Equivalent additional damping ratio of TMD under random earthquake
HE Hui1,2, TAN Ping1,2, LIN Songwei3, XIANG Yue1,2, LAN Li1,2
1. Department of Civil and Architecture Engineering, Hunan Institute of Technology , Hengyang 421002, China;
2. School of Civil Engineering, Guangzhou University, Guangzhou 510006, China;
3. Guangdong Architectural Design & Research Institute Co., Ltd., Guangzhou 510405, China
Abstract：The effective supplemental damping ratio of TMD added to structure under the random seismic ground motion excitations was researched in this paper. Firstly, the Kanai-Tajimi power spectral density function of ground acceleration was described as the filtering effect of the site, which was expressed in transfer function form, and the displacement dynamic amplification factor of structure to bedrock was then derived. Combined with the SRSS methodology, the analytical expression of the effective supplemental damping ratio of TMD added to the each modal of structure was given using mean square value of structural displacement response as a criterion. Finally, the solving procedure of the effective supplemental damping ratio of TMD was demonstrated by a view tower, and the analysis results shown that it was reasonable to use effective supplemental damping ratio to evaluate TMD damping performance, furthermore, the control effect of structural displacement could be evaluated precisely by the proposed analytical expression of the effective supplemental damping ratio of TMD.
贺辉1,2，谭平1,2,林松伟3,向越1,2，兰李1,2. 随机地震作用下TMD等效附加阻尼比研究[J]. 振动与冲击, 2022, 41(1): 107-115.
HE Hui1,2, TAN Ping1,2, LIN Songwei3, XIANG Yue1,2, LAN Li1,2. Equivalent additional damping ratio of TMD under random earthquake. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(1): 107-115.
[1] 欧进萍.结构振动控制：主动、半主动和智能控制[M].北京:科学出版社,2003.
[2] 李春祥, 刘艳霞. 高层建筑TMD风振控制优化设计[J]. 计算力学学报, 2001, 18(1)：69-73.(LI Chunxiang, LIU Yanxia. Optimum design of TMD for suppressing vibration of tall buildings subjected to wind[J]. Chinese Journal of Computational Mechanics, 2001, 18(1)：69-73. (in Chinese))
[3] 王肇民.高耸结构振动控制[M].上海:同济大学出版社,1997.
[4] 瞿伟廉.高层建筑和高耸结构的风振控制设计[M].武汉:武汉测绘科技大学出版社,1991.
[5] McNamara R J . Tuned Mass Dampers for Buildings[J]. ASCE Journal of Structural Division, 1977, 103(9):1785-1798.
[6] Luft R W. Optimal tuned mass dampers for buildings[J]. Journal of the structural division, 1979, 105(12):2766-2772.
[7] 王肇民. 电视塔结构TMD风振控制研究与设计[J]. 建筑结构学报, 1994, 015(005):2-13. (WANG Zhaomin, Study and design of TMD wind vibration control of TV tower structures[J]. Journal of Building Structures, 1994, 015(005):2-13. (in Chinese))
[8] Tanaka H , Mak C Y . Effect of tuned mass dampers on wind induced response of tall buildings[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1983, 14(1-3):357-368.
[9] Kaynai AM, Veneziano D, Biggs JM. Seismic effectiveness of tuned mass dampers[J]. Journal of Structural Engineering, ASCE 1981, 107(8):1465–84.
[10] Sladek JR, Klingner RE. Effect of tuned mass dampers on seismic response[J]. Journal of Structural Engineering, ASCE 1983, 109(8):2004–9.
[11] Chowdhury AH, Iwuchukwu MD, Garske JJ. Past and future of seismic effectiveness of tuned mass dampers[J]. In: Proceedings of the 2nd International Symposium on Structural Control, Ontario, Canada, 1985, 105-27.
[12] Wu J , Chen G , Lou M . Seismic effectiveness of tuned mass dampers considering soil–structure interaction[J]. Earthquake Engineering & Structural Dynamics, 1999, 28(11):1219–1233..
[13] Pinkaew T , Lukkunaprasit P , Chatupote P . Seismic effectiveness of tuned mass dampers for damage reduction of structures[J]. Engineering Structures, 2003, 25(1): 39-46.
[14] Villaverde R , Koyama L A . Damped resonant appendages to increase inherent damping in buildings[J]. Earthquake Engineering & Structural Dynamics, 1993, 22(6):491-507.
[15] Sadek F , Mohraz B , Taylor A W , et al. A method of estimating the parameters of tuned mass dampers for seismic applications[J]. Earthquake Engineering and Structural Dynamics, 1997, 26(6):617-635.
[16] Kanai, Kiyoshi. Semi-empirical formula for the seismic characteristics of ground(Structure)[J]. Transactions of the Architectural Institute of Japan, 1957, 57.1:281-284.
[17] Tajimi, H. A statistical method of determining the maximum response of a building structure during an earthquake[C]. Proc World Conference on Earthquake Engineering. 1960.
[18] 白国良, 朱丽华.基于现行抗震规范的Kanai-Tajimi模型参数研究[J]. 世界地震工程, 2004, 020(003):114-118. (BAI Guoliang, ZHU Lihua. Study on the parameters of Kanai-Tajimi model based on the code(GB50011-2001)[J]. World Earthquake Engineering, 2004, 020(003):114-118. (in Chinese))
[19] 薛素铎, 王雪生, 曹资.基于新抗震规范的地震动随机模型参数研究[J]. 土木工程学报, 2003, 036(005):5-10. (XUE Suduo, WANG Xuesheng, CAO Zi. Parameters study on seismic random model based on the new seismic code[J]. China Civil Engineering Journal, 2003, 036(005):5-10. (in Chinese))
[20] Den Hartog J P. Mechanical vibration[M]. NY: McGraw Hill, 1956.
[21] Spencer B F , Johnson E A , Ramallo J C . "Smart" Isolation for Seismic Control.[J]. JSME International Journal Series C, 2000, 43(3):704-711.
