Footbridge lateral vibration remains an unsolved problem and is characterized by the following: (1) pedestrians are sensitive to bridge vibration, which causes the pedestrian’s excitation being dependent on the bridge vibration; (2) pedestrian lateral excitation is a stochastic process rather than a perfect periodic load. Therefore, footbridge lateral vibration is essentially a complex nonlinear stochastic vibration system. Thus far, an effective method of dealing with such nonlinear stochastic vibration of footbridges remains lacking. A framework based on the probability density evolution (PDE) method is presented. For the mathematical model, the parameter resonance model is used to describe the pedestrian-bridge interaction while treating the pedestrian lateral excitation as a narrow-band process. For the analysis method, PDE is used to solve the nonlinear stochastic equations in combination with the number theoretical and finite difference methods. The proposed method establishes a new approach in studying footbridge lateral vibration. First, PDE based on the small sample strategy avoids the large amount of computation. Second, the randomness of both structural parameters and pedestrian lateral excitation could be taken into consideration by the proposed method. Third, based on the probability results with rich information, the serviceability, dynamic reliability, and random stability analyses are realized in a convenient manner.
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