纵向剪切波作用下长型地下结构与地基动力相互作用研究
|
摘要
为了研究在剪切波沿地下长型结构纵向传播情况下,惯性力对地下结构与地基动力相互作用的影响,基于Winkler地基模型和Euler-Bernoulli梁模型,分别建立了长型地下结构的静力平衡方程、自由振动方程和强迫振动方程。通过振型叠加法将偏微分方程简化为常微分方程;利用微分算子法分别求得静力平衡方程;自由振动方程和强迫振动方程的解析解。通过算例计算,比较并分析了静力平衡方程解与强迫振动方程解的差别。结果表明在算例取值情况下,惯性力对结构振动的影响较小;而在地基基床系数k很小或轴向力N很大时,惯性力的影响才较为显著。
To study the influence of inertia force on dynamic interaction between underground structure and foundation when shear wave propagates along axial direction of long underground structure,static equilibrium equation,free vibration motion equation and forced vibration motion equation were established based on Winkler foundation model and Euler- Bernoulli beam model. By applying mode superposition method we simplified partial differential equation into ordinary differential equation. These equations were solved analytically based on differential operator method. Numerical example was given and the results for static case and forced vibration case were compared. Comparison shows that the influence of inertial force on forced vibration of structure is relatively small in the given case,and is relatively significant when foundation bed coefficient k is small or axial force N is large.
To study the influence of inertia force on dynamic interaction between underground structure and foundation when shear wave propagates along axial direction of long underground structure,static equilibrium equation,free vibration motion equation and forced vibration motion equation were established based on Winkler foundation model and Euler- Bernoulli beam model. By applying mode superposition method we simplified partial differential equation into ordinary differential equation. These equations were solved analytically based on differential operator method. Numerical example was given and the results for static case and forced vibration case were compared. Comparison shows that the influence of inertial force on forced vibration of structure is relatively small in the given case,and is relatively significant when foundation bed coefficient k is small or axial force N is large.
引文
[1]郑永来,杨林德,李文艺,周健.地下建筑结构抗震[M].上海:同济大学出版社,2005.Zheng yong-lai,Yang lin-de,Li wen-yi,Zhou jian.Earthquake Resistance of Underground Building Structure[M].Shanghai:Tongji University Press,2005.(in Chinese).
[2]张维.日本兵库县南部地震灾区现场震害考察[J].工程抗震,1995,1:2.Zhang wei.In-situ Seismic Damage Investigation of South Hyogo in Japan[J].Earthquake Resistant Engineering,1995,1:2.(in Chinese).
[3]王瑞民,罗奇峰.阪神地震中地下结构和隧道的破坏现象的浅析[J].灾害学,1998,13(2):63-66.Wang rui-min,Analysis on Failure Phenomena of Underground Structures and Tunnels[J].Journal of Catastrophology,1998,13(2):63-66.(in Chinese).
[4]杨光,沈繁銮.日本阪神地震灾害的一些调查统计数据[J].华南地震,2005,25(1):83-86.Yang guang,Shen fan-luan.Investigatiory Statistical Data of Seismic Damage of Kobe in Japan[J].South China Journal of Seismology,2005,25(1):83-86.(in Chinese).
[5]Newmark,N.M.Problems in wave propagation in soil and rock[C].International Symposium on Wave Propagation and Dynamic Properties of Earth Materials.Albuquerque NM:University of New Mexico Press,1968.
[6]陈灿寿,戚承志,钱七虎等.浅埋地下结构顶板在竖向地震作用下的动力响应[J].世界地震工程,2010,26(4):86-92.Chen can-shou,Qi cheng-zhi,Qian qi-hu,et al.Dynamic Response of the Roof Slab of a Shallowly Buried Underground Structure Under Vertical Seismic Excitation[J].World Earthquake Engineering,2011(4):86-92.(in Chinese).
[7]于翔,钱七虎,赵跃堂等.地铁工程结构破坏的竖向地震力影响分析[J].解放军理工大学学报(自然科学版),2001,2(3):75-77.Yu xiang,Qian qi-hu.Analysis of Vertical Earthquake Influence on Damage to Subway Structures[J].Journal of PLA University of Science and Technology(Natural Science Edition),2001,3,75-77.(in Chinese).
[8]国胜兵,赵毅,赵跃堂等.地下结构在竖向和水平地震荷载作用下的动力分析[J].地下空间,2002,22(4):314-319.Guo Sheng-bing,Zhao yi,Zhao yue-tang.The Dynamic Analysis of Underground Structures under Horizontal and Vertical Seismic Excitation[J].Chinese Journal of Underground Space and Engineering,2002,22(4):314-319.(in?Chinese).
[9]Graff K.Wave Motion in Elastic Solids[M].Dover Publications.Inc.,New York,1975.
[10]St John C M,Zahrah T F.Aseismic design of underground structures[J].Tunnelling and Underground Space Technology,1987,2(2):165-197.
[11]Corrado V,D'Acunto B,Fontana N,et al.Inertial Effects on Finite Length Pipe Seismic Response[J].Mathematical Problems in Engineering,2012,2012:1-14.
[12]龙驭球.弹性地基梁的计算[M].北京:人民教育出版社,1981.Long yu-qiu.Calculation of Elastic Foundation Beam[M].Beijing:People's Education Press,1981.(in Chinese).
[13]Timoshenko S,Young D H,Weaver W.工程中的振动问题(第四版)[M].胡人礼译.北京:人民铁道出版社,1978.
[14]顾晓鲁,钱鸿缙,刘惠珊,汪时敏.地基与基础[M].北京:中国建筑工业出版社,2003.Gu xiao-lu,Qian hong-jin,Liu hui-shan,Wang shi-min.Soil and Foundation[M].Beijing:China Architecture&Building Press,2003.(in Chinese).
[2]张维.日本兵库县南部地震灾区现场震害考察[J].工程抗震,1995,1:2.Zhang wei.In-situ Seismic Damage Investigation of South Hyogo in Japan[J].Earthquake Resistant Engineering,1995,1:2.(in Chinese).
[3]王瑞民,罗奇峰.阪神地震中地下结构和隧道的破坏现象的浅析[J].灾害学,1998,13(2):63-66.Wang rui-min,Analysis on Failure Phenomena of Underground Structures and Tunnels[J].Journal of Catastrophology,1998,13(2):63-66.(in Chinese).
[4]杨光,沈繁銮.日本阪神地震灾害的一些调查统计数据[J].华南地震,2005,25(1):83-86.Yang guang,Shen fan-luan.Investigatiory Statistical Data of Seismic Damage of Kobe in Japan[J].South China Journal of Seismology,2005,25(1):83-86.(in Chinese).
[5]Newmark,N.M.Problems in wave propagation in soil and rock[C].International Symposium on Wave Propagation and Dynamic Properties of Earth Materials.Albuquerque NM:University of New Mexico Press,1968.
[6]陈灿寿,戚承志,钱七虎等.浅埋地下结构顶板在竖向地震作用下的动力响应[J].世界地震工程,2010,26(4):86-92.Chen can-shou,Qi cheng-zhi,Qian qi-hu,et al.Dynamic Response of the Roof Slab of a Shallowly Buried Underground Structure Under Vertical Seismic Excitation[J].World Earthquake Engineering,2011(4):86-92.(in Chinese).
[7]于翔,钱七虎,赵跃堂等.地铁工程结构破坏的竖向地震力影响分析[J].解放军理工大学学报(自然科学版),2001,2(3):75-77.Yu xiang,Qian qi-hu.Analysis of Vertical Earthquake Influence on Damage to Subway Structures[J].Journal of PLA University of Science and Technology(Natural Science Edition),2001,3,75-77.(in Chinese).
[8]国胜兵,赵毅,赵跃堂等.地下结构在竖向和水平地震荷载作用下的动力分析[J].地下空间,2002,22(4):314-319.Guo Sheng-bing,Zhao yi,Zhao yue-tang.The Dynamic Analysis of Underground Structures under Horizontal and Vertical Seismic Excitation[J].Chinese Journal of Underground Space and Engineering,2002,22(4):314-319.(in?Chinese).
[9]Graff K.Wave Motion in Elastic Solids[M].Dover Publications.Inc.,New York,1975.
[10]St John C M,Zahrah T F.Aseismic design of underground structures[J].Tunnelling and Underground Space Technology,1987,2(2):165-197.
[11]Corrado V,D'Acunto B,Fontana N,et al.Inertial Effects on Finite Length Pipe Seismic Response[J].Mathematical Problems in Engineering,2012,2012:1-14.
[12]龙驭球.弹性地基梁的计算[M].北京:人民教育出版社,1981.Long yu-qiu.Calculation of Elastic Foundation Beam[M].Beijing:People's Education Press,1981.(in Chinese).
[13]Timoshenko S,Young D H,Weaver W.工程中的振动问题(第四版)[M].胡人礼译.北京:人民铁道出版社,1978.
[14]顾晓鲁,钱鸿缙,刘惠珊,汪时敏.地基与基础[M].北京:中国建筑工业出版社,2003.Gu xiao-lu,Qian hong-jin,Liu hui-shan,Wang shi-min.Soil and Foundation[M].Beijing:China Architecture&Building Press,2003.(in Chinese).
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心