不同阻尼模型对地铁振动下结构动力响应分析的影响研究

田源; 黄羽立; 王一星; 陆新征; 许镇

doi:10.6052/j.issn.1000-4750.2022.08.0729

不同阻尼模型对地铁振动下结构动力响应分析的影响研究

doi: 10.6052/j.issn.1000-4750.2022.08.0729

田源^1, ,,
黄羽立^2,,
王一星^2,,
陆新征^2,,
许镇^1,

1.
城镇化与城市安全研究院，土木与资源工程学院，北京科技大学，北京 100083
2.
土木工程安全与耐久教育部重点实验室，清华大学土木工程系，北京 100084

基金项目: 国家自然科学基金项目(52121005)；北京市科技新星计划项目(Z191100001119115)

详细信息

作者简介:
黄羽立(1980−)，男，广东人，博士，主要从事工程结构抗震研究(E-mail: huangyl@mail.tsinghua.edu.cn)

王一星(1996−)，女，辽宁人，博士生，主要从事非结构抗震研究(E-mail: 15734068335@163.com)

陆新征(1978−)，男，安徽人，教授，博士，主要从事结构数值模拟与防灾减灾研究(E-mail: luxz@tsinghua.edu.cn)

许　镇(1986−)，男，北京人，教授，博士，主要从事城市综合数字防灾研究(E-mail: xuzhen@ustb.edu.cn)

通讯作者:
田　源(1991−)，男，辽宁人，副教授，博士，主要从事城市与复杂工程安全与防灾减灾研究(E-mail: ytian@ustb.edu.cn)

中图分类号: TU311.3
计量
- 文章访问数: 226
- HTML全文浏览量: 90
- PDF下载量: 115
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-23
- 修回日期: 2022-10-10
- 网络出版日期: 2022-10-29
- 刊出日期: 2023-02-01

INFLUENCE OF DAMPING MODELS ON STRUCTURAL DYNAMIC RESPONSE ANALYSES UNDER SUBWAY-INDUCED VIBRATIONS

TIAN Yuan^{1
, ,},
HUANG Yu-li^2
,,
WANG Yi-xing^2
,,
LU Xin-zheng^2
,,
XU Zhen^1
,

1.
Research Institute of Urbanization and Urban Safety, School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 在结构的弹性动力响应分析中，阻尼具有重要的影响，直接决定了结构的耗能与衰减行为。准确地理解不同的阻尼模型的适用条件对实际工程问题的分析具有重要意义。地铁振动激励下的结构动力响应分析具有以下特点：地铁振动激励强度小，结构通常保持弹性，结构的动力响应行为直接受阻尼影响，合理的阻尼耗能对于分析结果的可靠性至关重要；地铁振动的频域范围宽，容易激发结构的多组高阶竖向振型，分析中需要合理考虑各阶振型的阻尼行为。各类阻尼模型由于建立在不同的基本假设之上，适用范围各有不同。粘性阻尼模型和滞变阻尼模型是结构动力分析中常见的两类阻尼模型，为明确不同阻尼模型在地铁振动激励下的结构动力响应分析问题中的特点，从两类模型中各选取了一个典型代表(分别为Rayleigh阻尼和通用频变阻尼)，并针对四类常见的典型结构(混凝土框架结构、钢框架结构、混凝土剪力墙结构、钢框架-支撑框筒结构)进行了分析。研究结果表明：采用Rayleigh阻尼时，需根据结构动力特性与荷载频率分布合理定义参考频率区间，相对于覆盖荷载主要频率的参考区间，仅覆盖结构自身前10阶竖向振型的参考频率区间过窄，在该文的频率区间下，后者的顶层竖向峰值加速度比前者小49%~92%；通用频变阻尼只需直接定义预期的阻尼-频率关系，与宽参考频率区间的Rayleigh阻尼模型相比，顶层竖向峰值加速度在其75%~156%，对不同的结构、同一结构的不同位置均不同。
- 地铁振动 /
- Rayleigh阻尼 /
- 通用频变阻尼 /
- 加速度 /
- 阻尼频域耗能分布
Abstract: In the elastic dynamic response analysis of a structure, damping has an important influence and directly determines the energy dissipation and decay behavior of the structure. An accurate understanding of the applicable conditions of different damping models is of great significance for the analysis of practical engineering problems. The main characteristics of dynamic structural response analyses under subway-induced vibration excitations are: The subway vibration excitation intensity is small, and the structure usually remains elastic. Thus, the dynamic response of the structure is directly affected by the damping, and a reasonable damping energy dissipation is essential for the reliability of the analysis results; the frequency domain of subway-induced vibration is wide, and it is easy to excite the high-order vertical vibration pattern of the structure. Hence, the damping behavior of each order needs to be reasonably considered in the analysis. Different damping models are based on different basic assumptions and have different applicable conditions. Viscous damping and hysteretic damping are two types of commonly adopted damping models. In order to clarify the characteristics of different damping models in the structural dynamic response analysis under subway-induced vibration excitations, one typical representative for each type of damping models (Rayleigh damping and universal rate-dependent damping, respectively) is selected, and four common types of typical structures (concrete frame structure, steel frame structure, concrete shear wall structure, and steel frame-braced core tube structure) were analyzed. The results show that: When Rayleigh damping is used, the reference frequency range needs to be reasonably defined according to the structural dynamic characteristics and the external excitation frequency distribution. Compared with the Rayleigh damping model with the reference frequency range covering the main frequency of the external excitations, the model with the reference frequency range covering only the first 10 orders of vertical vibration mode is too narrow. In the cases of this paper, the vertical peak acceleration of the latter is 49% and 92% less than that of the former; the universal rate-dependent damping only requires direct definition of the expected damping-frequency relationship. The peak vertical roof accelerations of cases using the universal rate-dependent damping are 75%-156% of those adopting the Rayleigh damping model with a wide reference frequency range. The influence of damping models may differ for different structures and different locations of the same structure.
- subway-induced vibration /
- Rayleigh damping /
- universal rate-dependent damping /
- acceleration /
- energy dissipation of damping in the frequency domain

HTML全文

图 1 Rayleigh阻尼耗能情况

Figure 1. Energy dissipation of Rayleigh damping

下载: 全尺寸图片幻灯片

图 2 通用频变阻尼耗能情况

Figure 2. Energy dissipation of universal rate-dependent damping

下载: 全尺寸图片幻灯片

图 3 案例分析结构的三维图和平面图　/m

Figure 3. 3D view and plan view of each case study structure

下载: 全尺寸图片幻灯片

图 4 实测地铁引起竖向振动时程

Figure 4. Recorded subway-induced vertical vibration time history

下载: 全尺寸图片幻灯片

图 5 竖向振动时程的傅里叶谱

Figure 5. Fourier spectrum of each vertical vibration

下载: 全尺寸图片幻灯片

图 6 混凝土框架的各层峰值竖向加速度

Figure 6. Peak vertical acceleration at each story of the concrete frame

下载: 全尺寸图片幻灯片

图 7 混凝土框架顶层在1/3倍频程带的均方根加速度

Figure 7. Root mean square of the roof acceleration of the concrete frame in one-third octaves

下载: 全尺寸图片幻灯片

图 8 钢框架的各层峰值竖向加速度

Figure 8. Peak vertical acceleration at each story of the steel frame

下载: 全尺寸图片幻灯片

图 9 钢框架顶层在1/3倍频程带的均方根加速度

Figure 9. Root mean square of the roof acceleration of the steel frame in one-third octaves

下载: 全尺寸图片幻灯片

图 10 混凝土剪力墙的各层峰值竖向加速度

Figure 10. Peak vertical acceleration at each story of the concrete shear wall structure

下载: 全尺寸图片幻灯片

图 11 混凝土剪力墙顶层在1/3倍频程带的均方根加速度

Figure 11. Root mean square of the roof acceleration of the concrete shear wall structure in one-third octaves

下载: 全尺寸图片幻灯片

图 12 钢框架-支撑框筒结构的各层峰值竖向加速度

Figure 12. Peak vertical acceleration at each story of the steel frame-braced core tube structure

下载: 全尺寸图片幻灯片

图 13 钢框架-支撑框筒结构顶层在1/3倍频程带的均方根加速度

Figure 13. Root mean square of the roof acceleration of the steel frame-braced core tube structure in one-third octaves

下载: 全尺寸图片幻灯片

表 1 案例分析结构的基本信息

Table 1. Basic information of each case study structure

结构	高度/m	层数/层	包含单元
混凝土框架结构	33	7	梁、柱、楼板
钢框架结构	24.2(29.2)	6(7)	梁、柱、楼板
混凝土剪力墙结构	54.2(60)	18(20)	梁、剪力墙、楼板
钢框架-支撑框筒结构	166	37	梁、柱、支撑、楼板
注：括号中的高度和层数表示结构局部最高处的高度和层数。

下载: 导出CSV

表 2 OpenSees模型基本信息

Table 2. Basic information of the OpenSees models

模型	节点数	单元数		截面数
模型	节点数	dispBeam Column	Shell DKGQ	Fiber	LayeredShell
混凝土框架结构	1376	1895	788	461	10
钢框架结构	2847	3252	1130	75	18
混凝土剪力墙结构	17 192	6895	13 960	695	27
钢框架-支撑框筒结构	15 568	21 228	7326	56	6

下载: 导出CSV

表 3 模型基本动力特性与原模型相对误差

Table 3. Relative error of the fundamental dynamic characteristics for the established models

特性	相对误差/(%)
特性	混凝土框架结构	钢框架结构	混凝土剪力墙结构	钢框架-支撑框筒结构
T₁	1.4	1.2	−1.8	0.7
T₂	0.1	3.4	−5.5	0.2
T₃	1.8	3.5	−0.3	1.8
T₄	1.2	1.0	3.2	0.7
T₅	0.1	2.8	−3.5	0.2
T₆	1.4	2.1	0.1	1.3

下载: 导出CSV

表 4 案例分析结构的总重力与竖向自振频率

Table 4. Gravity load and fundamental frequencies along the height of each case study structure

结构	总重力/kN	第1阶竖向自振频率/Hz	第10阶竖向自振频率/Hz
混凝土框架结构	9.58×10⁴	6.15	10.09
钢框架结构	4.95×10⁴	7.17	12.24
混凝土剪力墙结构	2.05×10⁵	8.38	19.24
钢框架-支撑框筒结构	7.83×10⁵	2.17	6.27

下载: 导出CSV

表 5 阻尼模型定义信息

Table 5. Information of damping definition for each structure

结构	阻尼模型	编号	阻尼比	频率区间/Hz
混凝土框架结构	Rayleigh阻尼	CF-RL1	0.05	[6.15, 10.09]
	Rayleigh阻尼	CF-RL2		[6.15, 100]
	通用频变阻尼	CF-URD		[0.05, 500]
钢框架结构	Rayleigh阻尼	SF-RL1	钢：0.02；混凝土：0.05	[7.17, 12.24]
	Rayleigh阻尼	SF-RL2		[7.17, 100]
	通用频变阻尼	SF-URD		[0.05, 500]
混凝土剪力墙结构	Rayleigh阻尼	CS-RL1	0.05	[8.38, 19.24]
	Rayleigh阻尼	CS-RL2		[8.38, 100]
	通用频变阻尼	CS-URD		[0.05, 500]
钢框架-支撑框筒结构	Rayleigh阻尼	ST-RL1	钢：0.02；混凝土：0.05	[2.17, 6.27]
	Rayleigh阻尼	ST-RL2		[2.17, 100]
	通用频变阻尼	ST-URD		[0.05, 500]

下载: 导出CSV

表 6 混凝土框架的顶层峰值竖向加速度

Table 6. Peak vertical roof acceleration of the concrete frame

竖向激励	阻尼方案	峰值加速度/(m·s⁻²)	相对RL2的差异/(%)
D01	CF-RL1	0.048	−70.1
	CF-RL2	0.161	−
	CF-URD	0.175	8.5
D02	CF-RL1	0.097	−70.7
	CF-RL2	0.332	−
	CF-URD	0.326	−1.7

下载: 导出CSV

表 7 钢框架的顶层峰值竖向加速度

Table 7. Peak vertical roof acceleration of the steel frame

竖向激励	阻尼方案	峰值加速度/(m·s⁻²)	相对RL2的差异/(%)
D01	CF-RL1	0.038(0.038)	−56.9(−58.6)
	CF-RL2	0.089(0.092)	−
	CF-URD	0.138(0.069)	55.7(−24.9)
D02	CF-RL1	0.063(0.068)	−49.1(−54.4)
	CF-RL2	0.124(0.149)	−
	CF-URD	0.131(0.125)	6.1(−15.9)
注：括号外的值为SF1处结果，括号内的值为SF2处结果。

下载: 导出CSV

表 8 混凝土剪力墙的顶层峰值竖向加速度

Table 8. Peak vertical roof acceleration of the concrete shear wall structure

竖向激励	阻尼方案	峰值加速度/(m·s⁻²)	相对RL2的差异/(%)
D01	CF-RL1	0.040(0.040)	−64.1(−59.2)
	CF-RL2	0.112(0.097)	−
	CF-URD	0.166(0.114)	49.1(18.0)
D02	CF-RL1	0.072(0.080)	−54.3(−52.9)
	CF-RL2	0.159(0.171)	−
	CF-URD	0.230(0.183)	44.7(7.1)
注：括号外的值为CS1处结果，括号内的值为CS2处结果。

下载: 导出CSV

表 9 钢框架-支撑框筒结构的顶层峰值竖向加速度

Table 9. Peak vertical roof acceleration of the steel frame-braced core tube structure

竖向激励	阻尼方案	峰值加速度/(m·s⁻²)	相对RL2的差异/(%)
D01	CF-RL1	0.003	−88.3
	CF-RL2	0.026	−
	CF-URD	0.037	41.5
D02	CF-RL1	0.004	−91.8
	CF-RL2	0.047	−
	CF-URD	0.048	1.5

下载: 导出CSV

参考文献(31)

[1]	XU R, LI X C, YANG W, et al. Field measurement and research on environmental vibration due to subway systems: A case study in eastern China [J]. Sustainability, 2019, 11(23): 11236835. doi: 10.3390/su11236835
[2]	胡皓宇, 杨军, 潘鹏. 轨道交通致建筑物振动的相关规范比较研究[J]. 建筑结构, 2017, 47(7): 5 − 13. HU Haoyu, YANG Jun, PAN Peng. Comparative research on urban rail transit-induced building vibrations related specifications [J]. Building Structure, 2017, 47(7): 5 − 13. (in Chinese)
[3]	FEI Y F, TIAN Y, HUANG Y L, et al. Influence of damping models on dynamic analyses of a base-isolated composite structure under earthquakes and environmental vibrations [J]. Engineering Mechanics, 2022, 39(3): 201 − 211.
[4]	赵娜. 地铁上盖物业的振动舒适度研究[D]. 武汉: 武汉理工大学, 2012. ZHAO Na. Vibration serviceability research on top head estates of subway [D]. Wuhan: Wuhan University of Technology, 2012. (in Chinese)
[5]	李顺. 地铁运行对高层建筑振动及舒适度影响研究[D]. 哈尔滨: 哈尔滨工业大学, 2020. LI Shun. Research on the influence of subway operation on the vibration and comfort of high-rise buildings [D]. Harbin: Harbin Institute of Technology, 2020. (in Chinese)
[6]	CHENG Z G, LIAO W J, CHEN X Y, et al. A vibration recognition method based on deep learning and signal processing [J]. Engineering Mechanics, 2021, 38(4): 230 − 246.
[7]	STRUTT J W. The theory of sound [M]. Cambridge, UK: Cambridge University Press, 1877: 97 − 98.
[8]	WILSON E L, PENZIEN J. Evaluation of orthogonal damping matrices [J]. International Journal for Numerical Methods in Engineering, 1972, 4(1): 5 − 10. doi: 10.1002/nme.1620040103
[9]	路德春, 高泽军, 孔凡超, 等. 地铁列车运行诱发地面邻近建筑振动的数值模拟研究[J/OL]. 土木与环境工程学报(中英文), 2022: 1 − 13. [2022-10-17]. https://kns.cnki.net/kcms/detail/50.1218.TU.20220517.1032.002.html. LU Dechun, GAO Zejun, KONG Fanchao, et al. Numerical study on vibration of ground building adjacent to metro induced by operation of subway train [J/OL]. Journal of Civil and Environmental Engineering, 2022: 1 − 13. [2022-10-17]. https://kns.cnki.net/kcms/detail/50.1218.TU.20220517.1032.002.html. (in Chinese)
[10]	王佳欣. 地铁运行引起住宅建筑振动对人体烦恼度影响研究[D]. 北京: 北京交通大学, 2021. WANG Jiaxin. The influence of residential building vibration caused by metro trains operation on human annoyance [D]. Beijing: Beijing Jiaotong University, 2021. (in Chinese)
[11]	金峤, 任玺茗, 孙丽. 地铁列车振动对邻近综合体高层建筑的影响分析[J]. 沈阳建筑大学学报(自然科学版), 2021, 37(2): 227 − 234. JIN Qiao, REN Ximing, SUN Li. Analysis on influence of subway train vibration on adjacent high-rise complex buildings [J]. Journal of Shenyang Jianzhu University (Natural Science), 2021, 37(2): 227 − 234. (in Chinese)
[12]	李守继, 楼梦麟. 阻尼对地铁引起地面振动计算的影响[J]. 合肥工业大学学报(自然科学版), 2010, 33(1): 89 − 93. LI Shouji, LOU Menglin. Influence of damping on the caculation of subway-induced ground vibration [J]. Journal of Hefei University of Technology, 2010, 33(1): 89 − 93. (in Chinese)
[13]	NAKAMURA N. Time history response analysis using extended Rayleigh damping model [J]. Procedia Engineering, 2017, 199: 1472 − 1477. doi: 10.1016/j.proeng.2017.09.408
[14]	PUTHANPURAYIL A M, LAVAN O, CARR A J, et al. Elemental damping formulation: An alternative modelling of inherent damping in nonlinear dynamic analysis [J]. Bulletin of Earthquake Engineering, 2016, 14(8): 2405 − 2434. doi: 10.1007/s10518-016-9904-9
[15]	孙攀旭, 杨红. 改进滞变阻尼模型的时域计算方法[J]. 工程力学, 2021, 38(4): 8 − 19. doi: 10.6052/j.issn.1000-4750.2020.05.0313 SUN Panxu, YANG Hong. Time-domain calculation method based on improved hysteretic damping model [J]. Engineering Mechanics, 2021, 38(4): 8 − 19. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.05.0313
[16]	LUCO J E, LANZI A. A new inherent damping model for inelastic time-history analyses [J]. Earthquake Engineering & Structural Dynamics, 2017, 46(12): 1919 − 1939.
[17]	LEE C L. Proportional viscous damping model for matching damping ratios [J]. Engineering Structures, 2020, 207: 110178. doi: 10.1016/j.engstruct.2020.110178
[18]	刘晶波, 杜修力. 结构动力学[M]. 北京: 机械工业出版社, 2005: 66 − 69. LIU Jingbo, DU Xiuli. Dynamics of structures [M]. Beijing: China Machine Press, 2005: 66 − 69. (in Chinese)
[19]	CHOPRA A K. Dynamics of structures: Theory and applications to earthquake engineering [M]. 4th ed. Prentice Hall: Upper Saddle River, 2011: 106.
[20]	HUANG Y L, STURT R, WILLFORD M. A damping model for nonlinear dynamic analysis providing uniform damping over a frequency range [J]. Computers & Structures, 2019, 212: 101 − 109.
[21]	TIAN Y, FEI Y F, HUANG Y L, et al. A universal rate-dependent damping model for arbitrary damping-frequency distribution [J]. Engineering Structures, 2022, 255: 113894. doi: 10.1016/j.engstruct.2022.113894
[22]	KIMBALL A L, LOVELL D E. Internal friction in solids [J]. Physical Review, 1927, 30(6): 948 − 959. doi: 10.1103/PhysRev.30.948
[23]	LOMNITZ C. Linear dissipation in solids [J]. Journal of Applied Physics, 1957, 28(2): 201 − 205. doi: 10.1063/1.1722707
[24]	CREMER L, HECKL M. Structure-borne sound [M]. 3rd ed. Berlin: Springer, 2005: 191 − 196.
[25]	张弛. 基于倒塌分析的不规则结构和中美钢结构抗震性能研究[D]. 北京: 清华大学, 2021. ZHANG Chi. Study on seismic performance of irregular structures and Chinese and American steel structures based on collapse analysis [D]. Beijing: Tsinghua University, 2021. (in Chinese)
[26]	LU X Z, XIE L L, GUAN H, et al. A shear wall element for nonlinear seismic analysis of super-tall buildings using OpenSees [J]. Finite Elements in Analysis and Design, 2015, 98: 14 − 25. doi: 10.1016/j.finel.2015.01.006
[27]	LU X Z, TIAN Y, CEN S, et al. A high-performance quadrilateral flat shell element for seismic collapse simulation of tall buildings and its implementation in OpenSees [J]. Journal of Earthquake Engineering, 2018, 22(9): 1662 − 1682. doi: 10.1080/13632469.2017.1297269
[28]	栗润德. 地铁列车引起的地面振动及隔振措施研究[D]. 北京: 北京交通大学, 2009. LI Runde. Study on the Metro induced ground vibrations and isolation measures [D]. Beijing: Beijing Jiaotong University, 2009. (in Chinese)
[29]	JGJ/T 441−2019, 建筑楼盖结构振动舒适度技术标准[S]. 北京: 中国建筑工业出版社, 2020. JGJ/T 441−2019, Technical standard for human comfort of the floor vibration [S]. Beijing: China Architecture & Building Press, 2020. (in Chinese)
[30]	XU J J, HUANG Y L, QU Z. An efficient and unconditionally stable numerical algorithm for nonlinear structural dynamics [J]. International Journal for Numerical Methods in Engineering, 2020, 121(20): 4614 − 4629.
[31]	许德峰, 戴君武, 杨永强, 等. 地铁沿线建筑的振动实测和数值模拟分析[J]. 建筑结构, 2021, 51(增刊 2): 697 − 701. XU Defeng, DAI Junwu, YANG Yongqiang, et al. Study vibration measurement and numerical simulation analysis of buildings along subway [J]. Building Structure, 2021, 51(Suppl 2): 697 − 701. (in Chinese)