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

Shiping Huang , Huijian Zhang , Piaohua Chen , Yazhi Zhu , Enrique Zuazua

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.

Key Words

beam bridge; bridge vibration; multiple constraints; natural frequency; vibration mode

Address

Shiping Huang — School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R. China; China-Singapore International Joint Research Institute, Guangzhou 510700, P.R. China; Chair of Computational Mathematics, Fundación Deusto, Avda. de las Universidades 24, 48007 Bilbao, Basque Country, Spain
Huijian Zhang — School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R. China
Piaohua Chen — School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R. China
Yazhi Zhu — Department of Structural Engineering, Tongji University, Shanghai 200092, P.R. China
Enrique Zuazua — Chair in Dynamics, Control and Numerics, Alexander von Humboldt-Professorship, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; Chair of Computational Mathematics, Fundación Deusto, Avda. de las Universidades 24, 48007 Bilbao, Basque Country, Spain; Departamento de Matematicas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

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