高架桥梁地震碰撞分析及控制
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
强烈地震作用下,高架桥梁相邻桥跨之间由于存在动力特性的差异,或者受到非一致地震动作用的影响,容易遭受碰撞破坏。强烈地震作用下高架桥梁碰撞过程中存在复杂的材料非线性、几何非线性和接触非线性,碰撞机理复杂。此外,针对地震所引发的高架桥梁碰撞,如何采用工程措施降低结构的震害,是需要迫切解决的问题。
     本文针对高架桥梁在强烈地震作用下的碰撞机理及控制措施,采用显式非线性有限元分析技术和简化分析方法相结合的方法,研究了地震碰撞破坏机理和控制方法,主要内容包括:
     (1)通过显式非线性有限元分析软件LS-DYNA,针对某三跨简支悬臂梁桥的精细化建模,研究了地震动幅值、主梁周期、伸缩缝间距和支座阻尼比等结构参数变化对结构碰撞动力特性的影响及结构的碰撞机理。
     (2)针对在高架桥梁伸缩缝处安装橡胶缓冲材料,以减轻强震作用下高架桥梁碰撞的工程技术措施,通过显式非线性有限元精细化建模和分析,研究了橡胶缓冲材料的剪切模量、厚度和摩擦系数等参数对减轻结构碰撞动力响应的影响。探讨了采用橡胶缓冲材料减轻高架桥梁地震碰撞的可行性以及材料参数选择的方法。
     (3)通过理论与试验相结合的技术手段,研究了采用MR阻尼器对高架桥梁在强烈地震作用下碰撞动力响应的半主动控制方法。分析过程中以Kelvin和Hertz阻尼模型模拟结构间的碰撞,基于LQG控制算法提出了高架桥梁碰撞的半主动控制策略,并进行了试验验证。此外,基于高架桥梁模型振动台碰撞试验结果,建立了一套识别了Kelvin和Hertz阻尼模型的方法。分析结果表明,目前以结构轴向刚度作为Kelvin模型碰撞刚度的取值方法,与试验所识别的结果存在较大差异,如何对碰撞简化分析模型参数进行合理取值,是值得进一步深入研究的课题。
     (4)针对双向地震作用下,高架桥梁由于微小质量偏心所引起的非轴向点面碰撞,提出了高架桥梁二维点接触碰撞的摩擦接触模型,并建立了相应的力学分析模型。通过双向地震动输入下的高架桥梁振动台模型试验,验证了摩擦接触模型以及所建立的结构力学分析模型用来模拟结构扭转碰撞的正确性。试验结果也表明,高架桥梁的微小扭转容易导致结构的点面扭转碰撞,在结构抗震设计中应予以重视。
Highway bridge is sensitive to pounding damage due to either the difference of dynamic characteristics between the neighboring segments or the effects of asynchronous earthquake when subjected to strong earthquake excitations. During the structural pounding, highway bridge behaves complex inherent characteristics of material nonlinear, geometric nonlinear and contact nonlinear, which make the impact mechanism very complex. Furthermore, aiming at the seismic-induced pounding of highway bridges, how to prevent the structural pounding using suitable engineering technique is an important issue that should be solved.
     This dissertation investigates the pounding mechanism and the pounding reduction technique by using the explicit nonlinear finite element approach and the simplified impact model approach. The main contents include:
     (1) Based on the refining finite element model of a three-span highway bridge, it investigates the pounding mechanism and the effects of the earthquake amplitude, natural frequency of the main span, expansion joint separation and the damping ratio of the base-isolation system on the dynamic responses of the structures.
     (2) By using rubber cushion material, it investigated the possibility of using the rubber cushion material for the pounding reduction of the highway bridges. The effects of the shear modulus, thickness and the friction coefficient of the material for the performance of the pounding reduction is also investigated by using the explicit nonlinear finite element approach for establishing the parametric selection principle of the rubber cushion material for the pounding reduction of highway bridge.
     (3) With the theoretical and experimental techniques, the possibility of using MR dampers for preventing the pounding damage of highway bridges is investigated with semi-active control method. During the analysis, it uses the Kelvin and Hertz damp impact model for modeling the structural pounding and develops the semi-active control strategy based on the LQG control algorithm through experiment validation. The analytical results indicate that there are significant difference between the theoretical impact stiffness with structural axial stiffness and the identified impact stiffness. How to determine the parameters of the impact model is an important issue that should be investigated in future.
     (4) Considering the torsion-induced pounding of highway bridge due to mass eccentricity, it investigates the point-to-surface impact and proposes the corresponding friction-contact impact model for highway bridge with bi-directional earthquake excitations. The analytical model of the highway bridge with point-to-surface pounding is also established. Through the shaking table test with bi-directional earthquake inputs, it validates the accuracy of the proposed friction-contact impact model and the analytical model of the structure with point-to-surface pounding. The experimental results indicate that the torsion-induced pounding of the highway bridges should be paid more attention during the seismic design.
引文
1周高瞻.三种减隔震装置在连续梁桥中应用的研究.北京工业大学硕士学位论文. 2007年5月: 1~4
    2杨迪雄.隔震结构优化设计和工程数值方法中的混沌.大连理工大学博士学位论文. 2004年5月: 1~2
    3 C. J. Wang, M. H. Shih.. Performance Study of A Bridge Involving Sliding Decks and Pounded Abutment During A Violent Earthquake. Engineering Structures. 2007, (29): 802
    4 C. J. Wang. Failure Study of a Bridge Subjected to Pounding and Sliding Under Severe Ground Motions. International Journal of Impact Engineering. 2007, (34): 216~217
    5 P. Zhu, M. Abe, Y. Fujino. Evaluation of Pounding Countermeasures and Serviceability of Elevated Bridges During Seismic Excitation Using 3D Modeling. Earthquake Eng Struct. Dyn. 2004, (33): 591~592
    6 F. D. Julian, T. Hayashikawa, T. Obata. Seismic Performance of Isolated Curved Viaducts Equipped with Deck Unseating Prevention Cable Restrainers. Journal of Constructional Steel Research. 2007, (63): 237~238
    7林万杰.大跨长联预应力混凝土连续梁桥地震反应分析.西南交通大学硕士学位论文. 2006年6月: 1~4
    8 N. Makris, P. C. Chang. Effect of Viscous, Viscoplastic and Friction Damping on the Response of Seismic Isolated Structures. Earthquake Engineering and Structural Dynamics. 2000
    9 V. Jeng, W. L. Tzeng. Assessment of Seismic Pounding Hazard for Taipei City. Engineering Structures, 2000, (22): 459~460
    10 S. A. Anagnostopoulos. Earthquake Induced Pounding: State of the Art Proceedings of the 10th European Conference on Earthquake Engineering, Vienna, Austria. 1995, (2): 897~905
    11 A. Filiatrault, M. Cervantes, B. Folz, H. Prion. Pounding of Buildings During Earthquakes: A Canadian perspective, Canadian Journal of Civil Engineering. 1994, (21): 251~265
    12 S. H. Kim, M. Shinozuka. Effects of Seismically Induced Pounding at Expansion joints of Concrete Bridges Journal of Engineering Mechanics. 2003,129(11): 1225~1226
    13 R. DesRoches, S. Muthukumar. Implication of Seismic Pounding on the Longitudinal Response of Multi-span Bridges-An Analytical Persperctive. Earthquake Engineering and Engineering Vibration. 2003, 3(1): 1~2
    14 R. Jankowski, K. Wilde and Y. Fujino. Reduction of Pounding Effects in Elevated Bridges During Earthquakes. Earthquake Eng. Struct. Dyn. 2000, (29): 195~196
    15 N. Chouw, H. Hao. Significance of SSI and Non-uniform Near-fault Ground Motions in Bridge Response II: Effect on Response with Modular Expansion Joint. Engineering Structures. 2007: 1~2
    16 B. Andrawes. Seismic Response and Analysis of Multiple Frame Bridges Using Superelastic Shape Memory Alloys. Doctor degree dissertation of Georgia Institute of Technology. 2005: 6~16
    17 N. Chouw, H. Hao. Study of SSI and Non-uniform Ground Motion Effect on Pounding Between Bridge Girders. Soil Dynamic and Earthquake Engineering. 2005: 1~2
    18 Y. A. Khulief, A. A. Shabana. Dynamic Analysis of Constrained System of Rigid and Flexible Bodies with Intermittent Motion. Journal of Mechanisms, Transmissions, and Automation in Design. 1986, (108): 38~45
    19 R. Sany, A. A. Shabana, On The Use of the Momentum Balance in the Impact Analysis of Constrained Elastic Systems. Journal of Vibration and Acoustics. 1996, 112(2): 119~126.
    20 A. S. Ulsoy, R .A Scot. .Dynamics of A Radically Rotating Beam with Impact, Partl:Theoretical and Computational Model; part2: Experimental and Simulation Results. Journal of Vibration and Acoustics. 1990, (112): 65~77.
    21 S. A. Anagnostopoulos. Pounding of Buildings in Series During Earthquakes. Earthquake Engineering and Structural Dynamics. 1988, (16): 443~456
    22 R. Jankowski, K. Wilde and Y. Fujino. Pounding of Superstructure Segments in Isolated Elevated Bridge During Earthquakes. Earthquake Engineering and Structural Dynamics. 1998, (27): 487~502
    23 G. L. Fenves, R. Desroches. Evaluation of the Response of I-10/215 Interchange Bridge Near San Bernardino in the 1992 Landers and Big Bear Earthquakes.California Strong Motion Instrumentation Program.Sacramento, Calif. 1995
    24 M. Papadrakakis, H. Mouzakis, S. Bitzarakis. Dynamic Contact Between Adjacent Structures Using a Formulation with Lagrange Multipliers. Proceedings of the European Conference on Structural Dynamics. 1991: 913
    25张雷明,刘西拉.框架结构倒塌分析中的几个问题.上海交通大学学报. 2001, (35): 1578~1582
    26 M. Papadrakakis, C. Apostolopoulou. Three-dimensional Simulation of Structural Pounding During Earthquakes. Journal of Engineering Mechanics. 1996, (12): 424~431
    27 A. Ruagnrassamee, K. Kawashima. Control of Nonlinear Bridge Response with Pounding Effect by Variable Dampers. Engineering Structures. 2003, (25): 593~594
    28 K. Kasai, B. F. Maison. Building Pounding Damage During the1989 Loma Prieta Earthquake. Engineering Structures. 1997, 19(3): 195~207
    29 B. F. Maison, K. Kasai. Analysis for Type of Structural Pounding. Journal of Structural Engineering. 1990, 116(4): 957~977
    30 K. Kawashima, S. Unjoh. Impact of Hanshin/Awajie Earthquake on Seismic Design and Seismic Strengthening of Highway Bridges. Strural Eng./Earthquake Eng. 1996, 13(2): 211~240
    31 S. Tanimura, K. Mimura, T. Nonaka. Dynamic Failure of Structures Due to the Great Hanshin-Awaji Earthquake. International Journal of Impact Engineering. 2000, (24): 583~584
    32 S. Rashidi, M. A. Saadeghvaziri. Seismic Modeling of Multi-span Simply-supported Bridges Using ADINA. Computer and Structures. 1997, 64(5): 1025~1027
    33 G. Zanardo; H. Hao, C. Modena. Seismic Response of Multi-span Simply Supported Bridges to A Spatially Varying Earthquake Ground Motion. Earthquake Engineering and Structural Dynamics. 2002, (31): 1325~1327
    34 J. H. Lin, C. C. Weng. Spectral analysis on pounding probalility of adjacent buildings. Engineering Structures. 2001, (23): 768~778
    35李忠献,岳福青.城市桥梁地震碰撞反应研究与发展.地震工程与工程振动.第25卷第4期, 2005年8月: 91~96
    36 R. DesRoches, S. Muthukumar. Effect of Pounding and Restrainers on Seismic Response of Multiple-frame Bridges. Journal of Structural Engineering. 2002, (128): 860~861
    37 C. P. Pantelides, X. Ma. Linear and Nonlinear Pounding of Structural Systems. Compute and Structure, 1998, 66(1):79~80
    38 N. Chouw, H. Hao. Reduction of Pounding Responses of Bridges Girders with Soil-structure Interaction Effects to Spatial Near Source Ground Motions. Proc of 13th World Conference on Earthquake Engineering. Vancouve. B. C. Canada, 2004
    39 G. Zanardq, H. Haq, C. Modern Seismic Response of Multi-span Simply Supported Bridges to A Spatially Varying Earthquake Ground Motions. Earthquake Engineering and Structural Dynamics. 2002, (31): 1325~1345
    40 K. Sanghyd, L. Sangwoo. Dynamic Behaviors of the Bridge Considering Pounding and Friction Effects Under Seismic Excitations. Joumal of Structural Engineering and Mechanics. 2000, (10): 621~633
    41 M. A. Saadeghvaziri, A. R. Yazdani, S. Rashidi. Effects of Soil Structure Interaction on Longitudinal Seismic Response of MSSS Bridges. Journal of Soil Dynamics and Earthquake Engineering. 2000, (20): 231~242
    42王丽.大跨度立交桥抗震设计理论与方法.北京工业大学博士学位论文. 2005年四月: 1~81
    43王东升,冯启民,凌贤长,翟桐.桥梁非线性地震反应分析若干问题研究现状.地震工程与工程振动.第22卷第1期, 2002年2月: 65
    44段文中.地震作用下钢筋混凝土梁桥梁间碰撞响应分析及防止措施研究.西安理工大学硕士学位论文. 2007年12月: 5~9
    45 R. J. Pinnington. Collision Dynamics of Two Adjacent Oscillators. Journal of Sound and Vibration. 2003, (268): 343~344
    46王军文,李建中,范立础.桥梁结构地震碰撞效应及防落梁措施研究现状.公路交通科技.第24卷第5期2007年5月: 72~75
    47 C. Y. Tham. Reinforced Concrete Perofration and Penetration Simulation Using AUTODYN-3D. Finite Elements in Analysis and Design, 2005, (41): 1401~1410
    48 Y. S. Tai, C. C. Tang. Numerical Simulation: The Dynamic Behavior of Reinforced Concrete Plates Under Normal Impact. Theory Fracture Mechanics. 2006, (45): 117~127
    49 W. S. Tseng, J. Penzien. Analytical Investigations of the Seismic Response of Long Multiple-span Highway Bridges. Report No. EERC-73-12, Earthquake Engineering Research Center. University of California, Berkelev, 1973
    50 K. Kawashima, J. Penzien. Correlative Investigation on Theoretical and Experimental Dynamic Behavior of A Model Bridge Structure. Report No. EERC-76-26, Earthquake Engineering Reseanch Center. Univetsity of California, Berkeley, 1976.
    51 P. K. Malhotra, J. H. Moth, F. S. Anthong. Seismic Interaction at Separation Joints of An Instrumented Concrete Bridge. Earthquake Engineering and Structural Dynamics. 1995, 24(3): 1055~1067
    52王东升,冯启民,王国新.基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型.工程力学. 2004年02期: 157~166
    53周艳,张雷明,刘西拉.美国Cypress高架桥地震倒塌的仿真分析.岩石力学与工程学报. 2005, (24): 3035~3044
    54 K. Praveen, P. K. Malhotra. Dynamics of Seismic Pounging at Expansion Joints of Concrete Bridges. Journal of Engineering Mechanics. 1998, 124(7): 794~802
    55 C. J. Athanassiadou, G. G. Penelis.Elastic and Inelastic System Interaction Under An Earthquake Motion. Proc. 7th Hellenic Conf. on Concrete.Patras, Greece. 1985, (1): 211~216
    56 C. J. Athanassiadou, G. G. Penelis, A. J. Kappos. Seismic Response of Adjacent Buildings with Similar or Different Dynamic Characteristics. Earthquake Spectra. 1994, (10): 293~317
    57 G. E. Stavroulakis, K. M. Abdalla. Contact Between Adjacent Structures. Struct. Engrg. 1991, 117(10): 2838~2850
    58 R. O. Davis. Pounding of Buildings Modeled by An Impact Oscillator. Earthquake Engineering and Structural Dynamics. 1992, (21): 253~274
    59 W. B. Cross, N. R. Jones. Seismic Performance of Joist-Pocket Connections: I. Modeling II. Application. Journal of Structural Engineering. 1993, 119(10):2986~3007
    60 H. C. Tsai, Dynamic Analysis of Base-isolated Shear Beams Bumping Against Stops. Eatrhquake Engineering and Structural Dynamics. 1997, (26): 515~528
    61 P. Zhu, M. Abe, Y. Fujino. Modeling Three-dimensional Nonlinear Seismic Performance of Elevated Bridges with Emphasis on Pounding of Girders. Earthquake Engineering and Structural Dynamics. 2002, (31):1 891~1913
    62孟宪锋,朱晞.梁式桥防止地震碰撞及落梁装置与措施的研究进展.工程抗震与加固改造.第27卷第2期, 2005年4月: 71~74
    63于海龙,朱唏.地震作用下简支梁桥梁间碰撞的反应性能.北方交通大学学报.第28卷第1期, 2004年2月: 43~46
    64 V. Mier, A. F. Pruijssers, H. W. Reinhardt, T. Monnier. Load-time Response of Colliding Concrete Bodies. Journal of Structural Engineering. 1991, (117): 354~374.
    65 M. Papadrakakis, H. P. Mouzakis. Earthquake Simulator Testing of Pounding Between Adjacent Buildings. Earthquake Engineering and Structural Dynamics. 1995, 24(6): 811~834
    66 A. Filiatrault, P. Wagner, S. H. Cherry. Analytical Prediction of Experimental Building Pounding. Earthquake Engineering and structural Dynamics. 1995, (24): 1131~1154
    67 K. T. Chau, X. X. Wei, X. Guo. Experimental and Theoretical Simulations of Seismic Poundings Between Two Adjacent Structures. Earthquake Engineering and Structural Dynamics. 2003, (32): 537~554
    68 K. T. Chau, X. X. Wei. Pounding of Structures Modelled as Non-linear Impacts of Two Oscillators. Earthquake Engineering and Structural Dynamics. 2001, 30 (5): 633–651
    69 Y. Kajita. Fundamental Study on Aseismic Evaluation of Elevated Bridge Systems with Consideration of Pounding of Girders. PhD Thesis, Kyoto University, Japan
    70李忠献,张勇,岳福青.地震作用下隔震简支梁桥碰撞反应的振动台试验.地震工程与工程振动.第27卷第2期, 2007年4月: 152~153
    71 J. P. Yao. Concept of Structural Control. J. Struct. Div. ASCE. 1972, 98(7): 1567~1574
    72李娟.层间隔震结构理论与试验研究.西安建筑科技大学硕士学位论文. 2006年3月: 1~4
    73 Edited by T. T. Soong, M. Constantinou. Passive and Active Structural Vibration Control in Civil Engineering. International Centre for Mechanical Sciences, CISM Courses and Lectures-No. 345, Springer Verlag Wien-New York. 1994: 255~269
    74 B. F. Spencer, S. Nagarajaiah. State-of The Art of Structural Control. Journal of Structural Engineering. 2003, (129): 845~856
    75 M. D. Symans, M. C. Constantinou. Semi-active Control Systems for Seismic Protection of Structures: A State-of the Art Review. Engineering Structures.1999, (21): 467~487
    76元兴军.桥梁减震半主动控制研究.中国地震局地球物理研究所博士学位论文. 2006年6月: 3~8
    77范立础.现代化桥梁抗震设计若干问题.同济大学学报. 1997, (4): 110~112
    78程更人.考虑参数不确定性及多模态气动祸合的桥梁风致振动控制系统的研究. .同济大学博士学位论文. 2000年9月: 35~42
    79 M. C. Constantiou. Fluid Viscous Dampers in Application of Seismic Energy Dissipation and Seismic Isolation. Passive Energy Dissipation and Active Control. 1993, (2): 581~592.
    80 J. P. Ou, B. Wu. Recent Advances in Research on and Application of Passive Energy dissipation Systems. Earthquake Engineering and Engineering Vibration. 1996, (1): 530~531
    81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. 1999, (1): 46~47
    82李爱群等.南京电视塔风振的混合振动控制研究.建筑结构学报. 1996, (3): 19~20
    83贝伟明.建筑结构利用磁流变阻尼器减震的优化设计.大连理工大学硕士学位论文. 2006年6月: 4~7
    84 T. T. Soong, Active Structural Control: Theory and Practice. Longman Scientific and Technical, Essex, England, 1990
    85 J. N. Yang, A. Akbarpour, P. Ghaemmaghami. New Optimal Control Algorithms for Atructural Control. Engineering Mechanics. 1987, (113): 1369~1386.
    86 J. N. Yang, H. L. Wong. Optimal Control of Nonlinear Structures. Journal of Applied Mechanics. 1988, (55): 931~938.
    87 J. N. Yang, J. C. Wu, et al. Control of Sliding-isolated Buildings Using Sliding-mode Control. Journal of Structural Engineering. 1996, (122): 179~186.
    88 M. Yoshida, B. F. Spencer. "Smart" Base Isolation Strategies Employing Magnetorheological Damper. Journal of Engineering Mechanics. 2002, (128): 540~551.
    89 M. A. Rohman, H. H. Leipholz. Structural Control by Pole Assignment Method. Journal of Engineering Mechanics. 1978, (104): 1157~1175.
    90 G. Mei, A. Kareem, J. C. Kantor. Real-time Model Predictive Control ofStructures Under Earthquake. Earthquake Engineering and Structural Dynamics. 2001, (30): 995-1019
    91欧进萍.结构振动控制-主动、半主动和智能控制.北京科学出版社. 2003年: 2~24
    92 J. N. Yang, et al. Active Control of Two-cable-stayed Bridge. Journal of the Engineering Mechanics. 1979, EM4: 677~694.
    93 J. N. Yang, J. C. Wu, K. Kawashima, S. Unjoh. Hybrid Control of Seismically Excited Bridge Structures. Journal of Earthquake Engineering and Structural Dynamics. 1995, 24(11):1437~1451
    94 K. Kawashima, S. Unjoh, H. lida, H. Mukai. Effectiveness of the Variable Damper for Reducing Seismic Response of Highway Bridges. Proceedings of Second U.S.-Japan Workshop on Earthquake Protective Systems for Bridges, PWRI, Tsukuba Science City, Japan, 1992: 479~493.
    95 B. F. Spencer, E. A. Johnson, J. C. Rtamallo. "Smart" Isolation for Seismic Control. Journal, Special Issue on Frontiers of Motion and Vibration Control. 2000, 43(3): 704~711.
    96 J. C. Ramallo, E. A. Johnson,, B. F. Spencer, M. K. Sain. Smart Base Isolation Systems. Journal of Engineering Mechanics. 2002, 128(10): 1088~1099
    97 J. C. Ramallo, H. Yoshioka, B. F. Spencer. System Identification of "Smart" Base Isolation Systems. Journal of Structural Engineering. 2002
    98欧进萍,关新春.磁流变耗能器性能的试验研究.地震工程与工程振动. 1999, (19): 76~81
    99颜桂云.地震、风激励作用下高层建筑振动控制的研究.浙江大学博士学位论文. 2005年6月: 12~13
    100 B. F. Spencer, et al. Controlling building: A New Frontier in Feedback, Special Issue of the IEEE Control Systems Magazine on Emerging Technology. 1997, 17(6): 19~35
    101罗小宝.基于振动控制理论的斜拉桥抗震仿真研究.东南大学硕士学位论文. 2006年3月: 6~7
    102 M. D. Symans, S. W. Kelly, Fuzzy Logic Control of Bridges Structures Using Intelligent Semi-active Seismic Isolation Systems, Earthquake Engineering and Structural Dynamics. 1999, (28): 512~513
    103 H. L. Jeng, C. C. Weng. Probability Analysis of Seismic Pounding of Adjacent Buildings. Earthquake Engineering and Structural Dynamics. 2001,(30): 1539~1557
    104 J. Penzien. Evaluation of Building Separation Distance Required to Prevent Pounding During Strong Earthquakes. Earthquake Engineering and Structural Dynamics. 1997, (26): 849~858
    105 H. L. Jeng. Separation Distance to Avoid Seismic Pounding of Adjacent Buildings. Earthquake Engineering and Structural Dynamics. 1997, (26): 395~403
    106 D. L. Garcia. Discussion on: Critical Building Separation Distance in Reducing Pounding Risk Under Earthquake Excitation. Structural Safty. 2005, (27): 393~395
    107 R. DesRoches, E. Choj, T. L. Roberto. Seismics Response of Multiple Span Steel Bridges in Central and Southeastern United States II Retrofitted. Journal of Bridge Engineering. 2004, (9): 473~479
    108 R. DesRoches, M. Delemont. Seismic Retrofit of Simply Supported Bridges Using Shape Memory Alloys. Engineer Structure. 2002, 24(5): 325~332
    109 K. Kawashima, G. Shoji. Effect of Restrainers to Mitigate Pounding Between Adjacent Decks Subjected to A Strong Ground Motion. Paper No 1435, 12WCEE. Auckland, New Zealand, 2000
    110 S. H. Kim, S. W. Lee, J. H. Won, H. S. Mha. Dynamic Behaviors of Bridges Under Seismic Excitations with Pounding Between Adjacent Girders. Paper No.1815, 12WCEE, 2000
    111 M. Q. Feng, J. M. Kim, M. Shinozuka. Viscoelastic Damper at Expansion Joints for Seismic Protection of Bridges. Journal of Bridge Engineering. 2000, (5): 67~74.
    112 M. Q. Feng, J. M. Kim, M. Shinozuka. Energy Dissipating Restrainers for Highway Bridges. Soil Dynaanics and Earsthqake Engineering. 2000, (19): 65~69
    113 W. Tanzo, A. Tsuzuki. Enhanced Seismic Lateral Load Distribution in Continuous Span Bridges Fitted with Viscoelastic Devices. The Eleventh Conference on Earthquake Engineering, Paper No.1528, Mexico, 1996
    114 M. Makola, J. Abdullah, et al. Use of A Shared Tuned Mass Damper (STMD) to Reduce Vibration and Pounding in Adjacent Structures. Earthquake Engineering and Structural Dynamics. 2001, (30): 1185~1201
    115 A. Caner, E. Dogan, P. Zia. Seismic Performance of Multi Simple-spanBridges Retrofitted with Links Labs. Journal of Bridge Engineering. 2002: 85~93
    116韩维.斜碰撞振动系统动力学研究.南京航空航天大学博士学位论文. 2003年6月: 1~22
    117杨永强.地震落梁与结构碰撞的数值模拟研究.中国地震局工程力学研究所硕士学位论文. 2007年5月: 8~15
    118 R. Jankowski. Non-linear Viscoelastic Modelling of Earthquake-induced Structural Pounding. Earthquake Engineering and Structural Dynamics. 2005, (34): 595~611
    119 S. Muthukumar. A Contact Element Approach with Hysteresis Damping for the Analysis and Design of Pounding in Bridges. Georgia Institute of Technology doctor thesis, November, 2003: 11~13
    120卓秋林.公路简支斜梁桥地震反应分析.福州大学硕士学位论文. 2004年12月: 92~95
    121 S. Muthukumar, R. DesRoches. A Hertz Contact Model with Non-linear Damping for Pounding Simulation. Earthquake Engng. Struct. Dyn. 2006, (35): 816–819
    122谢旭,高博青,吴善幸,苟昌焕.柔性橡胶支座上的桥梁结构地震碰撞响应分析.浙江大学学报.第38卷第6期, 2004年6月: 726
    123尚晓江,苏建宁等编著. ANSYS/LS-DYNA动力分析方法与工程实例.中国水利水电出版社. 2006年1月: 3~11
    124时党勇,李裕春,张胜民.基于ANSYS/LS-DYNA8.1进行显式动力分析.清华大学出版社. 2005年1月: 1~89
    125唐晖.显式积分格式及其在波动有限元模拟中的应用研究.中国地震局地球物理研究所硕士学位论文. 2005年6月: 9~17
    126吴卫国,姜河蓉,杨茨祥.桥墩防护装置在船舶撞击载荷作用下的动态响应分析.武汉理工大学学报.第28卷第4期, 2004年8月: 482~483
    127赖跃.重型车辆与半刚性护栏碰撞的有限元分析.同济大学工学硕士学位论文. 2006年2月: 17~18
    128樊莉,谭南林,沈栋平.基于显式动力学的滚动轴承接触应力有限元分析.北京交通大学学报.第30卷第4期, 2006年8月: 109~110
    129 P. T. Petersen. Dynamics of Ship Collisions. Ocean Engineering, 1982, 9(4): 295~329
    130 V. K. Agarwal, J. M. Niedzwecki, J. W. Lindt. Earthquake Induced Poundingin Friction Varying Base Isolated Buildings. Engineering Strucyure. 2007: 1~5
    131刘欣.弹性碰撞理论在齿轮线外啮合冲击力及冲击动应力计算中的应用研究.中南大学硕士学位论文. 2007年5月: 18~24
    132李裕春,时党勇,赵远. LS-DYNA基础理论与工程实践.中国水利水电出版社. 2006年4月: 72~88
    133朱孟巍.船舶与海洋平台碰撞的动力特性研究,武汉理工大学硕士学位论文. 2006年4月: 34~35
    134王胜光.螺纹副联接结构中接触非线性问题的研究与软件开发.中国科学院硕士学位论文. 2005年1月: 15~17
    135王君杰,颜海泉,钱烨.基于碰撞仿真的桥梁碰撞力规范公式的比较研究.公路交通科技.第23卷第2期, 2006年2月: 69~70
    136雷雨成,严斌,程昆.车辆典型薄壁梁碰撞仿真中接触摩擦问题的研究.机械设计与制造.第3期, 2004年6月: 110~111
    137 T. Weirzbicki, W. Abramowicz. Development and Implementation of Special Element for Crash Analysis. SAE paper, No. 880895
    138白金泽.基于神经网络方法的鸟撞飞机风挡反问题研究.西北工业大学博士学位论文. 2003年3月: 47~51
    139雷镭.双圆弧弧锥齿轮接触应力的有限元分析.天津大学硕士学位论文. 2006年2月: 34~37
    140郭毅之,金先龙,丁峻宏,曹文宏,陈宏.沉管隧道地震响应分析中的三维接触模型与算法研究.应用力学学报.第23卷第1期, 2006年3月: 48~50
    141 JT/GQB.公路桥涵标准图,中国交通部1999年5月24日
    142 G. C. Marano, S. Sgobba. Stochastic Energy Analysis of Seismic Isolated Bridges. Soil Dynamics and Earthquake Engineering. 2007, (27): 759-773
    143刘建成,顾永宁,胡志强.桥墩在船桥碰撞中的响应及损伤分析.公路.第10期, 2002年10月: 34~35
    144 R. Rossi, M. K. Alves, H. A. Qureshi. A Model for the Simulation of Powder Compaction Processes. Journal of Materials Processing Technology. 2007, (182): 286~288
    145 S. Dolarevic, A. Ibrahimbegovic. A Modified Three-surface Elasto-plastic Cap Model and Its Numerical Implementation. Computer and Structures. 2007, (85): 419~420
    146 P. Jonsen, H. A. Haggblad. Fracture Energy Based Constitutive Models forTensile Fracture of Metal Powder Compacts. International Journal of Solids and Structures. 2007: 1~3
    147 Livermore Software Technology Corporation. LS-DYNA Keyword User Manual. Version 970, April 2003: 8.3~20.302
    148黄羽立. FRP约束混凝土的分析与本构模型.清华大学硕士学位论文. 2005年5月: 49~53
    149 A. R. Khoei, H. DorMohammadi, A. R. Azami. A Three-invariant Cap Plasticity Model with Kinematic Hardening Rule for Powder Materials. Journal of Materials Processing Technology. 2007, (188): 680~684
    150滕祥泉.非比例阻尼空间结构弹动力有限元时程分析.天津大学硕士学位论文. 2003年12月: 11
    151邹晋华.钢管混凝土框架-抗震墙非线性地震响应分析西南交通大学硕士学位论文. 2003年5月: 41~42
    152赵雅丽.大跨度钢管混凝土拱桥的地震响应分析.浙江大学硕士学位论文. 2005年3月: 37
    153 GB50011~2001.建筑抗震设计规范.中华人民共和国国家标准: 9~32
    154林万杰.大跨长联预应力混凝土连续梁桥地震反应分析.西南交通大学硕士学位论文. 2006年3月: 46
    155崔俊,王凯,武建军.叠层橡胶支座在桥梁结构中的应用.河南科学.第20卷第5期, 2002年10月: 592
    156张伟东,孙韶峰,朱德功.立交桥梁防冲撞装置的设计与使用.铁道建筑.第1期, 2003年: 21
    157章熙冬.锻锤基础中的橡胶垫.中国建筑工程出版社. 1980年2月: 22~27
    158 G. James. Advanced Modern Engineering Mathematics(2nd edn). Addison-Wesley:Edinburgh, England, 1999
    159 B. F. Spencer, S. J. Dyke, J. D. Sain, Carlson. Phenomenological Model of A Magnetorheological Damper. Journal of Engineering Mechanics (ASCE). 1997, (123): 230~238.
    160 A. K. Wahed, J. L. Sproston, G. K. Schleyer. Electrorheological and Magnetorheological Fluids in Blast Resistant Design Applications. Materials and Design. 2002, (34): 391~404
    161 W. H. Li, H. Du, G. Chen, N. Q. Guo. Experimental and Modeling Approaches of MR Behaviors Under Large Step Strains. Material Science and Engineering. 2003, (340): 251~257
    162 M. Ahmadian, J. A. Norris. Experimental Analysis of Magnetorheological Dampers When Subjected to Impact and Shock Loading. Communications in Nonlinear Science and Numerical Simulation. 2008, (13): 1978~1985
    163 S. S. Sahasrabudhe, S. Nagarajaiah. Semi-active Control of Sliding Isolated Bridges Using MR Dampers: An Experimental and Numerical Study. Earthquake Engineering and Structural Dynamics. 2005, (34): 965~983
    164 J. N. Yang, Z. Li, S. Vongchavalitkul. A Generalization of Optimal Control Theory: Linear and Nonlinear Structures, Report no NCEER-92-0026, State university of New York at Buffalo, Buffalo, NY
    165 F. Sadek, B. Mohraz. Semiactive Control Algorithm for Structures with Variable Dampers. Journal of Engineering Mechanics. 1998, (124): 981~990