Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect
Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2021/6690753 |
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| author | Zhou Chen Hongxin Lin Deyuan Deng Wanjie Xu Hanwen Lu Zepeng Chen |
| author_facet | Zhou Chen Hongxin Lin Deyuan Deng Wanjie Xu Hanwen Lu Zepeng Chen |
| author_sort | Zhou Chen |
| collection | DOAJ |
| description | Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude. |
| format | Article |
| id | doaj-art-8db8f4728d2c40de824906befbea6961 |
| institution | Kabale University |
| issn | 1687-8094 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj-art-8db8f4728d2c40de824906befbea69612025-02-03T01:20:38ZengWileyAdvances in Civil Engineering1687-80942021-01-01202110.1155/2021/6690753Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay EffectZhou Chen0Hongxin Lin1Deyuan Deng2Wanjie Xu3Hanwen Lu4Zepeng Chen5School of Transportation and Civil Engineering &ArchitectureSchool of Transportation and Civil Engineering &ArchitectureChina Construction Steel Engineering Co., Ltd.Guangzhou College of Technology and BusinessSchool of Transportation and Civil Engineering &ArchitectureSchool of Transportation and Civil Engineering &ArchitecturePedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude.http://dx.doi.org/10.1155/2021/6690753 |
| spellingShingle | Zhou Chen Hongxin Lin Deyuan Deng Wanjie Xu Hanwen Lu Zepeng Chen Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect Advances in Civil Engineering |
| title | Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect |
| title_full | Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect |
| title_fullStr | Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect |
| title_full_unstemmed | Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect |
| title_short | Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect |
| title_sort | lateral parametric vibration of footbridge under pedestrian excitation considering the time delay effect |
| url | http://dx.doi.org/10.1155/2021/6690753 |
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