Vehicle–bridge interaction analysis by the state-space method and symplectic orthogonality
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The dynamic properties of bridges can be extracted from the dynamic responses of the vehicles passing on these bridges. This paper proposes a method for the vehicle–bridge interaction analysis of continuous beam bridges with different spans and variable cross sections using numerical methods that are high in computational efficiency. Herein, the vehicle is simplified as a spring–damper–mass system and coupled to the bridge by its interactional force in the governing equations based on the Timoshenko beam theory. According to the symplectic orthogonality of the state vectors, the orthogonality of the mode shapes of the Timoshenko beams is proved, and the dynamic responses of the continuous beam bridges with different spans and variable cross sections can be solved by the mode superposition method. More complicated factors, such as harmonic load on vehicles, noise in measurement, and roughness of pavements, can also be conveniently taken into account. Finally, the proposed method is demonstrated using some numerical examples and applied to a real bridge. The results indicate that the method is convenient, efficient, and precise for engineering applications.
KeywordsVehicle–bridge interaction State-space method Symplectic orthogonality Structural health monitoring
This work was supported by the National Natural Science Foundation of China (Nos. 51478422 and 51878603).
- 1.Li, J., Su, M., Fan, L.: Natural frequency of railway girder bridges under vehicle loads. J. Bridge Eng. 8(4), 199–203 (2003). https://doi.org/10.1061/(ASCE)1084-0702(2003)8:4(199) CrossRefGoogle Scholar
- 2.Kong, X., Cai, C.S., Deng, L., Zhang, W.: Using dynamic responses of moving vehicles to extract bridge modal properties of a field bridge. J. Bridge Eng. 22(6), 04017018 (2017). https://doi.org/10.1061/(ASCE)BE.1943-5592.0001038 CrossRefGoogle Scholar
- 4.Zhu, Z., Yu, Z., Jiang, L., Gao, M.: Analysis of bridge-ground vibrations induced by moving loads of high-speed train. J. Vib. Eng. 25(5), 548–555 (2012). (In Chinese)Google Scholar
- 5.Chen, L., Jiang, L., Tao, L., Yu, Z.: Seismic response analysis of high-speed vehicle-bridge considering soil–structure interaction. Rock Soil Mech. 33(10), 3162–3170 (2012). (In Chinese)Google Scholar
- 6.Willis, R.: Report of the Commissioners Appointed to Inquire into the Application of Iron to Railway Structures (Appendix B). William Cloves and Sons, London (1849)Google Scholar
- 7.Stokes, G.G.: Discussion of a differential equation relating to the breaking of railway bridges. Trans. Camb. Philos. Soc. 8(5), 707–735 (1849)Google Scholar
- 19.An, N., Xia, H., Zhan, J.W.: Experimental verification of bridge system identification based on dynamic response of passing vehicle. In: Xia, H., Takemiya, H. (eds.) Environmental Vibrations: Prediction, Monitoring, Mitigation and Evaluation, Vols I And II, pp. 1101–1105. Science Press, Beijing (2009)Google Scholar
- 21.Bu, J.Q., Law, S.S., Zhu, X.Q.: Innovative bridge condition assessment from dynamic response of a passing vehicle. J. Eng. Mech. 132(12), 1372–1379 (2006). https://doi.org/10.1061/(ASCE)0733-9399(2006)132:12(1372) CrossRefGoogle Scholar
- 22.Zhan, J.W., Xia, H., An, N.: Damage diagnosis method for railway bridges based on train dynamic responses. China Railw. Sci. 33(3), 35–39 (2012). https://doi.org/10.1061/10.3969/j.issn.1001-4632.2012.03.06. (in Chinese)CrossRefGoogle Scholar
- 32.Shen, X.D.: Dynamic and static problems for composite beams with partial interaction. Doctorial Dissertation, Zhejiang University (2012) (in Chinese) Google Scholar