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Analytical solution for horizontal seismic response of shaft structure primary lining and secondary lining
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Bu ZAHNG1, 2, Li-dong LU1, Zi-lan ZHONG1, 2, Ruo-yu JI1, Xiu-li DU1, 2
Journal of Vibration Engineering | 2024, 37(12) : 2003 - 2011
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Journal of Vibration Engineering | 2024, 37(12): 2003-2011
Analytical solution for horizontal seismic response of shaft structure primary lining and secondary lining
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Bu ZAHNG1, 2, Li-dong LU1, Zi-lan ZHONG1, 2, Ruo-yu JI1, Xiu-li DU1, 2
Affiliations
  • 1Faculty of Architecture,Civil and Transportation Engineering,Beijing University of Technology,Beijing 100124,China
  • 2Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,China
Published: 2024-12-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.12.002
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Based on the elastic foundation beam theory,the mechanical model for the seismic response of the vertical shaft is established. The shaft primary lining and secondary lining are simplified as Euler Bernoulli beams and the normal interaction between the primary lining and secondary lining is simulated by using uniformly distributed springs. The differential governing equations of the shaft under the horizontal seismic excitation are derived. The rapid solution of the horizontal seismic response of the primary lining and secondary lining is achieved through the distributed transfer function method and the correctness of the analytical solution is verified by comparison with the finite element numerical simulation method. The peak seismic response at the top of the shaft is parametrically analyzed from the perspectives of elastic foundation stiffness,secondary lining stiffness,shaft outer diameter,and stiffness of the elastic connection layer between the primary and secondary linings,respectively. The results show that the peak seismic response at the top of the secondary lining is greater than that of the primary lining. With the increase of the elastic foundation stiffness,the peak response of the top of the primary lining and the secondary lining decreases. The increase of secondary lining stiffness leads to the obvious increase of peak response at the top of secondary lining. With the increase of the shaft outer diameter,the peak response of both the primary and secondary linings increase significantly. When the elastic connection layer stiffness increases,the peak response of the primary lining increases slightly,but the peak response of the secondary lining decreases significantly.

seismic resistance of underground structures  /  shaft seismic response  /  shaft primary lining  /  elastic foundation beam
Bu ZAHNG, Li-dong LU, Zi-lan ZHONG, Ruo-yu JI, Xiu-li DU. Analytical solution for horizontal seismic response of shaft structure primary lining and secondary lining[J]. Journal of Vibration Engineering, 2024 , 37 (12) : 2003 -2011 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.12.002
Year 2024 volume 37 Issue 12
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doi: 10.16385/j.cnki.issn.1004-4523.2024.12.002
  • Receive Date:2022-12-16
  • Online Date:2026-02-12
  • Published:2024-12-28
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  • Received:2022-12-16
  • Revised:2023-02-07
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Affiliations
    1Faculty of Architecture,Civil and Transportation Engineering,Beijing University of Technology,Beijing 100124,China
    2Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,China
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表12种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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