Structural Engineering and Mechanics

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Analytical study on free vertical and torsional vibrations of two- and three-pylon suspension bridges via d'Alembert's principle

  • Zhang, Wen-ming (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Wang, Zhi-wei (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Zhang, Hao-qing (China Railway Major Bridge Reconnaissance & Design Institute Co., Ltd) ;
  • Lu, Xiao-fan (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Liu, Zhao (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
  • Received : 2019.10.28
  • Accepted : 2020.06.15
  • Published : 2020.11.10
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Abstract

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

Keywords

Acknowledgement

The work described in this paper was financially supported by the National Natural Science Foundation of China under the Grant 51678148, the Natural Science Foundation of Jiangsu Province (BK20181277) and the National Key R&D Program of China (No. 2017YFC0806009), which are gratefully acknowledged.

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