The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration sta...The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration stability.At present,the Lyapunov method is mainly used to analyze such stability.However,this method is qualitative,and it cannot quantitatively analyze the vibration stability probability.In this study,a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE)is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge.The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge.A combination of the IEVIE method and the probability density evolution(PDE)method is then proposed,in which the IEVIE method is utilized to determine vibration stability.The PDE method is used to obtain the reliability of vibration stability.The proposed method is successfully applied to the Millennium Bridge,and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods.The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.展开更多
基金National Natural Science Foundation of China under Grant No.51608207,the Natural Science Foundation of Guangdong Province,China under Grant No.2019A1515011941,and China Scholarship Council under Grant Nos.201806155102 and 201906155028。
文摘The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration stability.At present,the Lyapunov method is mainly used to analyze such stability.However,this method is qualitative,and it cannot quantitatively analyze the vibration stability probability.In this study,a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE)is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge.The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge.A combination of the IEVIE method and the probability density evolution(PDE)method is then proposed,in which the IEVIE method is utilized to determine vibration stability.The PDE method is used to obtain the reliability of vibration stability.The proposed method is successfully applied to the Millennium Bridge,and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods.The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.
