Structural Engineering and Mechanics

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An energy-based vibration model for beam bridges with multiple constraints

  • Huang, Shiping (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Zhang, Huijian (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Chen, Piaohua (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Zhu, Yazhi (Department of Structural Engineering, Tongji University) ;
  • Zuazua, Enrique (Dynamics, Control and Numerics, Alexander von Humboldt-Professorship, Department of Data Science, Friedrich-Alexander-Universitat Erlangen-Nurnberg)
  • Received : 2021.07.10
  • Accepted : 2022.01.21
  • Published : 2022.04.10
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Abstract

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

Keywords

Acknowledgement

S.P. Huang was supported by the National Natural Science Foundation of China (NSFC) (grant no. 11672108,11202080) and the Fundamental Research Funds for the Central Universities. Zuazua's project has received funding from the European Research Council (ERC) under the European Unionas Horizon 2020 research and innovation programme (grant agreement NO. 694126-DyCon). The work of both authors was partially supported by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain) and by the Air Force Office of Scientific Research (AFOSR) under Award NO. FA9550-18-1-0242. The work of E.Z. was partially funded by the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.765579-ConFlex, the Grant ICON-ANR-16-ACHN-0014 of the French ANR and the Transregio 154 Project "Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks" of the German DFG.

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