or more than its critical value. When the increasing load parameter passes through the critical value, a jump phenomenon is observed for the lateral mode and the vertical mode is saturated. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of the jump phenomenon), described in the paper, is the condition for the beginning of the second step—the process of interaction between applied forces and the lateral mode of vibration.