人行桥振动舒适度的设计与评价理论研究
|
摘要
近年来,研究人群的不同活动对结构的影响正在引起国际结构工程界的关注。人们逐渐意识到在一些人群活动较为密集的结构如人行桥中出现的人群不应该只看作结构的静荷载,在人群的不同活动下,结构的动力效应十分明显。人行桥由行人激起的振动一般不会导致结构本身的破坏,但会影响到桥上行人的舒适性。近期许多柔性人行桥出现了人行荷载导致的大幅度振动问题,这表明在结构设计中必须考虑振动舒适度的要求。
人行桥振动舒适度问题是本文的研究重点,总的研究工作分成四部分:首先,系统回顾了关于人行荷载的己有研究成果,介绍了步行激励荷载的时域模型和频域模型;对各种规范提出的计算模型进行了介绍和比较,在此基础上,推导并建立了单人和人群过桥的运动方程,并提出了简化实用方法。建立了基于烦恼率模型的人行桥振动舒适度评价方法,此评价方法可以综合考虑多频率、多振型的情况;最后,介绍了采用TMD抑制人行桥振动的理论,并且讨论了不同MTMD优化设计参数对人行桥振动控制的影响。
Recent years, the research about how the activities of different kinds of crowd influence the structural response is attracting more attentions in the fields of international civil engineering. People gradually realize that the crowd in some structures such as footbridges where the activities of crowd are more severe can not be seen as static loads. Under these different activities, the dynamic phenomenon in the structure is rather obvious. The excitation of a footbridge by a pedestrian passing over it can be unpleasant for a person walking or standing on the bridge, but usually not destructive for the structure itself. Recent excessive pedestrian-induced vibrations of many slender footbridges have especially shown that vibration serviceability limit states are very important requirements in any structural design.
The main focus of this thesis was on the vibration serviceability of footbridge. The work was divided into four subtasks. Firstly, development of research on walking load has been reviewed, and two types of such models are introduced: time- and frequency-domain models. Secondly, design criteria and load models proposed by various standards were introduced and a comparison was made. Based on that, the motion equations for single-person and crowds crossing the bridge have been established, including a suggested design formulation for practical use. Following that, a new theory for footbridge vibration serviceability design is proposed in this research on the basis of annoyance rate, which can consider multi-frequency and multi-mode situation. Finally, the available solution by using TMD to control vibration problems was studied, and the controlling effect with different MTMD parameters optimization methods was discussed.
人行桥振动舒适度问题是本文的研究重点,总的研究工作分成四部分:首先,系统回顾了关于人行荷载的己有研究成果,介绍了步行激励荷载的时域模型和频域模型;对各种规范提出的计算模型进行了介绍和比较,在此基础上,推导并建立了单人和人群过桥的运动方程,并提出了简化实用方法。建立了基于烦恼率模型的人行桥振动舒适度评价方法,此评价方法可以综合考虑多频率、多振型的情况;最后,介绍了采用TMD抑制人行桥振动的理论,并且讨论了不同MTMD优化设计参数对人行桥振动控制的影响。
Recent years, the research about how the activities of different kinds of crowd influence the structural response is attracting more attentions in the fields of international civil engineering. People gradually realize that the crowd in some structures such as footbridges where the activities of crowd are more severe can not be seen as static loads. Under these different activities, the dynamic phenomenon in the structure is rather obvious. The excitation of a footbridge by a pedestrian passing over it can be unpleasant for a person walking or standing on the bridge, but usually not destructive for the structure itself. Recent excessive pedestrian-induced vibrations of many slender footbridges have especially shown that vibration serviceability limit states are very important requirements in any structural design.
The main focus of this thesis was on the vibration serviceability of footbridge. The work was divided into four subtasks. Firstly, development of research on walking load has been reviewed, and two types of such models are introduced: time- and frequency-domain models. Secondly, design criteria and load models proposed by various standards were introduced and a comparison was made. Based on that, the motion equations for single-person and crowds crossing the bridge have been established, including a suggested design formulation for practical use. Following that, a new theory for footbridge vibration serviceability design is proposed in this research on the basis of annoyance rate, which can consider multi-frequency and multi-mode situation. Finally, the available solution by using TMD to control vibration problems was studied, and the controlling effect with different MTMD parameters optimization methods was discussed.
引文
1魏建东.与人群有关的桥梁垮塌事故.中外公路. 2005.25(6):78-82
2和丕状.桥梁美学.北京:人民交通出版社, 1999
3 Shijin Y. and Dongzhou H. Aesthetic consideration for urban pedestrian bridge design. Journal of Architectural Engineering. 1997, 3(1):3-8
4 H. Bachmann, W. Ammann. Vibrations in Structures-Induced by Man and Machines, Structural Engineering Documents, Vol. 3e, International Association of Bridge and Structural Engineering (IABSE), Zürich, 1987.
5 H. Bachmann. Practical cases of structures with man-induced vibrations, in: Symposium/Workshop on Serviceability of Buildings, Ottawa, Canada, May 16–18, 1988, pp. 419–434.
6 H. Bachmann. Case studies of structures with man-induced vibrations, Journal of Structural Engineering 118 (3) (1992) 631–647.
7 H. Bachmann. Vibration upgrading of gymnasia, dance halls and footbridges, Structural Engineering International 2 (2) (1992) 118–124.
8 Y. Fujino, B.M. Pacheco, S. Nakamura, P. Warnitchai. Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge, Earthquake Engineering and Structural Dynamics 22 (1993) 741–758.
9 P. Dallard, A.J. Fitzpatrick, A. Flint, S. Le Bourva, A. Low, R.M. Ridsdill-Smith, M. Willford. The London Millennium Footbridge, Structural Engineer 79 (22) (2001) 17–33.
10 T. Fitzpatrick, P. Dallard, S. Le Bourva, A. Low, R. Ridsdill Smith and M. Willford. Linking London: The Millennium Bridge. The Royal Academy of Engineering. June 2001.
11 P. Dallard, T. Fitzpatrick, A. Flint, A. Low, R. Ridsdill Smith, M. Willford, and M. Roche. London Millennium Bridge: Pedestrian-Induced Lateral Vibration. ASCE Journal of Bridge Engineering, November-December 2001, pages 412-417.
12 S-I. Nakamura. Lateral vibration on a pedestrian cable-stayed bridge. IABSE Journal of Structural Engineering International, volume 12, no. 4, 2002, pages 295-300.
13 S-I. Nakamura. Model for lateral excitation of footbridges by synchronous walking. ASCE Journal of Structural Engineering, January 2004, pages 32-37.
14袁旭斌.人行桥人致振动特性研究.同济大学博士学位论文. 2006.7
15 A. N. Blekherman. Swaying of pedestrian bridges. Journal of Bridge Engineering. 2005, 10(2):142-150
16 J.M.W. Brownjohn, A. Pavic, P. Omenzetter. A spectral density approach for modeling continuous vertical forces on pedestrian structures due to walking, Canadian Journal of Civil Engineering 31 (1) (2004) 65–77.
17 British Standards Institution (BSI). (1978).“British standard specification for loads; steel, concrete and composite bridges, Part 2.”BS5400, London.
18 Ontario Ministry of Transportation, Toronto. Ontario Highway Bridge Design Code, 1983
19 J. Smith. Vibration of structures: applications in civil engineering design. Chapman and hall, 1988
20 Y. Matsumoto, T. Nishioka, H. Shiojiri and K. Matsuzaki. Dynamic design of footbridges. IABSE Proceedings. 1978:1-15
21 Y. Matsumoto, S. Sato, T. Nishioka and Shiojiri H. Study on dynamic design of pedestrian over-bridges in consideration of characteristics of pedestrians. Proc JSCE. 1972, (205):63-70
22 N. Poovardom, S.Kanchanosot and P. Warnitchai. Application of non-linear multiple tuned mass dampers to suppress man-induced vibrations of a pedestrian bridge. Earthquake Engineering and Structural Dynamics. 2003, 32(7):1117-1131
23叶正强,李爱群,丁幼亮等.某大跨人行天桥的消能减振设计(一).特种结构. 2003, Vo1.20, No.l :68-70
24 F.C. Harper, W.J. Warlow, B.L. Clarke. The forces applied to the floor by the foot in walking, National Building Studies, Research Paper 32, Department of Scientific and Industrial Research, Building Research Station, London, 1961.
25 F.W. Galbraith, M.V. Barton. Ground loading from footsteps, Journal of the Acoustic Society of America 48 (5)(1970) 1288–1292.
26 J. Blanchard, B.L. Davies, J.W. Smith. Design criteria and analysis for dynamic loading of footbridges, in:Proceedings of the DOE and DOT TRRL Symposium on Dynamic Behaviour of Bridges, Crowthorne, UK, May 19,1977, pp. 90–106.
27 S.V. Ohlsson. Floor Vibration and Human Discomfort, PhD Thesis, Chalmers University of Technology, G?teborg, Sweden, 1982 (in English).
28 S.C. Kerr. Human Induced Loading on Staircases, PhD Thesis, Mechanical Engineering Department, University College London, UK, 1998.
29 T.P. Andriacchi, J.A. Ogle, J.O. Galante. Walking speed as a basis for normal and abnormal gait measurements, Journal of Biomechanics 10 (1977) 261–268.
30 J.H. Rainer, G. Pernica, D.E. Allen. Dynamic loading and response of footbridges, Canadian Journal of Civil Engineering 15 (1) (1988) 66–71.
31 B.R Eliss. On the response of long-span floors to walking loads generated by individuals and crowds. The Structural Engineering. 2000,78(10):17-25
32 J. Skorecki. The design and construction of a new apparatus for measuring the vertical forces exerted in walking: a gait machine, Journal of Strain Analysis 1 (5) (1966) 429–438.
33 J. Blanchard, B.L. Davies, J.W. Smith, Design criteria and analysis for dynamic loading of footbridges, in: Proceedings of the DOE and DOT TRRL Symposium on Dynamic Behaviour of Bridges, Crowthorne, UK, May 19, 1977, pp. 90–106.
34 P.E. Eriksson. Vibration of Low-Frequency Floors—Dynamic Forces and Response Prediction, PhD Thesis, Unit for Dynamics in Design, Chalmers University of Technology, G?teborg, Sweden, 1994.
35 S. Zivanovic, A. Pavic, P. Reynolds. Vibration serviceability of footbridges under human-induced excitation: a literature review. Journal of Sound and Vibration 2005, 279:1-74.
36 C. Y. Tuan and W. E. Saul(1985). "Loads due to spectator movements." Journal of Structural Engineering, ASCE, 111(2), 418-434.
37 A. Ebrahimpour and R. L. Sack(1992). "Design live loads for coherent crowd harmonic movements." Journal of Structural Engineering, ASCE, 110(2), 401-418.
38谢庆森,王秉权.安全人机工程,天津:天津大学出版社, 1999
39 Y. Matsumoto, S. Sato, T. Nishioka, H. Shiojiri. A study on design of pedestrian over-bridges, Transactions of JSCE 4 (1972) 50–51.
40 S.C. Kerr, N.W.M. Bishop, Human induced loadingon flexible staircases, Engineering Structures 23 (2001)37–45.
41 H. Bachmann, A.J. Pretlove, H. Rainer. Dynamic forces from rhythmical human body motions, in: Vibration Problems in Structures: Practical Guidelines, Birkh?user, Basel, 1995, Appendix G.
42 M. Yoneda. A simplified method to evaluate pedestrian-induced maximum response of cable-supported pedestrian bridges, in: Proceedings of the International Conference on the Design and Dynamic Behaviour of Footbridges, Paris, France, November 20–22, 2002.
43 P. Young, Improved floor vibration prediction methodologies, ARUP Vibration Seminar, October 4, 2001.
44 R.L. Pimentel and P. Waldron. Guidelines for the vibration serviceability limit state of pedestrian bridges. International Seminar on Structural Assessment-The Role of Large and Full Scale Testing. London. 1996, 339-346
45 S. Yao, J. Wright, A. Pavic, P. Reynolds. Forces generated when bouncing or jumping on a flexible Structure, in: Proceedings of the International Conference on Noise and Vibration, Vol. 2, Leuven, Belgium, September 16-18,2002, pp.563-572
46 A. Mcrobie, G. Morgenthal, J. Lasenby and M. Ringer. Section model tests on human-structure lock-in. Proceeding of the Civil Engineering: Bridge Engineering. 2003, 156(BE2):71-79
47 M. Willford. Dynamic actions and reactions of pedestrians. Proceedings of the International Conference on the Design and Dynamic Behaviour of Footbridges. Paris, France, 2002, 66-73
48 S. H. Strogatz, D. M. Abrams, F. A. McRobie, B. Eckhardt and E. Ott. Crowd synchrony on the Millennium Bridge. Nature. 438(7064):43, 2005
49 G. P. Tilly. Cullington D.W. and Eyre R. Dynamic behaviour of footbridge. IABSE. 1984, 26(84):13-24
50 Eurocode 5, Design of Timber Structures–Part 2: Bridges, ENV 1995-2: 1997, European Committee for Standardization, Brussels, Belgium, 1997.
51 D. Allen and T. Murray. Design criterion for vibration due to walking. Engineering Journal. 1993,30(4):117-129
52 F. Hauksson. Dynamic behaviour of footbridges subjected to pedestrian-induced vibrations. Master’s thesis, Lund University, Sweden, 2005
53董霜,朱元清.环境振动对人体的影响.噪声与振动控制. 2004(3):22-25
54威廉.冯特著,李维沈烈敏译,人类与动物心理学论稿,杭州:浙江教育出版社,1997
55 H. Reiher, F.J Meister. The sensitiveness of the human body to vibrations, Forschung (VDI-Berlin),1931:381-386
56 ISO 6897, Guide to the Evaluation of Responses of Occupants of Fixed Structures especially Building and Off-shore Structures, to Low-frequency Horizontal Motion (0.063 to 1 Hz), International Standards Organization, 1984
57 M.J. Griffin. Handbook of Human Vibration. London: Academic Press. 1994
58瞿伟廉,李桂清.自立式高耸结构抗风可靠性分析的改进方法.建筑结构学报, 1989, 10(4):1-9
59张清泉,方兴华.支撑钢框架结构抗风安全度与舒适度对比分析.华南理工大学学报, 1998,26(7):120-123
60董安正,赵国藩.高层建筑结构舒适度可靠性分析.大连理工大学学报,2002, 42(4):472-476
61金伟良,宋志刚.高层建筑风振舒适度的不确定性分析.建筑科学2002, 18(2):127-131
62 M. Holiky. Fuzzy probability optimization of building performance. Automation in Construction,1999, 8(4):437-443
63宋志刚.基于烦恼率模型的工程结构振动舒适度设计新理论. Ph.D. thesis.浙江大学, 2003
64杨楚屏,张玉芬.利用模糊数学评价各因素对乘坐舒适性的影响,西安公路交通大学学报, 17(1) 1997: 68-74
65杨伦标,高英仪编著,模糊数学原理及应用,广州:华南理工大学出版社, 1995
66孟庆茂,常见华.实验心理学.北京:北京师范大学出版社, 1999.
67 M.J. Griffin and E.M. Whitham. Individual Variability and Its Effect on Subjective and Biodynamic Response to Whole-Body Vibration, Journal of Sound and Vibration, Vo1.58 No. 2, 1978:239- 250.
68涂瑞和,方丹群等.用模糊数学原理评价城市居民对环境振动的主观反应.中国环境科学, 1990, 10(5): 356-359.
69朱滢主编.实验心理学.北京:北京大学出版社, 2000
70 H. Bachmann, A. Pretlove, H. Rainer. Vibration problems in structures: practical guidelines. Basel: Birkhauser Verlag, 1995
71 Eurocode, Basis of Structural Design - prAnnex A2. EN1990: 2002. European Committee for Standardization, Brussels, Belgium 2002.
72 G. W. Housner, L. A. Bergman, T. K. Caughey, et al. Structural Control: Past, present, and Future. Journal of Engineering Mechanics. September, 1997, (2):897-958.
73杨宜谦,张锻等.用调频质量阻尼器抑制铁路桥梁竖向共振的研究.中国铁道科学, 1998, 3 (1):12-18.
74黄维平,强士中.大跨度悬索桥环境振动的双向TMD控制.地震工程与工程振动, 1993, 3 (1):100-103
75 K. Xu, T. Igusa. Dynamic characteristics of multiple substructures with closely spaced frequencies. Earthquake Engineering & Structural Dynamics. 1992, 21:1059-1070
76 H. Yamaguchi, N. Harnpornchai. Fundamental characteristics of multiple tuned mass dampers. Earthquake Engineering & Structural Dynamics, 1993, 22:51-62
77 R. S. Jangid. Dynamic characteristics of structures with multiple tuned mass dampers. Struct. Eng. Mech. 1995, (3):497-509.
78 A. Kareem, S. Kline. Performance of multiple tuned mass dampers under random loading. Struct. Engng. ASCE, 1995, 121:348-361.
79 R.S. Jangid. Optimum multiple tuned mass dampers for base-excited undamped system. Earthquake Engineering & Structural Dynamics. 1999, 28:1041-1049. 1999, 28:1041-1049.
80 Li Chunxiang. Performance of multiple tuned mass dampers for attenuating undesirable oscillations of structures under the ground acceleration. Earthquake Engineering & Structural Dynamics. 2000, 29:1405-1421
81李黎,黄尚斌,张卉.结构振动控制中MTMD的基本特性研究.工程力学, 2000,17(2):90-96
82蔡国平,孙峰. MTMD控制结构地震反应特性研究.工程力学, 2000, 17(3):55-59
83 Ming Gu, S. R. Chen, C. C. Chang. Parametric study on multiple tuned massdampers for buffeting control of Yangpu Bridge. Journal of Wind Engineering and Industrial Aerodynanmics, 2001, 89:987-1000.
84余钱华,胡世德,范立础.桥梁结构MTMD被动控制的理论研究和实桥分析.世界地震工程, 2001, 17(3): 105-108.
85董志强,段宝岩,仇元鹰.大射电望远镜馈源舱的风激振动及其TMD减振设计研究.应用力学学报, 2002, 19(3):116-119.
86李春祥,韩传峰.高层钢结构顺风向风振加速度的MTMD控制.振动与冲击, 2002, 21(1):69-72.
87刘保东,朱烯. MTMD系统抗震控制研究.工程力学, 2003, 20(1):127-130
88李春祥,刘艳霞,王肇民.地震作用下结构的基于阻尼柔性连接MTMD控制.应用力学学报, 2003, 20(2):116-120.
89丁文镜.减振理论.清华大学出版社, 1988: 207-211
90 G. B. Warburton. Optimum Absorber Parameters for Minimizing Vibration Response, Earthquake Engineering and Structura1 Dynamics Vol. 9, 251-262(1981)
91 G. B. Warburton. Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, Earthquake Engineering and structural Dynamics Vol.10, 381-401(1982)
92 Hsiang-Chuan Tsai and Guan-Cheng Lin. Optimum Tuned-Mass dampers for Minimizing Steady-State Response of Support-Excited and Damped System, Earthquake Engineering and Structural Dynamics Vol. 22, 957-973(1993)
93 Ho-Chul Kwon, Man-Cheol Kim and In-Won Lee. Vibration Control of Bridges under Moving Loads. Computers & Structures. 1998,66(4):473-480
94李春祥.大跨桥梁结构扭转振动的MTMD控制研究.特种结构, 2002, 19(4):66-70
95李春样,刘艳霞,王肇民.基于平稳过滤有色噪声地震动模型的MTMD性能评价.计算力学学报, 2003, 20(2):204-211
96 Li Chunxiang. Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF. Earthquake Engineering and Structural Dynamics, 2002, 37:897-919
97李春祥.地震作用下基于ADMF和不同参数组合的最优MTMD.计算力学学报, 2002, 19(3):291-298.
2和丕状.桥梁美学.北京:人民交通出版社, 1999
3 Shijin Y. and Dongzhou H. Aesthetic consideration for urban pedestrian bridge design. Journal of Architectural Engineering. 1997, 3(1):3-8
4 H. Bachmann, W. Ammann. Vibrations in Structures-Induced by Man and Machines, Structural Engineering Documents, Vol. 3e, International Association of Bridge and Structural Engineering (IABSE), Zürich, 1987.
5 H. Bachmann. Practical cases of structures with man-induced vibrations, in: Symposium/Workshop on Serviceability of Buildings, Ottawa, Canada, May 16–18, 1988, pp. 419–434.
6 H. Bachmann. Case studies of structures with man-induced vibrations, Journal of Structural Engineering 118 (3) (1992) 631–647.
7 H. Bachmann. Vibration upgrading of gymnasia, dance halls and footbridges, Structural Engineering International 2 (2) (1992) 118–124.
8 Y. Fujino, B.M. Pacheco, S. Nakamura, P. Warnitchai. Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge, Earthquake Engineering and Structural Dynamics 22 (1993) 741–758.
9 P. Dallard, A.J. Fitzpatrick, A. Flint, S. Le Bourva, A. Low, R.M. Ridsdill-Smith, M. Willford. The London Millennium Footbridge, Structural Engineer 79 (22) (2001) 17–33.
10 T. Fitzpatrick, P. Dallard, S. Le Bourva, A. Low, R. Ridsdill Smith and M. Willford. Linking London: The Millennium Bridge. The Royal Academy of Engineering. June 2001.
11 P. Dallard, T. Fitzpatrick, A. Flint, A. Low, R. Ridsdill Smith, M. Willford, and M. Roche. London Millennium Bridge: Pedestrian-Induced Lateral Vibration. ASCE Journal of Bridge Engineering, November-December 2001, pages 412-417.
12 S-I. Nakamura. Lateral vibration on a pedestrian cable-stayed bridge. IABSE Journal of Structural Engineering International, volume 12, no. 4, 2002, pages 295-300.
13 S-I. Nakamura. Model for lateral excitation of footbridges by synchronous walking. ASCE Journal of Structural Engineering, January 2004, pages 32-37.
14袁旭斌.人行桥人致振动特性研究.同济大学博士学位论文. 2006.7
15 A. N. Blekherman. Swaying of pedestrian bridges. Journal of Bridge Engineering. 2005, 10(2):142-150
16 J.M.W. Brownjohn, A. Pavic, P. Omenzetter. A spectral density approach for modeling continuous vertical forces on pedestrian structures due to walking, Canadian Journal of Civil Engineering 31 (1) (2004) 65–77.
17 British Standards Institution (BSI). (1978).“British standard specification for loads; steel, concrete and composite bridges, Part 2.”BS5400, London.
18 Ontario Ministry of Transportation, Toronto. Ontario Highway Bridge Design Code, 1983
19 J. Smith. Vibration of structures: applications in civil engineering design. Chapman and hall, 1988
20 Y. Matsumoto, T. Nishioka, H. Shiojiri and K. Matsuzaki. Dynamic design of footbridges. IABSE Proceedings. 1978:1-15
21 Y. Matsumoto, S. Sato, T. Nishioka and Shiojiri H. Study on dynamic design of pedestrian over-bridges in consideration of characteristics of pedestrians. Proc JSCE. 1972, (205):63-70
22 N. Poovardom, S.Kanchanosot and P. Warnitchai. Application of non-linear multiple tuned mass dampers to suppress man-induced vibrations of a pedestrian bridge. Earthquake Engineering and Structural Dynamics. 2003, 32(7):1117-1131
23叶正强,李爱群,丁幼亮等.某大跨人行天桥的消能减振设计(一).特种结构. 2003, Vo1.20, No.l :68-70
24 F.C. Harper, W.J. Warlow, B.L. Clarke. The forces applied to the floor by the foot in walking, National Building Studies, Research Paper 32, Department of Scientific and Industrial Research, Building Research Station, London, 1961.
25 F.W. Galbraith, M.V. Barton. Ground loading from footsteps, Journal of the Acoustic Society of America 48 (5)(1970) 1288–1292.
26 J. Blanchard, B.L. Davies, J.W. Smith. Design criteria and analysis for dynamic loading of footbridges, in:Proceedings of the DOE and DOT TRRL Symposium on Dynamic Behaviour of Bridges, Crowthorne, UK, May 19,1977, pp. 90–106.
27 S.V. Ohlsson. Floor Vibration and Human Discomfort, PhD Thesis, Chalmers University of Technology, G?teborg, Sweden, 1982 (in English).
28 S.C. Kerr. Human Induced Loading on Staircases, PhD Thesis, Mechanical Engineering Department, University College London, UK, 1998.
29 T.P. Andriacchi, J.A. Ogle, J.O. Galante. Walking speed as a basis for normal and abnormal gait measurements, Journal of Biomechanics 10 (1977) 261–268.
30 J.H. Rainer, G. Pernica, D.E. Allen. Dynamic loading and response of footbridges, Canadian Journal of Civil Engineering 15 (1) (1988) 66–71.
31 B.R Eliss. On the response of long-span floors to walking loads generated by individuals and crowds. The Structural Engineering. 2000,78(10):17-25
32 J. Skorecki. The design and construction of a new apparatus for measuring the vertical forces exerted in walking: a gait machine, Journal of Strain Analysis 1 (5) (1966) 429–438.
33 J. Blanchard, B.L. Davies, J.W. Smith, Design criteria and analysis for dynamic loading of footbridges, in: Proceedings of the DOE and DOT TRRL Symposium on Dynamic Behaviour of Bridges, Crowthorne, UK, May 19, 1977, pp. 90–106.
34 P.E. Eriksson. Vibration of Low-Frequency Floors—Dynamic Forces and Response Prediction, PhD Thesis, Unit for Dynamics in Design, Chalmers University of Technology, G?teborg, Sweden, 1994.
35 S. Zivanovic, A. Pavic, P. Reynolds. Vibration serviceability of footbridges under human-induced excitation: a literature review. Journal of Sound and Vibration 2005, 279:1-74.
36 C. Y. Tuan and W. E. Saul(1985). "Loads due to spectator movements." Journal of Structural Engineering, ASCE, 111(2), 418-434.
37 A. Ebrahimpour and R. L. Sack(1992). "Design live loads for coherent crowd harmonic movements." Journal of Structural Engineering, ASCE, 110(2), 401-418.
38谢庆森,王秉权.安全人机工程,天津:天津大学出版社, 1999
39 Y. Matsumoto, S. Sato, T. Nishioka, H. Shiojiri. A study on design of pedestrian over-bridges, Transactions of JSCE 4 (1972) 50–51.
40 S.C. Kerr, N.W.M. Bishop, Human induced loadingon flexible staircases, Engineering Structures 23 (2001)37–45.
41 H. Bachmann, A.J. Pretlove, H. Rainer. Dynamic forces from rhythmical human body motions, in: Vibration Problems in Structures: Practical Guidelines, Birkh?user, Basel, 1995, Appendix G.
42 M. Yoneda. A simplified method to evaluate pedestrian-induced maximum response of cable-supported pedestrian bridges, in: Proceedings of the International Conference on the Design and Dynamic Behaviour of Footbridges, Paris, France, November 20–22, 2002.
43 P. Young, Improved floor vibration prediction methodologies, ARUP Vibration Seminar, October 4, 2001.
44 R.L. Pimentel and P. Waldron. Guidelines for the vibration serviceability limit state of pedestrian bridges. International Seminar on Structural Assessment-The Role of Large and Full Scale Testing. London. 1996, 339-346
45 S. Yao, J. Wright, A. Pavic, P. Reynolds. Forces generated when bouncing or jumping on a flexible Structure, in: Proceedings of the International Conference on Noise and Vibration, Vol. 2, Leuven, Belgium, September 16-18,2002, pp.563-572
46 A. Mcrobie, G. Morgenthal, J. Lasenby and M. Ringer. Section model tests on human-structure lock-in. Proceeding of the Civil Engineering: Bridge Engineering. 2003, 156(BE2):71-79
47 M. Willford. Dynamic actions and reactions of pedestrians. Proceedings of the International Conference on the Design and Dynamic Behaviour of Footbridges. Paris, France, 2002, 66-73
48 S. H. Strogatz, D. M. Abrams, F. A. McRobie, B. Eckhardt and E. Ott. Crowd synchrony on the Millennium Bridge. Nature. 438(7064):43, 2005
49 G. P. Tilly. Cullington D.W. and Eyre R. Dynamic behaviour of footbridge. IABSE. 1984, 26(84):13-24
50 Eurocode 5, Design of Timber Structures–Part 2: Bridges, ENV 1995-2: 1997, European Committee for Standardization, Brussels, Belgium, 1997.
51 D. Allen and T. Murray. Design criterion for vibration due to walking. Engineering Journal. 1993,30(4):117-129
52 F. Hauksson. Dynamic behaviour of footbridges subjected to pedestrian-induced vibrations. Master’s thesis, Lund University, Sweden, 2005
53董霜,朱元清.环境振动对人体的影响.噪声与振动控制. 2004(3):22-25
54威廉.冯特著,李维沈烈敏译,人类与动物心理学论稿,杭州:浙江教育出版社,1997
55 H. Reiher, F.J Meister. The sensitiveness of the human body to vibrations, Forschung (VDI-Berlin),1931:381-386
56 ISO 6897, Guide to the Evaluation of Responses of Occupants of Fixed Structures especially Building and Off-shore Structures, to Low-frequency Horizontal Motion (0.063 to 1 Hz), International Standards Organization, 1984
57 M.J. Griffin. Handbook of Human Vibration. London: Academic Press. 1994
58瞿伟廉,李桂清.自立式高耸结构抗风可靠性分析的改进方法.建筑结构学报, 1989, 10(4):1-9
59张清泉,方兴华.支撑钢框架结构抗风安全度与舒适度对比分析.华南理工大学学报, 1998,26(7):120-123
60董安正,赵国藩.高层建筑结构舒适度可靠性分析.大连理工大学学报,2002, 42(4):472-476
61金伟良,宋志刚.高层建筑风振舒适度的不确定性分析.建筑科学2002, 18(2):127-131
62 M. Holiky. Fuzzy probability optimization of building performance. Automation in Construction,1999, 8(4):437-443
63宋志刚.基于烦恼率模型的工程结构振动舒适度设计新理论. Ph.D. thesis.浙江大学, 2003
64杨楚屏,张玉芬.利用模糊数学评价各因素对乘坐舒适性的影响,西安公路交通大学学报, 17(1) 1997: 68-74
65杨伦标,高英仪编著,模糊数学原理及应用,广州:华南理工大学出版社, 1995
66孟庆茂,常见华.实验心理学.北京:北京师范大学出版社, 1999.
67 M.J. Griffin and E.M. Whitham. Individual Variability and Its Effect on Subjective and Biodynamic Response to Whole-Body Vibration, Journal of Sound and Vibration, Vo1.58 No. 2, 1978:239- 250.
68涂瑞和,方丹群等.用模糊数学原理评价城市居民对环境振动的主观反应.中国环境科学, 1990, 10(5): 356-359.
69朱滢主编.实验心理学.北京:北京大学出版社, 2000
70 H. Bachmann, A. Pretlove, H. Rainer. Vibration problems in structures: practical guidelines. Basel: Birkhauser Verlag, 1995
71 Eurocode, Basis of Structural Design - prAnnex A2. EN1990: 2002. European Committee for Standardization, Brussels, Belgium 2002.
72 G. W. Housner, L. A. Bergman, T. K. Caughey, et al. Structural Control: Past, present, and Future. Journal of Engineering Mechanics. September, 1997, (2):897-958.
73杨宜谦,张锻等.用调频质量阻尼器抑制铁路桥梁竖向共振的研究.中国铁道科学, 1998, 3 (1):12-18.
74黄维平,强士中.大跨度悬索桥环境振动的双向TMD控制.地震工程与工程振动, 1993, 3 (1):100-103
75 K. Xu, T. Igusa. Dynamic characteristics of multiple substructures with closely spaced frequencies. Earthquake Engineering & Structural Dynamics. 1992, 21:1059-1070
76 H. Yamaguchi, N. Harnpornchai. Fundamental characteristics of multiple tuned mass dampers. Earthquake Engineering & Structural Dynamics, 1993, 22:51-62
77 R. S. Jangid. Dynamic characteristics of structures with multiple tuned mass dampers. Struct. Eng. Mech. 1995, (3):497-509.
78 A. Kareem, S. Kline. Performance of multiple tuned mass dampers under random loading. Struct. Engng. ASCE, 1995, 121:348-361.
79 R.S. Jangid. Optimum multiple tuned mass dampers for base-excited undamped system. Earthquake Engineering & Structural Dynamics. 1999, 28:1041-1049. 1999, 28:1041-1049.
80 Li Chunxiang. Performance of multiple tuned mass dampers for attenuating undesirable oscillations of structures under the ground acceleration. Earthquake Engineering & Structural Dynamics. 2000, 29:1405-1421
81李黎,黄尚斌,张卉.结构振动控制中MTMD的基本特性研究.工程力学, 2000,17(2):90-96
82蔡国平,孙峰. MTMD控制结构地震反应特性研究.工程力学, 2000, 17(3):55-59
83 Ming Gu, S. R. Chen, C. C. Chang. Parametric study on multiple tuned massdampers for buffeting control of Yangpu Bridge. Journal of Wind Engineering and Industrial Aerodynanmics, 2001, 89:987-1000.
84余钱华,胡世德,范立础.桥梁结构MTMD被动控制的理论研究和实桥分析.世界地震工程, 2001, 17(3): 105-108.
85董志强,段宝岩,仇元鹰.大射电望远镜馈源舱的风激振动及其TMD减振设计研究.应用力学学报, 2002, 19(3):116-119.
86李春祥,韩传峰.高层钢结构顺风向风振加速度的MTMD控制.振动与冲击, 2002, 21(1):69-72.
87刘保东,朱烯. MTMD系统抗震控制研究.工程力学, 2003, 20(1):127-130
88李春祥,刘艳霞,王肇民.地震作用下结构的基于阻尼柔性连接MTMD控制.应用力学学报, 2003, 20(2):116-120.
89丁文镜.减振理论.清华大学出版社, 1988: 207-211
90 G. B. Warburton. Optimum Absorber Parameters for Minimizing Vibration Response, Earthquake Engineering and Structura1 Dynamics Vol. 9, 251-262(1981)
91 G. B. Warburton. Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, Earthquake Engineering and structural Dynamics Vol.10, 381-401(1982)
92 Hsiang-Chuan Tsai and Guan-Cheng Lin. Optimum Tuned-Mass dampers for Minimizing Steady-State Response of Support-Excited and Damped System, Earthquake Engineering and Structural Dynamics Vol. 22, 957-973(1993)
93 Ho-Chul Kwon, Man-Cheol Kim and In-Won Lee. Vibration Control of Bridges under Moving Loads. Computers & Structures. 1998,66(4):473-480
94李春祥.大跨桥梁结构扭转振动的MTMD控制研究.特种结构, 2002, 19(4):66-70
95李春样,刘艳霞,王肇民.基于平稳过滤有色噪声地震动模型的MTMD性能评价.计算力学学报, 2003, 20(2):204-211
96 Li Chunxiang. Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF. Earthquake Engineering and Structural Dynamics, 2002, 37:897-919
97李春祥.地震作用下基于ADMF和不同参数组合的最优MTMD.计算力学学报, 2002, 19(3):291-298.