中文摘要：

针对叠层橡胶隔震支座与地下室悬臂柱组成的串联隔震体系的P-△效应及叠层橡胶隔震支座转动问题，通过简化建立考虑P-△效应、叠层橡胶隔震支座转动及悬臂柱柱身变形的上部结构与独立悬臂柱串联隔震体系的力学模型，推导出考虑P-△效应及叠层橡胶隔震支座转动共同作用下的串联隔震体系的频率方程，然后通过数值的方法求解该串联隔震体系的频率与振型。根据Betti定律，推导出考虑P-△效应及叠层橡胶隔震支座转动的串联隔震体系的广义质量及广义荷载，然后通过振型叠加法求解串联隔震体系的地震响应。最后应用该地震响应求解方法对一实际工程进行仿真及参数分析。结果显示本文考虑P-△效应、叠层橡胶隔震支座转动及悬臂柱柱身变形的串联隔震体系动力响应求解方法能方便地计算悬臂柱的变形、柱顶转角以及结构的动力响应；悬臂柱水平名义刚度与隔震支座水平刚度之比较小时，悬臂柱与隔震支座组成的串联隔震体系的地震响应与隔震支座底部固结直接积分法得到的响应差别较大，随着悬臂柱刚度的增加，差别迅速减小，可根据刚度比确定独立悬臂柱的截面；在保证隔震效果的情况下，隔震支座竖向刚度应尽量加大，以减小隔震支座转角；当悬臂柱支撑的隔震结构隔震支座底部按固结计算时，P-△效应主要影响下部独立悬臂柱的响应，计算独立悬臂柱的响应需考虑P-△效应的影响。

英文摘要：

Abstract： In order to consider P-△ effect and rotation of isolation bearings existing in the serially isolated system with laminated rubber isolation bearings and cantilever columns in basement, mechanics model of this serially isolated system was established, and the associated frequency equation was derived. Then, the frequencies and the modes were solved by using a numerical method. Based on Betti＇ s theorem, the generalized mass and the stiffness of the serially isolated system considering P-△ effect and rotation of isolated bearings were presented , and the response of the serially isolated system were obtained by the mode superposition method. Finally, a practical isolated building was chosen as the example structure to analyze the seismic response and the effect of the parameters. The results show that the novel method considering P-△ effect, rotation of isolation bearings and deformation of cantilever columns can solve the deformation of cantilever column, rotation angle at the top of cantilever column and seismic response of the structure. When the ratio of the horizontal stiffness of the cantilever column to the isolation bearing is small, the difference of seismic response between serially isolated system and isolated system with rigid joint at the bottom of bearings is significant, and with the increase of the ratio of horizontal stiffness of the cantilever column to the isolation bearing, the difference will become smaller rapidly, then the section of cantilever column can be determined. The vertical stiffness of the isolation bearing should be as large as possible to decrease the rotation angle of the bearings. When the joint of bearing and the cantilever column of the serially isolated system can be taken as rigid joint to calculate the seismic response of structure, the p-Aeffect only have large influence to the response of the cantilever column, which indicates the P-△ effect should be considered in calculated response of the cantilever column.