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 exc...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, andrandom 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 anew method, IEVIE–SA, which combines the energy method based on the comparison between the input energyand the variation of intrinsic energy (IEVIE) and the stochastic averaging (SA) method. The improved Nakamuramodel was used to describe the lateral nonlinear stochastic vibration of a footbridge, whereby the IEVIE methodwas used to establish the criteria for judging the lateral vibrational stability. Additionally, the SA method was usedto deduce the corresponding backward Kolmogorov equation. Subsequently, the backward Kolmogorov equationwas combined with the stability criterion established by the IEVIE method to analyze the first passage stability. Theproposed method is a semi-analytical, quantitative method that only requires a small calculation. By applying theproposed method to the Millennium Bridge, method effectiveness was verified by comparing it with the MonteCarlo and traditional Lyapunov methods.展开更多
基金This research was supported by the National Natural Science Foundation of China(No.51608207)the Natural Science Foundation of Guangdong Province,China(No.2019A1515011941).
文摘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, andrandom 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 anew method, IEVIE–SA, which combines the energy method based on the comparison between the input energyand the variation of intrinsic energy (IEVIE) and the stochastic averaging (SA) method. The improved Nakamuramodel was used to describe the lateral nonlinear stochastic vibration of a footbridge, whereby the IEVIE methodwas used to establish the criteria for judging the lateral vibrational stability. Additionally, the SA method was usedto deduce the corresponding backward Kolmogorov equation. Subsequently, the backward Kolmogorov equationwas combined with the stability criterion established by the IEVIE method to analyze the first passage stability. Theproposed method is a semi-analytical, quantitative method that only requires a small calculation. By applying theproposed method to the Millennium Bridge, method effectiveness was verified by comparing it with the MonteCarlo and traditional Lyapunov methods.
