Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics
Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics
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.
Evolutionary power spectral density, Frequency domain method, Non-stationary stochastic vibrations, Perturbation method, Track irregularity, Vehicle-bridge system
Lei, Simian
a01b765c-e4c7-4470-8c4f-e75e2cf7a9c1
Ge, Yaojun
0a47856e-d839-4c19-9348-71951266e2e7
Li, Qi
193e5502-fc0d-4a67-8b41-ed4d8b560c2f
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5
15 January 2023
Lei, Simian
a01b765c-e4c7-4470-8c4f-e75e2cf7a9c1
Ge, Yaojun
0a47856e-d839-4c19-9348-71951266e2e7
Li, Qi
193e5502-fc0d-4a67-8b41-ed4d8b560c2f
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5
Lei, Simian, Ge, Yaojun, Li, Qi and Thompson, David
(2023)
Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics.
Mechanical Systems and Signal Processing, 183, [109637].
(doi:10.1016/j.ymssp.2022.109637).
Abstract
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.
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Accepted/In Press date: 29 July 2022
e-pub ahead of print date: 9 August 2022
Published date: 15 January 2023
Additional Information:
Funding Information:
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).
Publisher Copyright:
© 2022 Elsevier Ltd
Keywords:
Evolutionary power spectral density, Frequency domain method, Non-stationary stochastic vibrations, Perturbation method, Track irregularity, Vehicle-bridge system
Identifiers
Local EPrints ID: 469706
URI: http://eprints.soton.ac.uk/id/eprint/469706
ISSN: 0888-3270
PURE UUID: 11541c0f-605d-4329-904b-b687e4ec181c
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Date deposited: 22 Sep 2022 16:46
Last modified: 17 Mar 2024 02:44
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Author:
Simian Lei
Author:
Yaojun Ge
Author:
Qi Li
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