基于传递矩阵法的串联隔震体系稳定性分析
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摘要
针对串联隔震体系稳定性问题,利用传递矩阵法建立其临界荷载控制方程,并探讨了参数变化对临界荷载的影响.对单个叠层橡胶支座进行力学分析,建立其稳定性分析的场矩阵,进而利用传递矩阵法建立串联隔震体系稳定性分析的场矩阵,推导出临界荷载的控制方程.计算两种不同型号串联隔震体系的临界荷载,重点探讨叠层橡胶支座和地下室悬臂柱参数变化对串联隔震体系稳定性的影响.结果表明,叠层橡胶支座参数对串联隔震体系稳定性影响要比地下室悬臂柱明显,串联隔震体系的临界荷载值可用单个橡胶支座的临界荷载值近似等效.
Aiming at the stability of a serial seismic isolation system,the governing equation for critical load was established with a transfer matrix method,and the effect of parameter variation on critical load was investigated.The mechanical analysis was performed for single laminated rubber bearing,and the field matrix for the stability analysis of the rubber bearing was established.Furthermore,the transfer matrix method was used to establish the field matrix for the stability analysis of serial seismic isolation system,and the governing equation for critical load was derived.The critical load of two serial isolation systems was calculated,and the influence of parameter variation of both laminated rubber bearing and basement cantilever column on the stability of serial isolation system was emphatically investigated.The results show that the laminated rubber bearing exhibits more significant effect on the stability of serial isolation system than the basement cantilever column,and the critical load value of serial isolation system can be approximately equivalent to that of single laminated rubber bearing.
Aiming at the stability of a serial seismic isolation system,the governing equation for critical load was established with a transfer matrix method,and the effect of parameter variation on critical load was investigated.The mechanical analysis was performed for single laminated rubber bearing,and the field matrix for the stability analysis of the rubber bearing was established.Furthermore,the transfer matrix method was used to establish the field matrix for the stability analysis of serial seismic isolation system,and the governing equation for critical load was derived.The critical load of two serial isolation systems was calculated,and the influence of parameter variation of both laminated rubber bearing and basement cantilever column on the stability of serial isolation system was emphatically investigated.The results show that the laminated rubber bearing exhibits more significant effect on the stability of serial isolation system than the basement cantilever column,and the critical load value of serial isolation system can be approximately equivalent to that of single laminated rubber bearing.
引文
[1]Gent A N.Elastic stability of rubber compression springs[J].Journal of Engineering Mechanics,1964,6(4):318-326.
[2]Koh C G,Kelly J M.A simple mechanical model for electrometric bearings used in base isolation[J].Jour-nal of Engineering Mechanics,1988,30(12):933-943.
[3]Nagarajaiah S,Ferrell K.Stability of electrometric seismic isolation bearings[J].Journal of Strutural En-gineering,1999,125(9):946-954.
[4]Buckle I,Nagarajaiah S,Ferrell K.Stability of electro-metric isolation bearings:experimental study[J].Journal of Strutural Engineering,2002,128(1):3-11.
[5]Kelly J M.Tension buckling in multilayer elastomeric bearings[J].Journal of Engineering Mechanics,2003,129(12):1363-1368.
[6]Warm G P,Whittaker A,Constantinou M.Vertical stiffness of electrometric and lead-rubber seismic isolation bearings[J].Journal of Strutural Engineering,2007,133(9):1227-1236.
[7]Liu W G,He W F,Feng D M.Vertical stiffness and deformation analysis models of rubber isolators in compression and compression-shear states[J].Journal of Engineering Mechanics,2009,135(9):945-952.
[8]Yang Q R,Liu W G,He W F.Tensile stiffness and deformation model of rubber isolators in tension and tension-shear states[J].Journal of Engineering Mechanics,2010,136(4):429-437.
[9]周锡元,韩淼,曾德民,等.橡胶支座与R/C柱串联隔震体系水平刚度系数[J].振动工程学报,1999,12(2):157-165.(ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Horizontal rigidity coeffcient of the serial system of rubber bearing w ith column[J].Journal of Vibration Engineering,1999,12(2):157-165.)
[10]周锡元,韩淼,曾德民,等.组合橡胶支座及橡胶支座与柱串联系统的水平刚度计算方法[J].地震工程与工程振动,1999,19(4):67-75.(ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Calculation method of lateral stiffness of combined rubber bearing and serial system of bearing w ith columns[J].Earthquake Engineering and Engineering Vibration,1999,19(4):67-75.)
[11]刘庆潭.材料力学教程[M].北京:机械工业出版社,2006:313-321.(LIU Qing-tan.Course of material mechanics[M].Beijing:China Machine Press,2006:313-321.)
[2]Koh C G,Kelly J M.A simple mechanical model for electrometric bearings used in base isolation[J].Jour-nal of Engineering Mechanics,1988,30(12):933-943.
[3]Nagarajaiah S,Ferrell K.Stability of electrometric seismic isolation bearings[J].Journal of Strutural En-gineering,1999,125(9):946-954.
[4]Buckle I,Nagarajaiah S,Ferrell K.Stability of electro-metric isolation bearings:experimental study[J].Journal of Strutural Engineering,2002,128(1):3-11.
[5]Kelly J M.Tension buckling in multilayer elastomeric bearings[J].Journal of Engineering Mechanics,2003,129(12):1363-1368.
[6]Warm G P,Whittaker A,Constantinou M.Vertical stiffness of electrometric and lead-rubber seismic isolation bearings[J].Journal of Strutural Engineering,2007,133(9):1227-1236.
[7]Liu W G,He W F,Feng D M.Vertical stiffness and deformation analysis models of rubber isolators in compression and compression-shear states[J].Journal of Engineering Mechanics,2009,135(9):945-952.
[8]Yang Q R,Liu W G,He W F.Tensile stiffness and deformation model of rubber isolators in tension and tension-shear states[J].Journal of Engineering Mechanics,2010,136(4):429-437.
[9]周锡元,韩淼,曾德民,等.橡胶支座与R/C柱串联隔震体系水平刚度系数[J].振动工程学报,1999,12(2):157-165.(ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Horizontal rigidity coeffcient of the serial system of rubber bearing w ith column[J].Journal of Vibration Engineering,1999,12(2):157-165.)
[10]周锡元,韩淼,曾德民,等.组合橡胶支座及橡胶支座与柱串联系统的水平刚度计算方法[J].地震工程与工程振动,1999,19(4):67-75.(ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Calculation method of lateral stiffness of combined rubber bearing and serial system of bearing w ith columns[J].Earthquake Engineering and Engineering Vibration,1999,19(4):67-75.)
[11]刘庆潭.材料力学教程[M].北京:机械工业出版社,2006:313-321.(LIU Qing-tan.Course of material mechanics[M].Beijing:China Machine Press,2006:313-321.)
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