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Research on the lateral vibrational stability of footbridges has attracted increasing attention in recent years. However, this stability contains a series of complex mechanisms, such as nonlinear vibration, random excitation, and random stability. The Lyapunov method is regarded as an effective tool for analyzing random vibrational stability; however, it is a qualitative method and can only provide a binary judgment for stability. This study proposes a new method, IEVIE–SA, which combines the energy method based on the comparison between the input energy and the variation of intrinsic energy (IEVIE) and the stochastic averaging (SA) method. The improved Nakamura model was used to describe the lateral nonlinear stochastic vibration of a footbridge, whereby the IEVIE method was used to establish the criteria for judging the lateral vibrational stability. Additionally, the SA method was used to deduce the corresponding backward Kolmogorov equation. Subsequently, the backward Kolmogorov equation was combined with the stability criterion established by the IEVIE method to analyze the first passage stability. The proposed method is a semi-analytical, quantitative method that only requires a small calculation. By applying the proposed method to the Millennium Bridge, method effectiveness was verified by comparing it with the Monte Carlo and traditional Lyapunov methods.

Stability Reliability of the Lateral Vibration of Footbridges Based on the IEVIE-SA Method