工程科学与技术   2018, Vol. 50 Issue (6): 56-64

Design and Performance Study of Two New Sliding Relics Isolation Bearings
WANG Ya, YANG Weiguo, NIE Yansen, WANG Meng, LIU Pei
School of Civil Eng., Beijing Jiaotong Univ., Beijing 100044, China
Abstract: To ensure the safety of relics in museums, two new sliding relics isolation bearings were put forward, which are fixed stiffness bearing and variable stiffness bearing respectively. The " bearing-cabinet” finite element models (FEM) were established. Meanwhile, a museum FEM was established and the floor waves were extracted under different working conditions. The time history analysis of the " bearing-cabinet” FEM was carried out. The seismic isolation effect and applicability of two bearings were studied and the bearing design was completed. The results showed that the bearings can isolate the earthquake in both X and Y directions simultaneously. The variable stiffness bearing can also realize the seismic isolation target of earthquake with different intensities. The seismic isolation effect of fixed stiffness bearing and variable stiffness bearing is about 60%, 80% under the isolated floor waves and is about 90%, 95% under the non-isolated floor waves. The seismic isolation effect of variable stiffness bearing is better than fixed stiffness bearing. The design methods of two new sliding relics isolation bearings provides a necessary guidance for subsequent engineering application.
Key words: sliding relics isolation bearing    fixed stiffness    variable stiffness    seismic isolation effect

1 滑板型文物隔震支座

1.1 固定刚度隔震支座

 图1 固定刚度隔震支座示意图 Fig. 1 Three-dimension graph of fixed stiffness bearing

1.2 变刚度隔震支座

 图2 变刚度隔震支座示意图 Fig. 2 Three-dimension graph of variable stiffness bearing

2 隔震支座理论计算与有限元模型

2.1 固定刚度支座弹簧刚度

 图3 固定刚度支座计算简图 Fig. 3 Calculation diagram of fixed stiffness bearing

 $k = \left( {{m_{\rm{1}}} + {m_{\rm{2}}}} \right) \times {\left( {2{\text{π}} /T} \right)^{\rm{2}}}$ (1)

 ${F} = S \times k$ (2)

 ${{K} _{{\rm{spring}}}} = \frac{{\left( {{m_{\rm{1}}} + {m_{\rm{2}}}} \right) \times {{\left( {2{\text{π}} /T} \right)}^{\rm{2}}}}}{{{\rm{ta}}{{\rm{n}}^2}\theta }}$ (3)

 $k{\rm{ = }}{K_{{\rm{spring}}}} \times {\rm{ta}}{{\rm{n}}^{\rm{2}}}\theta$ (4)
2.2 变刚度支座弹簧刚度

 图4 变刚度支座计算简图 Fig. 4 Calculation diagram of variable stiffness bearing

 ${{K} _{{\rm{spring}}}} = \frac{{\left( {{m_{\rm{1}}} + {m_{\rm{2}}}} \right) \times {{\left( {2{\text{π}} /{T_1}} \right)}^{\rm{2}}}}}{{{\rm{ta}}{{\rm{n}}^2}{\theta _1}}}{\rm{ = }}\frac{{\left( {{m_{\rm{1}}} + {m_{\rm{2}}}} \right) \times {{\left( {2{\text{π}} /{T_2}} \right)}^{\rm{2}}}}}{{{\rm{ta}}{{\rm{n}}^2}{\theta _2}}}$ (5)

2.3 “支座–展柜”系统有限元模型

 图5 展柜原型与“支座–展柜”有限元模型 Fig. 5 Prototype and FEM of cabinet

 图6 变刚度支座模型弹簧的本构关系 Fig. 6 Constitutive relation of spring in variable stiffness bearing FEM

 ${F_1} = {K _1} \times {S\!\!_1},\;\;\;{F_2} = {F_1} + {K _2} \times \left( {{S\!\!_2} - {S\!\!_1}} \right)$ (6)

3 隔震支座时程分析及设计方法 3.1 博物馆模型时程分析

 图7 博物馆有限元模型 Fig. 7 FEM of museum

3.2 “支座–展柜”模型时程分析

3.2.1 固定刚度支座

 图8 罕遇地震–隔震结构楼层波作用下的反应谱 Fig. 8 Floor wave response spectrum under rare earthquake and isolation condition

 图9 罕遇地震–非隔震结构楼层波作用下的反应谱 Fig. 9 Floor wave response spectrum under rare earthquake and non-isolation condition

3.2.2 变刚度支座

“变刚度支座–展柜”系统模型的主要控制参数为两斜线段对应的弹簧刚度 ${K_1}$ ${K_2}$ 及水平位移 ${S\!\!_1}$ ${S\!\!_2}$ 。多遇地震下，支座在第1斜线段工作，对应 ${K_1}$ ${S\!\!_1}$ ；罕遇地震下，支座进入第2斜线段，对应 ${K_2}$ ${S\!\!_2}$ 。第2斜线段的刚度 ${K_2}$ 取固定刚度支座在3条（罕遇地震）楼层波下的最优刚度；第1斜线段刚度 ${K_1} < {K_2}$ 。水平位移 ${S\!\!_1}$ ${S\!\!_2}$ 根据不同地震工况的计算结果取值，由图6可知，当弹簧位移大于 ${S\!\!_2}$ 后刚度为0，为避免模型错误，应尽量保证 ${S\!\!_2}$ 的值足够大。

 图10 多遇地震–隔震结构楼层波作用下的反应谱 Fig. 10 Floor wave response spectrums under frequent earthquake and isolation condition

 图11 多遇地震–非隔震结构楼层波作用下的反应谱 Fig. 11 Floor wave response spectrums under frequent earthquake and non-isolation condition

3.2.3 两支座隔震效果对比

3.3 设计方法

 图12 滑板型文物隔震支座设计方法 Fig. 12 Design method of sliding relics isolation bearings

4 结　论

1）滑板型文物隔震支座可同时实现XY两方向的隔震，隔震原理清晰且装置构造简单。同时变刚度支座还可实现文物在不同强度地震强度下的隔震目的。

2）博物馆结构采取隔震与否对楼层波结果影响较大，隔震后楼层波加速度峰值明显降低，楼层波与地震波差距较大。故在进行文物支座设计时应采用楼层波作为分析输入。

3）固定刚度支座和变刚度支座在隔震楼层波下的平均隔震效果约为60%、80%，在非隔震楼层波下的平均隔震效果约为90%、95%；二者在各工况楼层波下的位移值相差不大。综合可得，变刚度支座整体的隔震效果要优于固定刚度支座，且非隔震楼层波下的隔震效果优于隔震楼层波。故在目前博物馆中均可采用文物隔震支座实现文物的防震，且变刚度支座适用效果更佳。

4）得到了两种新型滑板型文物隔震支座的设计方法，固定刚度支座和变刚度支座设计方法略有不同。该设计方法可为后续工程应用提供必要的指导依据。

 [1] Nobuyuki Kamba.Seismic mitigation for the museum objects[C]//International Symposium on Advances of Protection Devices for Museum Exhibits.Beijing,2015:40–51. [2] 中国住房和城乡建设部.建筑抗震设计规范:GB50011—2010[S].北京:中国建筑工业出版社,2010. [3] 中华人民共和国国家文物局.馆藏文物防震规范:WW/T 0069—2015[S].北京:文物出版社,2015. [4] Fulvio P, Nicola A. Earthquake damages to cultural heritage constructions and simplified assessment of artworks[J]. Engineering Failure Analysis, 2013, 34(1): 735-760. DOI:10.1016/j.engfailanal.2013.01.005 [5] Su Xiaoxue.Shockproof performance study on museum collection of movable cultural relics[D].Beijing:Beijing Jiaotong University,2013. 苏晓雪.馆藏可移动文物防震性能研究[D].北京: 北京交通大学,2013. [6] Bujar M,Scott G,Darron C,et al.Base isolation technologies for seismic protection of museum artifacts[C]//Proceedings of the 2003 IAMFA Annual Conference. San Francisco,2003. [7] Onem G,Tüzün C,Erdik M ,et al.Earthquake protection of museum displays by a low-cost base-isolation system[C]//4th World Conference on Structural Control and Monitoring.La Jolla,2006. [8] Berto L,Favaretto T,Saetta A. Seismic risk mitigation technique for art objects:experimental evaluation and numerical modeling of double concave curved surface sliders[J]. Bulletin of Earthquake Engineering, 2013, 11(5): 1817-1840. DOI:10.1007/s10518-013-9441-8 [9] Zhou qian,Yan Weiming. Development of isolation devices for free-standing museum cultural relics[J]. Journal of Disaster Prevention and Mitigation Engineering, 2013, 33(2): 147-154. [周乾,闫维明. 馆藏浮放文物隔震装置的开发与应用[J]. 防灾减灾工程学报, 2013, 33(2): 147-154. DOI:10.13409/j.cnki.jdpme.2013.02.006] [10] Wu Laiming,Wang Zhongliang. Research on protection from earthquake of the cultural relics in museum(2)—Motion in put on fortify criterion and structural response[J]. Sciences of Conservation and Archaeology, 2002, 14(B12): 119-138. [吴来明,王忠良. 博物馆文物的防震保护研究 (二)——设防地震动输入及结构地震反应[J]. 文物保护与考古科学, 2002, 14(B12): 119-138. DOI:10.16334/j.cnki.cn31-1652/k.2002.s1.014] [11] Nie Yansen.Study on isolation properties of sliding artifact isolation bearing[D].Beijing:Beijing Jiaotong University,2017. 聂焱森.滑动式文物隔震支座隔震性能研究[D].北京:北京交通大学,2017. [12] Anil K.结构动力学理论及其在地震工程上的应用[M].2版.北京:高等教育出版社,2007:49–60. [13] Shen Ping.Research on Passive controlling methods for showcase of cultural relics under seismic load [D].Beijing:Beijing Jiaotong University,2014. 沈萍.文物展柜地震响应被动控制方法研究[D].北京: 北京交通大学,2014. [14] Ge Jiaqi,Wang Yi,Zhang Ling,et al. Performance-based study on whole process of metro induced vibration of the Chengdu Museum[J]. Journal of Building Structures, 2015, 36(2): 27-34. [葛家琪,王毅,张玲,等. 地铁所致成都博物馆振动全过程性能化研究[J]. 建筑结构学报, 2015, 36(2): 27-34. DOI:10.14006/j.jzjgxb.2015.02.004] [15] Liu Xingang,Zhang Ling,Ma Botao,et al. Torsional effect control of irregular base isolation structure of the Chengdu Museum[J]. Journal of Building Structures, 2016, 37(11): 24-29. [刘鑫刚,张玲,马伯涛,等. 成都博物馆基础隔震不规则结构扭转效应控制研究[J]. 建筑结构学报, 2016, 37(11): 24-29. DOI:10.14006/j.jzjgxb.2016.11.004] [16] Liu Pei,Yang Wenjian. Comparative study on the ground motion selection methods in Chinese and American codes[J]. Structural Engineers, 2013, 29(6): 7-13. [刘沛,杨文健. 中美抗震设计中地震波选取方法比较研究[J]. 结构工程师, 2013, 29(6): 7-13. DOI:10.15935/j.cnki.jggcs.2013.06.007]