长型大截面地下结构的横向自由振动方程
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摘要
文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。
The general free lateral vibration motion equation of a long large cross-section underground structure is derived with the comprehensive consideration of internal damping,external damping,shear deformation,cross-sectional rotation inertia,axial force and model parameters.Free motion equations for several special cases may be obtained from this general equation.In this way,not only the Timoshenko's beam theory is extended,but also the basis for studying the influence of different factors on free and forced vibration of underground structures in future works is provided.
The general free lateral vibration motion equation of a long large cross-section underground structure is derived with the comprehensive consideration of internal damping,external damping,shear deformation,cross-sectional rotation inertia,axial force and model parameters.Free motion equations for several special cases may be obtained from this general equation.In this way,not only the Timoshenko's beam theory is extended,but also the basis for studying the influence of different factors on free and forced vibration of underground structures in future works is provided.
引文
[1]Wang J.Seismic design of tunnels:a simple state-of-the-art design approach monograph 7[J].Parsons Brinckerhoff Quade&Douglas,Inc.1993.
[2]孙超,薄景山,齐文浩,等.地下结构抗震研究现状及展望[J].世界地震工程,2009,25(2):94-99.SUN Chao,BO Jingshan,QI Wenhao,et al.Status and prospect of seismic research on underground structures[J].World Earthquake Engineering,2009,25(2):94-99.
[3]Stamos AA,Beskos DE.3-D seismic response analysis of long lined tunnels in half-space[J].Soil Dynamics and Earthquake Engineering,1996,15(2):111-118.
[4]Luco JE,BarrosFCP.Seismicresponseofacylindricalshellembeddedin alayered visco-elastichalf-space[J].I:formulation.EarthqukeEngi-neering and Structural Dynamics,1994,23(5):553-567.
[5]Constantpoulous IV,Motherwel JT,Hall JR.Dynamic analysis of tunnels[C]//April:Proceedings of the third international conference in geome-chanics,Aachen,1979.
[6]Navarro C,Samartin A.Simpilified longitudinal seismic analysis of buried tunnels[J].Software Engineering Workstations1988,4(1):3-10.
[7]St.John C M,Zahrah T F.Aseismic design of underground structures[J].Tunneling underground Space Technology,1987,2(2):165-197.
[8]Sanchez-Merino A L,Fernandez-Saez J,Navarro C.Simplified longitudinal seismic response of tunnel linings subjected to surface waves[J].SoilDynamics and Earthquake Engineering,2009,29(3):579-582.
[9]Stephen N.G.The second spectrum of Timoshenko beam theory—further assessment[J].Journal of Sound and Vibration,2006,292(1-2):372-389.
[10]Majkut L.Free and forced vibrations of Timoshenko beams described by single difference equation[J].Journal of Theoretical and Applied Me-chanics,2009,47(1):193-210.
[11]Bogacz R,Czyczula W.Response of beam on visco-elastic foundation to moving distributed load[J].Journal of Theoretical and Applied Mechan-ics,2008,46(4):763-775.
[12]Pasternak PL.On anew method ofanalysisofrigid andflexiblefoundation onanelasticsubsoil(in Russian)[A].Collection ofPapersofMoscowCivil Engineering Institute,1956,14:116-144.
[13]Sevaduri A P S.Elastic analysis of soil foundation interaction[M].Elsevier,Amsterdam,1979.
[2]孙超,薄景山,齐文浩,等.地下结构抗震研究现状及展望[J].世界地震工程,2009,25(2):94-99.SUN Chao,BO Jingshan,QI Wenhao,et al.Status and prospect of seismic research on underground structures[J].World Earthquake Engineering,2009,25(2):94-99.
[3]Stamos AA,Beskos DE.3-D seismic response analysis of long lined tunnels in half-space[J].Soil Dynamics and Earthquake Engineering,1996,15(2):111-118.
[4]Luco JE,BarrosFCP.Seismicresponseofacylindricalshellembeddedin alayered visco-elastichalf-space[J].I:formulation.EarthqukeEngi-neering and Structural Dynamics,1994,23(5):553-567.
[5]Constantpoulous IV,Motherwel JT,Hall JR.Dynamic analysis of tunnels[C]//April:Proceedings of the third international conference in geome-chanics,Aachen,1979.
[6]Navarro C,Samartin A.Simpilified longitudinal seismic analysis of buried tunnels[J].Software Engineering Workstations1988,4(1):3-10.
[7]St.John C M,Zahrah T F.Aseismic design of underground structures[J].Tunneling underground Space Technology,1987,2(2):165-197.
[8]Sanchez-Merino A L,Fernandez-Saez J,Navarro C.Simplified longitudinal seismic response of tunnel linings subjected to surface waves[J].SoilDynamics and Earthquake Engineering,2009,29(3):579-582.
[9]Stephen N.G.The second spectrum of Timoshenko beam theory—further assessment[J].Journal of Sound and Vibration,2006,292(1-2):372-389.
[10]Majkut L.Free and forced vibrations of Timoshenko beams described by single difference equation[J].Journal of Theoretical and Applied Me-chanics,2009,47(1):193-210.
[11]Bogacz R,Czyczula W.Response of beam on visco-elastic foundation to moving distributed load[J].Journal of Theoretical and Applied Mechan-ics,2008,46(4):763-775.
[12]Pasternak PL.On anew method ofanalysisofrigid andflexiblefoundation onanelasticsubsoil(in Russian)[A].Collection ofPapersofMoscowCivil Engineering Institute,1956,14:116-144.
[13]Sevaduri A P S.Elastic analysis of soil foundation interaction[M].Elsevier,Amsterdam,1979.
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