Abstract：As the damping model and equation of motion have significant impacts on the accuracy of structural dynamic analysis algorithms. Because the seismic behavior of base-isolation structures has remarkable characteristics, dynamic analysis algorithms for conventional structures may not be suitable for the base-isolated structures any more. From this point of view, this paper presents a study with the emphasis on the structural damping model and equations of motion with different seismic input. It is found that use of the conventional method to construct the damping matrix for the base-isolated structure will cause the superstructure produce damping force with the rigid displacement of the isolation bearing and this may cause significant in numerical accuracy loss. A new scheme is proposed for the determination of damping matrix of the base-isolated structure, and general expressions are presented in terms of the damping matrix of the superstructure and the damping constant of the isolation layer. Analytical expressions of structural matrices are presented for a shear-type model of base-isolated structures, and then a numerical study is conducted to demonstrate the feasibility and effectiveness of the proposed methods. The numerical results obtained confirm that use of the conventional method to construct the damping matrix for the base-isolated structure overestimates the damping effect of the structure, and the displacement input model overestimates the deformation of the isolation layer and underestimates superstructure responses, when the damping of the isolation layer is 0.3, the relative deviations can reach 34.6 and -31.1% , by using the displacement-velocity input model, the analysis results are consistent with the acceleration input model, so the displacement-velocity input model should be used instead of the traditional displacement input model.
Key words: base isolation; equation of motion; damping matrix; displacement input model; seismic motion input mode
李世渊1，谭平1,2,3，马海涛1,2,3. 基础隔震结构的运动方程与阻尼矩阵在动力响应分析中的适用性研究[J]. 振动与冲击, 2023, 42(1): 198-206.
LI Shiyuan1, TAN Ping1,2,3, MA Haitao1,2,3. Applicability of equation of motion and damping matrix of base-isolated structure in dynamic response analysis. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(1): 198-206.
[1] 田玉基, 杨庆山. 地震地面运动作用下结构反应的分析模型[J]. 工程力学, 2005, 22(5): 170-174.
TIAN Yuji, YANG Qingshan. Analysis models and methods for structural seismic responses [J]. Engineering Mechanics, 2005, 22(5): 170-174. (in Chinese)
[2] 柳国环, 李宏男, 林海. 结构地震响应计算模型的比较与分析[J]. 工程力学, 2009, 26(2): 10-15.
LIU Guohuan, LI Hongnan, LIN Hai. Comparision and evalution of models for structural seismic responses analysis [J]. Engineering Mechanics, 2009, 26(2): 1015. (in Chinese)
[3] 丁阳, 林伟, 李忠献. 大跨度空间结构多维多点非平稳随机地震反应分析[J]. 工程力学, 2007, 24(3): 97-103.
DING Yang, LIN Wei, LI Zhongxian. Non-stationary random seismic analysis of long-span spatial structures under multi-support and multi-dimensional earthquake excitations [J]. Engineering Mechanics, 2007, 24(3): 97-103. (in Chinese)
[4] 薛素铎, 王雪生, 曹资. 空间网格结构多维多点随机地震响应分析的高效算法[J]. 世界地震工程, 2004, 20(3): 43-49.
XUE Suduo, WANG Xuesheng, CAO Zi. An efficient algorithm for multi-dimensional and multi-support random seismic analysis of spatial reticulated structures [J]. World Earthquake Engineering, 2004, 20(3): 43-49. (in Chinese)
[5] 贾少敏, 王子琦, 赵雷, 等. 多点激励下隔震桥梁非线性随机振动的时域显式迭代模拟法[J]. 工程力学, 2018, 35(12): 116-123.
JIA Shaomin, WANG Ziqi, ZHAO Lei, et al. A simulation method based on explicit time-domain iteration scheme for nonlinear random vibration analysis of isolated bridges under multi-support excitation [J]. Engineering Mechanics, 2018, 35(12): 116-123. (in Chinese)
[6] 惠迎新, 王克海. 基于多点激励位移输入模型的跨断层桥梁地震动输入方法[J]. 东南大学学报 (自然科学版), 2015, 45(3): 557-562.
HUI Yingxin, WANG Kehai. Earthquake motion input method for bridges crossing fault based on multi-support excitation displacement input model [J]. Journal of Southeast University (Natural Science Edition), 2015, 45(3): 557-562. (in Chinese)
[7] 柳国环, 李宏男, 田利. 九江长江大桥在多点多维地震激励下的反应分析[J]. 振动与冲击, 2009, 28(9): 204-209.
LIU Guohuan, LI Hongnan, TIAN Li. Response analysis of Jiujiang Yangtze river highway bridge under spatially variable earthquake ground motions [J]. Journal of Vibration and Shock, 2009, 28(9): 204-209. (in Chinese)
[8] 国巍, 余志武, 国振. 多点激励下大跨隔震结构分析模型[J]. 华中科技大学学报 (自然科学版), 2012, 40(9): 101-105.
GUO Wei, YU Zhiwu, GUO Zhen. Analysis model for long-span isolated structure subjected to multi-support earthquake excitations [J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2012, 40(9): 101-105. (in Chinese)
[9] 何卫平, 周宜红, 何蕴龙. 地震动位移与加速度输入模型差异研究[J]. 应用力学学报, 2018, 35(1): 93-98.
HE Weiping, ZHOU Yihong, HE Yunlong. Difference between seismic input models based on displacement and acceleration [J]. Chinese Journal of Applied Mechanics, 2018, 35(1): 93-98. (in Chinese)
[10] Chopra A K. Dynamics of Structures: Theory and Applications to Earthquake Engineering [M]. Beijing: Higher Education Press, 2005.
[11] 杜永峰, 李慧, 苏磐石, 等. 非比例阻尼隔震结构地震响应的实振型分解法[J]. 工程力学, 2003, 20(4): 24-32.
DU Yongfeng, LI Hui, Spencer Jr B F, et al. Real modal superposition method for analysis of seismic response of non-proportionally damped isolated structures [J]. Engineering Mechanics, 2003, 20(4): 24-32. (in Chinese)
[12] 周国良, 李小军, 喻畑, 等. 结构地震作用的基底激励模型及其适用性[J]. 建筑结构学, 2010, 31(增2): 82-88.
ZHOU Guoliang, LI xiaojun, YU Yan, et al. Applicability research on base excitation models used in structural seismic response analysis [J]. Journal of Building Structures, 2010, 31(Suppl 2): 82-88. (in Chinese)
[13] Wilson E L. Three-dimensional static and dynamic analysis of structures: a physical approach with emphasis on earthquake engineering [M]. Berkley, California: Computers and Structures, Inc., 2002.
[14] De Domenico D, Falsone G, Ricciardi G. Improved response-spectrum analysis of base-isolated buildings: A substructure-based response spectrum method [J]. Engineering Structures, 2018, 162: 198-212.
[15] 杜永峰, 张迪, 党育, 等. 基础隔震结构简化模型的振动参数识别[J]. 世界地震工程, 2001, 17(2): 53-58.
DU Yongfeng, ZHANG Di, DANG Yu, et al. Identification of vibration parameters of simplified base isolation models [J]. World Earthquake Engineering, 2001, 17(2): 53-58. (in Chinese)
[16] 周福霖. 工程结构减震控制[M]. 北京: 地震出版社, 2007.
ZHOU Fulin. Vibration Control of Engineering Structures [M]. Beijing: Seismological Press, 2007. (in Chinese)
