Evolutionary power spectral density; Frequency domain method; Non-stationary stochastic vibrations; Perturbation method; Track irregularity; Vehicle-bridge system; Coupled systems; Evolutionary power spectral densities; Frequency-domain methods; Non-stationary stochastic vibration; Nonstationary; Stochastic vibration; Time-dependent characteristics; Control and Systems Engineering; Signal Processing; Civil and Structural Engineering; Aerospace Engineering; Mechanical Engineering; Computer Science Applications
Abstract :
[en] When a train passes over a bridge, the vibrations of the vehicles and the bridge are the result of non-stationary stochastic processes due to the time-dependent characteristics of the coupled vehicle-bridge system. The aim of this study is to generalize the frequency domain method to investigate the non-stationary random vibration of the coupled system subjected to the excitation of track irregularities with consideration of time-dependent characteristics. To illustrate the method, a three-span simply supported bridge traversed by a single railway vehicle is adopted as an example. The time-dependent frequency response function (FRF) of the coupled system is theoretically derived through solving ordinary differential equations with variable complex coefficients, and the perturbation method is adopted to improve the calculation efficiency. By combining this with Priestley's Evolutionary Spectra theory, the evolutionary power spectral density (PSD) of the non-stationary random response of the system is then derived. The transitions will occur when the wheels cross the joints between each bridge span and between the bridge and the adjacent roadway. By adopting mode shapes of the full structure, the change of states of the vehicle crossing multiple bridge spans and moving onto the roadway can be solved as a continuous process without separation. The proposed method is validated by comparisons with the Monte Carlo method, showing higher accuracy and efficiency when calculating the time-varying standard deviation of the response. It is found that the vibration of the vehicle is approximately stationary but with large variance due to the random track irregularities, while the bridge vibration follows a strongly non-stationary process with small randomness and is more related to the moving mass effect.
Disciplines :
Civil engineering
Author, co-author :
Lei, Simian ; Université de Liège - ULiège > Urban and Environmental Engineering ; Department of Bridge Engineering, Tongji University, Shanghai, China
Ge, Yaojun; Department of Bridge Engineering, Tongji University, Shanghai, China
Li, Qi; Department of Bridge Engineering, Tongji University, Shanghai, China ; Tibet Agriculture & Animal Husbandry University, Nyingchi, China
Thompson, David J.; Institute of Sound and Vibration Research, University of Southampton, Southampton, United Kingdom
Language :
English
Title :
Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics
CSC - China Scholarship Council NSCF - National Natural Science Foundation of China
Funding text :
The study was supported by the National Natural Science Foundation of China (grant numbers 51878501, and 51778495 and 51978527) and the China Scholarship Council (No. 202106260170).
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