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

李世渊1,谭平1,2,3,马海涛1,2,3

振动与冲击 ›› 2023, Vol. 42 ›› Issue (1) : 198-206.

PDF(1807 KB)
PDF(1807 KB)
振动与冲击 ›› 2023, Vol. 42 ›› Issue (1) : 198-206.
论文

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

  • 李世渊1,谭平1,2,3,马海涛1,2,3
作者信息 +

Applicability of equation of motion and damping matrix of  base-isolated structure in dynamic response analysis

  • LI Shiyuan1, TAN Ping1,2,3, MA Haitao1,2,3
Author information +
文章历史 +

摘要

结构阻尼模型和运动方程是影响结构抗震动力分析精度的关键因素。由于基础隔震结构地震响应具有显著的特殊性,因此普通非隔震结构地震响应算法未必适用。基于这一认识,重点研究基础隔震结构动力分析方法中采用的各种模型,考虑基于不同地震动输入的结构阻尼模型和运动方程。研究发现,采用现有常规方法构造隔震结构阻尼模型时,上部结构会随着隔震支座发生刚体位移时产生阻尼力,这将可能导致计算精度的显著降低。针对这一问题,提出了确定基础隔震结构阻尼矩阵的一般方法,给出了基于上部结构阻尼矩阵和隔震层阻尼常数的通用表达式。采用隔震结构剪切型模型,给出了结构矩阵的解析表达式,并以此为基础进行了算例验证。研究结果表明,目前常用的隔震结构阻尼模型可能会高估结构的阻尼作用,从而低估结构响应;采用位移输入模型会高估隔震层相对位移、低估上部结构响应,当隔震层等效阻尼比达到0.3时,相对偏差可达到34.6和-31.1%,而采用位移-速度输入模型可得到与加速度输入模型一致的分析结果,故应采用位移-速度输入模型代替传统的位移输入模型。
关键词:基础隔震;运动方程;阻尼矩阵;位移输入模型;地震动输入模型

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

关键词

基础隔震 / 运动方程 / 阻尼矩阵 / 位移输入模型 / 地震动输入模型

Key words

base isolation / equation of motion / damping matrix / displacement input model / seismic motion input mode

引用本文

导出引用
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[J]. Journal of Vibration and Shock, 2023, 42(1): 198-206

参考文献

[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): 1015. (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)

PDF(1807 KB)

Accesses

Citation

Detail

段落导航
相关文章

/