阻尼对地下隧道结构动力响应的影响
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摘要
用弹性地基梁来模拟地下隧道结构,推出考虑弯曲、轴力、剪切、内外阻尼以及在双参数地基模型上的振动方程。引用地下管道近似的位移计算方法,计算地下隧道结构,避免积分变换的繁琐,通过一种特殊的分离变量法,使得动力荷载以强加位移和速度的方式施加,实例计算中涉及内外阻尼项,可以方便地求出自振频率和阻尼比的表达式和考虑阻尼后结构位移衰减曲线,得出对于地下结构内阻尼的影响很小的结论。
The beam on elastic foundation model is used to simulate the underground tunnels structures;a vibration equation on two-parameter foundation considering the bending moment,axial force,shear deformation,external and internal damping is obtained.An approximate method for calculating of displacement of underground pipes is used to compute the displacement of underground tunnels structures,avoiding the trouble of integral transform.In numerical example involving the damping.it is convenient to use a special separated variable method to obtain natural frequencies and damping ratio,the attenuation of displacement considering damping.It is concluded that for underground structures,the effect of internal damping can be neglected.
The beam on elastic foundation model is used to simulate the underground tunnels structures;a vibration equation on two-parameter foundation considering the bending moment,axial force,shear deformation,external and internal damping is obtained.An approximate method for calculating of displacement of underground pipes is used to compute the displacement of underground tunnels structures,avoiding the trouble of integral transform.In numerical example involving the damping.it is convenient to use a special separated variable method to obtain natural frequencies and damping ratio,the attenuation of displacement considering damping.It is concluded that for underground structures,the effect of internal damping can be neglected.
引文
[1]郑永来,杨林德.地下结构抗震[M].上海:同济大学出版社,2005.
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[9]mer Civalek,Bakiztürk.Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation[J].Geomechanics and Engineering,2010,2(1):45-56.
[10]CAO Chang-yong,ZHONG Yang,LI Ming-liang.Dynamic analysis of Bernoulli-Euler Beam on two-Parameter foundation subjected to moving harmonic load[.DB/OL].中国科技论文在线,http://www.paper.edu.cn,2012-06-10.
[11]匡志平,刘竹钊,曹国安.地下结构纵向随机地震响应和极值分析[J].同济大学学报,2002,30(8):922-926.KUANG Zhi-ping,LIU Zhu-zhao,CAO Guo-an,Axial Random Seismic Response and External Value Analysis of Underground Structures[J].Journal of Tongji University,2002,30(8):922-926.
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[13]Filonenko-Borodich M M.(Russian).Some approximate theories of elastic foundation,Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universitet[J].Mekhanika,1940,46:3-18
[14]HETENYI M.Beams on elastic foundation[M].USA:The University of Michigan Press,1946.
[15]PASTERNAK P L.On a new method of analysis of rigid and flexible foundation on an elastic subsoil[C].//Collection of Papers of Moscow Civil Engineering Institute.Russian:[s.n.]1956:116-144.
[16]彭俊生,罗永坤.结构动力学抗震计算与SAP2000应用[M].四川:西南交通大学出版社,2006.
[17]戚承志,陈灿寿,陈剑杰,等.长形大截面地下结构的横向自由振动[C]//第二届全国工程安全与防护会议论文集.北京:[出版者不详],2010:865-869 QI Cheng-zhi,CHENG Canshou,CHENG Jianjie.Free lateral vibration of long large cross-section underground structure[C]//The Second National Conference on Security and protection Engineering.,Beijing:[s.n.],2010:865-869,
[18]薛定宇,陈阳泉.高等应用数学问题的MATLAB求解[M].北京:清华大学出版社,2008.
[2]CONSTANTOPOLOUS I V,MOTHERWEL J T,HALL J R.Dynamic analysis of tunnels[C]//Proceedings of third International Conference on Geomechanics.Aachen:[s.n.].1979.
[3]NAVARRO C,SAMARTIN A.Simplified longitudinal seismic analysis of buried tunnels[J].Softwatre Engineering Workstation,1988,4(1):3-10.
[4]JOHN C M,ZAHAH T F.Aseismic design of underground structures[J].Tunnelling and Underground Space Technology,1987,16,2(2):165-197.
[5]SHUKLA D K,RIZZO P C,STEPHENSON D E.Earthquake load analysis of tunnels and shafts[C]//Proceedings of the Seventh World Conference on Earthquake Engineering,1980:201-208.
[6]WANG T M,STEPHENS J E.Natural frequencies of Timoshenko beams on Pasternak foundations[J].Journal of Sound and Vibration.Turkish:National Commitee on Earthquake Engineering Press,1977,39:149-155.
[7]EISENBERGER M,CLASTORNIK J.Beams on variable two-parameter elastic foundation[J].Computers and Structures,1986,23:351-356.
[8]LOUDINI M,BOUKHETALA D,TADJINE M,et al.Application of timoshenko beam theory for deriving motion equationsof a lightweight elastic link robot manipulator[J].Journal of Automation,Robotics and Autonomous Systems,2006,5(2).11-18
[9]mer Civalek,Bakiztürk.Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation[J].Geomechanics and Engineering,2010,2(1):45-56.
[10]CAO Chang-yong,ZHONG Yang,LI Ming-liang.Dynamic analysis of Bernoulli-Euler Beam on two-Parameter foundation subjected to moving harmonic load[.DB/OL].中国科技论文在线,http://www.paper.edu.cn,2012-06-10.
[11]匡志平,刘竹钊,曹国安.地下结构纵向随机地震响应和极值分析[J].同济大学学报,2002,30(8):922-926.KUANG Zhi-ping,LIU Zhu-zhao,CAO Guo-an,Axial Random Seismic Response and External Value Analysis of Underground Structures[J].Journal of Tongji University,2002,30(8):922-926.
[12]SALIH N A.Dynamics of Nonlinear Beam on Elastic Foundation[C]//Proceedings of the World Congress on Engineering 2010.London:[s.n.],2010.
[13]Filonenko-Borodich M M.(Russian).Some approximate theories of elastic foundation,Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universitet[J].Mekhanika,1940,46:3-18
[14]HETENYI M.Beams on elastic foundation[M].USA:The University of Michigan Press,1946.
[15]PASTERNAK P L.On a new method of analysis of rigid and flexible foundation on an elastic subsoil[C].//Collection of Papers of Moscow Civil Engineering Institute.Russian:[s.n.]1956:116-144.
[16]彭俊生,罗永坤.结构动力学抗震计算与SAP2000应用[M].四川:西南交通大学出版社,2006.
[17]戚承志,陈灿寿,陈剑杰,等.长形大截面地下结构的横向自由振动[C]//第二届全国工程安全与防护会议论文集.北京:[出版者不详],2010:865-869 QI Cheng-zhi,CHENG Canshou,CHENG Jianjie.Free lateral vibration of long large cross-section underground structure[C]//The Second National Conference on Security and protection Engineering.,Beijing:[s.n.],2010:865-869,
[18]薛定宇,陈阳泉.高等应用数学问题的MATLAB求解[M].北京:清华大学出版社,2008.
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