减振隔振与整星及全箭动态特性相互影响的研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
整星减振、隔振技术能够有效地改善卫星发射过程中的振动环境。设计减振和隔振系统,必然要综合考虑其与卫星、运载火箭整体的耦合作用。无论是采用减振还是隔振技术措施,均会在一定程度上改变全箭系统的动力学特性。动力学特性的变化有可能对系统的飞行控制系统造成不利影响甚至控制失稳,尤其是低刚度隔振装置的加入有可能使星箭系统的基频大幅下降。另一方面,大型运载火箭结构的基频最低可达到1赫兹左右,并且模态密集,卫星的基频最低可达到10赫兹以下。振动抑制对象的大柔性特点也为相对独立的传统隔振系统设计、优化提出了高要求。本论文以星箭支架附加约束阻尼层和一般隔振装置为对象,研究整星减振、隔振与整星及全箭间动态特性的相互影响,从全箭的角度研究减振隔振技术方案的分析和设计。
     本文首先归纳总结了约束阻尼建模技术和分析方法,并根据整星减振、隔振的工程应用特点,建立了星箭连接支架和能够描述多种构型隔振平台的一般隔振装置的有限元模型和分析模型,发展了约束阻尼层结构混合坐标建模方法。并提取了描述一般隔振装置动力学特性的特征参数。
     本文应用矩阵特征值摄动方法,建立了约束阻尼层附加刚度和质量与星箭固有特性变化的关系,研究了附加约束阻尼层后全箭固有特性的变化。分析表明,整星减振技术措施对全箭固有频率、模态振型、振型斜率的影响均很小;星箭支架变形能占全箭模态总能量的比例是约束阻尼层阻尼贡献的重要参考量。适当降低现有支架的连接刚度,增大支架在低频模态的模态应变能比例,能够提高约束阻尼层的低频减振效果。
     本文建立了任意星、箭组合通过一般隔振装置连接的全箭振动传递导纳,并在此基础上推导出全箭固有频率基于导纳的非小量摄动解析解;从基于局部非小量的结构重分析思路出发,以星、箭振动传递导纳为指标,讨论整星隔振对全箭固有频率、模态振型、振型向量以及星箭振动传递特性带来的影响。研究结果表明,卫星与运载火箭的质量相差悬殊,在现有的全箭系统中用隔振装置替换原有支架,不会对运载火箭的模态振型及与控制系统设计有密切联系的振型斜率产生明显的影响。本文根据全箭横向振动传递特性与隔振装置特征参数的关系,提出了“共振-反共振相消”参数配置方法,并以此来对隔振性能进行优化。
     论文的最后部分详细的介绍了FY-2结构星转接锥附加约束阻尼层的整星减振技术工程实施,结合试验指出大型复杂结构阻尼减振试验中需要重点注意的现象及其成因。在整星隔振试验方面,地面试验边界条件与实际工作条件具有一定的差异,这种差异可能严重影响阻尼减振效果评价的正确性。
The whole-spacecraft vibration attenuation (WSVA) and isolation (WSVI) technique could significantly reduce the launch loads on the spacecraft during the trip to the orbit. The WSVA and WSVI must be analyzed and designed in a system-level of view, accounting for its coupling with the launch vehicle (LV) and spacecraft (SC). Actually, the dynamic characteristics of the whole LV and SC system will be changed to some extent after isolation treatments, which may bring some side-effects to the flight control system, e.g. the introduction of low frequency mode by the isolation may threat the stability of the flight control. On the other aspect, the LV typically has closely-spaced flexible modes with frequencies starting as low as 1 Hertz, and the SC may have modes with frequencies starting as low as 10 Hertz. Different from the classic isolation system design, the isolation of a flexible body from another one demands a special design methodology, specifically, from system-level. This dissertation focuses on studying the problems associated with WSVA/I design and developing design methodology at the system-level.
     Beginning with a literature survey of damping modeling and analysis methods, with a fully consideration of specific characteristics of the WSVA/I devices, LV and SC structure, high fidelity finite element models of PAF with/without the CDL is established. A mixture coordinate modeling method is also developed for the PAF with the CDL. An mechanical model of general isolation devices are established for further analysis of whole LV/SC System.
     An eigenvalue-perturbation method is developed based on Gerschgorin’s Circle Theorem, and then is applied to build the relational expression of the additional stiffness/mass of CDL and the perturbed modal parameters of the whole LV/SC system. With this expression, the influence on the dynamic parameters of whole LV/SC system is studied by simulation. The results indicate that this perturbation method is efficient and accurate for the system-level analysis. It also shows that the modal parameters such as nature frequencies, modal shapes and modal shape slopes, are only slightly changed by the CDL treatment. The modal strain energy ratio of PAF to whole system is a critical variable to evaluate the contribution of the CDL to the whole system damping. As indicated by the vibration isolation theory, properly lowering the stiffness of the PAF can increase its modal strain energy ratio as well as the effectiveness of vibration attenuation in the low frequency range.
     With transfer functions of LV and SC coupled by WSVI device, an analytical expression of the whole system nature frequency in terms of the general WSVI devices’parameters is derived. The interrelationship between the modal parameters of whole LV/SC system and parameters of the general WSVI devices is studied. Because the LV dominates the mass of the whole coupled system, the results show that, the modal shapes and modal shape slopes, which correlate closely to the flight control system, changed insignificantly by the replacement of WSVI devices to the current PAF. In this dissertation, a“pole-zero cancellation”method is proposed to design and majorize the isolation performance, which is a parameter configuration method to eliminate a certain resonance of a certain component on the SC.
     Finally, a CDL engineering implementation and vibration test is introduced which is carried out on the PAF of a prototype FY-2 satellite for suppressing the load transmission to its on-board instruments. On analysis of test results, abnormal phenomenon and their root causes discovered from the test are figured out. Moreover, there are differences between the boundary conditions in the ground test and that in the actual launch. These differences may bring incorrect conclusion to the performance evaluation of damping implemented in WSVI technique.
引文
1 P. S. Wilke, P. Alto, C. D. Johnson, etc. Payload isolation System for Launch Vehicles. SPIE Proceedings. 1997,3045:20~30
    2 A. S. Bicos, C. D. Johnson. Need for and Benefits of Launch Vibration Isolation. SPIE Proceedings. 1997.3045:14~19
    3潘坚,雷治大.阻尼减振技术在航天领域的应用.宇航材料工艺, 1991,4:87~90
    4丁爱康.减振合金在航天器上的应用.宇航材料工艺, 1993,4:87~90
    5 E. Quandt, A Ludwig. Magnetostrictive Actuation in Microsystem. Sensors and Actuators. 2000,81(1):275~280
    6 C. Padmanabhan, J. S. Kumar, N. Ganesan, S. Swarnamani. Active Control of Cylindrical Shell with Magnetostrictive Layer. Journal of Sound and Vibration. 2003,262(3):577~589
    7 J. R. Maly, G. P. Carmen, J. C. Goodding, et al. Passive Vibration Damping with Magnetostrictive Composite Material. SPIE Proceedings. 2007,6525:652515
    8 S. C. Pradhan. Vibration Suppression of FGM Shells Using Embedded Magnetostrictive Layers. International Jounal of Solids and Structures. 2005, 42(9-10):2465~2488
    9梁伟,刘冬欢.磁致伸缩铺层阻尼板壳结构的振动分析.复合材料学报. 2006, 23(6):186~191
    10 J. R. Maly, G. P. Carmen, J. C. Goodding, et al. Passive Vibration Damping with Magnetostrictive Composite Material. SPIE Proceedings. 2007,6525:652515
    11何慧敏,王雁冰,沈强等.材料导报. 2008,22(1):41~44
    12陈晔,刘允航,田国华等.聚氨酯/苯并噁嗪互穿聚合物网络的阻尼性能.上海交通大学学报. 2002,36(10):1506~1508
    13韩兆芳,梁瑞林,丁国芳.氯化丁基橡胶压电阻尼复合材料的研究.压电与声光. 2006,28(4):461~463
    14 T. Tetuya, H. Teruomi. Thrust Tube Capable of Efficiently Damping a Vibration. EUROPEAN PATENT:EP0531055B1, Aug,1993
    15王聪,徐世昌,牟全臣,黄文虎.某航天器仪器舱结构减振试验研究.机械强度. 2002,24(1):49~51
    16张军,谌勇,骆剑,华宏星.整星隔振技术的研究现状和发展.航空学报. 2005,26(3):179~183
    17 D. T. Ruebsamen. Evolved Launch Vibration Isolation System (ELVIS) Demonstration Unit Test Results. The S/C and L/V Dynamics Environments Workshop, the Aerospace Corporation, JUNE, 2003
    18 C. D. Johnson, P. S. Wike, K. R. Darling. Muti-axis Whole-spacecraft Vibration Isolation for Small Launch Vehicles. SPIE Proceedings. 2001,4331:162~174
    19 E. R. Fosness, K. K. Denoyer, A. Das, et al. Whole-spacecraft Isolation Development Effects at the USAF Phillips Laboratory. 11th AIAA/USU Conference on Small Satellites. 1997
    20 D. Toren, S. Osterberg, A. David. Load Vibration Isolation Apparatus. UNITED STATES PATENT:5947240, 1999
    21 C. D. John, On the Design and Testing of a Spacecraft Launch Vibration Isolation System (LVIS). Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 1997,2:1494~1499
    22 D. L. Edberg, C. D. John. L. P. Davis, et al. Development of a launch Vibration Isolation System. SPIE Proceedings. 1998,3045:31~37
    23 S. Osterberg. A. David. Load Isolation Apparatus. UNITED STATES PATENT: 5918865. 1999
    24 D. Toren, S. Osterburg, A. David. Heavy Load Vibration Isolation Apparatus. UNITED STATES PATENT:5803213, 1998
    25 Hubert, P. M. Dominique. Device for Suspension of a Payload in a Space Launch. UNITED STATES PATENT:6244541, 1999
    26 D. L. Edberg, Fukushima, D. Jeffrey, et al. Passive Lateral Vibration Isolation System for a Spacecraft Launch Vehicle. UNITED STATES PATENT:6012680, 2001
    27 J. R. Malya, S. A. Haskett, P. S. Wilke, et al. EELV Secondary Payload Adapter with Whole-spacecraft Isolation for Primary and Secondary Payloads. SPIE Proceedings. 2000, 3989:430~439
    28 C. Scott, S. A. Haskett, et al. EELV Secondary Payload Adapter (ESPA). SPIE Proceedings. 2000, 4136:27~35
    29 S Jeremy, G P Wegner. Evolved Expendable Launch Vehicle Secondary Payload Adapter. 15th Annual/USU Conference on Small Satellites. Logan Utah, Aug, 2001
    30 D Sciulli, Griffin, F Steven. Whole-spacecraft Hybrid Isolation System for Launch Vehicles. UNITED STATES PATENT:6135390, 2000
    31 F. Khorrami, J. Rastegar, R. S. Erwin. A Three Degree of Freedom Adaptive-passive Isolator for Launch Vehicle Payloads. SPIE Proceedings. 2000:164~176
    32 G. G. Karahalis. Whole-spacecraft Vibration Isolation Master’s Thesis. USA:OH. School of Engineering, 1999
    33 G. G. Karahalis, G. S. Agnes. Preliminary Analysis of Hybrid Launch Isolation for Spacecraft. SPIE Proceedings. 1999, 3674:360~370
    34 D. Sciulli, S. F. Griffin. Hybrids Launch Isolation System. SPIE Proceedings. 1999, 3674:352~359
    35 C. D. Johnson, P. S. Wilke. Whole-spacecraft Shock Isolation System. SPIE Proceedings. 2002, 4697:1~8
    36 G. R. Thomas, C. M. Fadick, B. J. Fram. Launch Vehical Payload Adapter Design with Vibration Isolation Features. SPIE Proceedings. 2005,5760:35~45
    37 J. R. Jarosh, G. S. Agnes, G. G. Karahalis. Adaptive Control for Payload Launch Vibration Isolation. SPIE Proceedings. 2001,4331:162~174
    38 E. Flint. Active/passive Counter-force Vibration Control and Isolation System. IEEE Aerospace Conference Proceedings. 2000,4:285~298
    39 M. E. Evert, P. C. Janzen, E. H. Anderson, et al. Active Vibration Isolation System for Launch Load Alleviation. SPIE Proceedings. 2004,5388:62~77
    40 L. Dewell, N. Pedreiro, C. Blaurock, et al. Precison Telescope Pointing and Spacecraft Vibration Isolation for the Terestrial Planet Finder Coronagraph. SPIE Proceedings. 2005,5899:589902
    41 K. C. Liu, C. Blaurock, G. E. Mosier. Pointing Control System Design and Performance Evaluation of TPF Coronagraph. SPIE Proceedings. 2004,5497: 437~448
    42 M. B. McMickell, T. Kreider, E. Hansen, et al. Optical Payload Isolation using the Miniature Vibration Isolation System (MVIS-II). SPIE Proceedings. 2007, 6527:652703
    43 W. Mark. Robust Control for Microgravity Vibration Isolation. Journal of Spacecraft and Rockets. 2005,42(1):152~160
    44 G. S. Hauge, M. E. Campbell. Sensors and Control of a Space-based Six-axis Vibration Isolation System. Journal of Sound and Vibration. 2004,269(3-5):913~931
    45 S. Hiraku, K. C. Park, M. Yasuyuki. Distributed and Localized Active Vibration Isolation in Membrane Structures. Journal of Spacecraft and Rockets.2006,43(5):1017~1116
    46 B. D. Keith. Structural Line-of-sight Jitter Analysis for MLCD. SPIE Proceedings. 2007,6665:666501
    47 T. Hindle, T. Davis, J. Fischer. Isolation, Pointing, and Suppression (IPS) System for High Performance Spacecraft. SPIE Proceedings. 2007,6527:652702
    48 J. F. Baldwin, S. G. Hutton. Natural Modes of Modified Structures. AIAA Journal. 1985, 23(11):1737~1743
    49 B. P. Wang, W. D. Pilkey. Eigenvalue Reanalysis of Locally Modified Structures Using a Generalized Rayleigh’s Method. AIAA Journal. 1986,24(6):983~990
    50吕振华.模态灵敏度分析.见:《科技综述百科全书》,北京出版社, 1993
    51 J. W. S. Rayleigh. The Theroy of Sound, 2nd edition, Vol. 1. Macmilan, London, 1894, reprinted by Dover, New York, 1945
    52 E. Shr?dinger. Quantisierungals eigenwertproblem. Annals of Physics. 1926, 80:437~490
    53胡海昌.多自由度结构固有振动理论.北京:科学出版社, 1987
    54胡海昌,陈德成,贺向东.固有频率集聚时处理振型的一个方法.固体力学学报, 1991,12(1):54~60
    55 K. M. Romstad, J. R. Hutchinson, K. H. Runge. Design Parameter Variation and Structural Response. International Journal for Numerical Methods in Engineering. 1973,5:337~349
    56王少龙,张德文,许婉丽.矩阵摄动法在应用上的发展.强度与环境, 1984, (1):1~9
    57 P. C. Brooks, R. S. Sharp. A computational Procedure Based on Eigenvalue Sensitivity Theory Applicable to Linear System Design. Journal of Sound and Vibration. 1987,114(1):13~18
    58吕振华,冯振东,方传流.线性特征值问题的高精度矩阵摄动法.振动工程学报. 1990,3(1):42~46
    59冯振东,吕振华.线性广义特征值问题重分析的分步摄动法.振动与冲击. 1991, 10(4):42~49
    60 D. Young. Vibration of a Beam with Concentrated Mass, Spring and Dashpot. Journal of Applied Mechanics. 1948,15:65~72
    61 W. F. Z. Lee, E. Saibel. Free Vibrations of Constrained Beams. Journal of Applied Mechanics. 1952,19:471~477
    62 Y. C. Das, D. R. Navaratna. Vibrations of Rectangular Plate with Concentrated Mass, Spring and Dashpot. Journal of Applied Mechanics, 1963, 30:31-36
    63 J. T. Weissenburger. Effect of Local Modification on the Vibration Characteristics of Linear Systems. Journal of Applied Mechanics. 1968,35(1):327~332
    64 R. J. Pamazal, V. W. Snyder. Local Modifications of Damped Linear Systems. AIAA Journal. 1971,9(11):2216~2221
    65 J. Hallquist, V. W. Snyder. Synthesis of Two Discrete Vibratory Systems Using Eigenvalue Modification. AIAA Journal. 1973,11(2):247~249
    66 J Hallquist. An Efficient Method for Determining the Effects of Mass Modifications in Damped Systems. Journal of Sound and Vibration. 1976, 44(3):449~459
    67朱光汉,郭平.局部修改对结构模态参数的影响范围.振动工程学报. 1988, 1(4):53~60
    68王小刚,卢秉恒,顾崇街.粘弹性阻尼修改后结构系统动特性的预测.应用力学学报. 1990, 7(2):1~8
    69杨晓伟,陈塑寰.结构参数大修改时的特征值重分析方法.力学学报. 2001,33(4):555~560
    70黄海,陈塑寰,孟光.摄动法结合Padé逼近在结构拓扑重分析中的应用.应用力学学报. 2005,22(2):155~158
    71 S. H. Chen, X. W. Yang, H. D. Lian. Comparison of Several Eigenvalue Reanalysis Methods for Modified Structures. Structural and Multidisciplinary Optimizaton. 2000,20(4):253~259
    72 B. S. Wu, Z. G. Li, S. H. Li. The Implementation of a Vector-valued Rational Approximate Method in Structural Reanalysis Problems. Computer Methods in Applied Mechanics and Engineering. 2003,192(13-14):1773~1784
    73孙亮,李顺华,李正光等.结构动力重分析的向量值有理逼近方法.吉林大学学报(理学版). 2005,43(3):258~261
    74张美艳,韩平畴.基于有利逼近和灵敏度分析的结构动力重分析方法。振动与冲击. 2006,25(4):50~52
    75 H. P. Chen. Efficient Methods for Determining Modal Parameters of Dynamic Structures with Large Modifications. Journal of Sound and Vibration. 2006,298(1-2): 462~470
    76吴晓明,陈塑寰. Epsilon算法在结构模态重分析中的应用.吉林大学学报(工学版). 2006,36(4):447~450
    77 P. Cacciola, N. Impollonia, G. Muscolino. A Dynamic Reanalysis Technique for General Structural Modifications under Deterministic or Stochastic Input. Computer and Structures. 2005,83(14):1076~1085
    78 C. Huang, S. H. Chen, Z. S. Liu. Structural Modal Reanalysis for Topological Modifications of Finite Element Systems. Engineering Structures. 2000, 22(4):304~310
    79 Z. J. Yang, S. H. Chen, X. M. Wu. A Method for Modal Reanalysis of Topological Modifications of Structures. International Jounal for Numerical Methods in Engineering. 2006,65(13):2203~2220
    80 F. Rong, S. H. Cheng, Y. D. Chen. Structural Modal Reanalysis for Topological Modifications with Extended Kirsch Method. Comput Methods in Applied Mechanics and Engineering. 2003,192(5-6):697~707
    81何建军,姜节胜.结构拓扑修改动力学重分析的单步摄动逆迭代法.西北工业大学学报. 2006,24(3):313~316
    82何建军.结构拓扑修改动力学重分析方法的研究.西北工业大学硕士学位论文. 2006:23~28
    83 J. J. He, J. S. Jiang. Modal Reanalysis Methods for Structural Large Topological Modifications with Added Degrees of Freedom and Non-classical Damping. Finite Elements in Analysis and Design. 2007,44(1-2):75~85
    84 Y. X. Su, B. Y. Duan, C. H. Zheng. Genetic Design of Kinematically Optimal Fine Tuning Stewart Platform for Large Spherical Radio Telescope. Mechatronics. 2001, 11(7):821~835
    85 Y. X. Su, B. Y. Duan, B. Peng, et al. Singularity Analysis of Fine Tuning Stewart Platform for Large Radio Telescope using Genetic Algorithm. Mechatronics. 2003, 13(5):413~425
    86 Z. Wang, L. K. Liu, G. T. Zheng. Optimal Design of Octo-Strut Vibration Isolation Platform. Journal of Guidance, Control, and Dynamics. 2006,29(3):749~753
    87邹贵平,唐立民.正交异性层合板的混合状态Hamilton元.复合材料学报. 1994, 11(3):20-22
    88杜华军.基于约束阻尼的蜂窝锥壳卫星适配器振动抑制研究.哈尔滨工业大学博士论文. 2003
    89罗祖道,李思简.各向异性材料力学.上海交通大学出版社. 1994:231-234
    90徐胜今,孔宪仁,王本利,马兴瑞,张晓超.正交异性蜂窝夹层板动、静力学问题的等效分析方法.复合材料学报. 2000, 17(3):92-95
    91 L. J. Gibson, M. F. Ashby, G. S. Schajer, C. I. Robertson. The Mechanics of Two-dimensional Cellular Materials. Proceedings of The Royal Society of London. 1982, Series A, 382:25~42
    92富明慧,尹久仁.蜂窝芯层的等效弹性参数.力学学报. 1999, 31(1):113~118
    93刘天雄,石银明,华宏星,李中付,朱继海,陈兆能.主动约束层阻尼振动控制技术现状及展望.振动与冲击. 2001,20(2):1~10
    94 G. A. Lesieutre, D. L. Mingori. Finite Element Modeling of Frequency-dependent Material Damping Using Augumenting Thermodynamic Fields. Journal of Guide and Control. 1990,13(6):1040~1050
    95 G. A. Lesieutre, E. Bianchini. Time Domain Modeling of Linear Viscoelasticity Using Anelastic Displacement Fields. ASME Journal of Vibration and Acoustics. 1995, 117:424~430
    96 M. J. Lam, D. J. Inman, W. R. Saunders. Vibration Control Through Passively Constrained Layer Damping and Active Control. Journal of Intelligent Material Systems and Structures. 1997,8:663~667
    97 S. A. Ravi, T. K. Kunka, B. C. Nakra. Response Reanalysis of Damped Beams Using Eigenparameter Perturbation. Journal of Sound and vibration. 1995,179:399~412
    98 P. K. Roy, N. Ganesan. Vibration and Damping Analysis of Circular Plates with Constrained Layer Damping Treatment. Computers and Structures. 1993,49:269~274
    99 X. S. Cao, M. H. Peter. Computational Prediction and Redesign for Viscoelastically Damped Structures. Computer Meth. And Mechanical Engineering. 1995, 125(1):1~16
    100 T. C. Ramesh, N. Ganesan. Finite Element Analysis of Cylindrical Shells with Constrained Viscoelastic Layer. Journal of Sound and Vibration. 1994, 172:359~370
    101 R. Rikards. Finite Element Analysis of Vibration and Damping of Laminated Composite. Composite Structures.1993, 24:193~244
    102 Y. P. Lu, J. C. Clemens, A. J. Roscoe. Vibration of Composite Plate Structures Consisting of a Constrained-layer Damping Sandwich with Viscoelastic Core. Journal of Sound and Vibration. 1992,158(3):552~558
    103 C. D. John, D. A. Kienholz. Finite Element Prediction of Damping in Structures with Constrained Viscoelastic Layers. AIAA Journal. 1982,20(9):1284~1290
    104刘丽坤.八作动器隔振平台及整星隔振研究.哈尔滨工业大学博士论文. 2005
    105李卿,王介康,曹亮. FY-2C业务静止气象卫星及发展展望.上海航天. 2005年增刊:1~8
    106陈闽慷,吴尚云. CZ-3A运载火箭.导弹与航天运载技术. 1999,5(5):1~8
    107龙乐豪. CZ-3A系列运载火箭.导弹与航天运载技术. 1999,3(3):1~6
    108程云鹏.矩阵论.西北工业大学出版社:244~258
    109于海昌.大型运载火箭振动试验振型斜率测试方法.强度与环境. 1996,3:46~53
    110于海昌,吴素春.运载器模态阻尼比的实验确定.振动与动态测试. 1985,4:1~10
    111 W. Heylen, S. Lammens, P. Sas.白化同,郭继忠译.模态分析理论与实践.北京理工大学出版社. 2001:110~119
    112韩增尧,曲广吉.航天器宽带随机振动响应分析.中国科学技术. 2002,1:24~30
    113李以农,郑玲,闻邦椿.螺栓接头非线性模型及其波能耗散.振动工程学报. 2003, 16(2):137~142
    114 A. D. Crocombe, R. Wang, G. Richardson. Estimating the Energy Dissipated in a Bolted Spacecraft at Resonance. Computers and Structures. 2006,84:340~350
    115 A. R. Kukreti, P. Biswas. Finite Element Analysis to Predict the Cyclic Hysteretic Behavior and Failure of End-plate Connection. Computers and Structures. 1997, 65:127~147
    116 J. Krzyzanowski, W. Skoczynski, K. Augul. Mechanism of Vibration Energy Dissipation in Flange Bolted Joints. Proceedings of the International Seminar on Modal Analysis, CONF 23. 1999,2:107~1076
    117傅俊庆,荣见华,张玉萍.螺栓连接接口轴向振动能量耗散特性研究.振动、测试与诊断. 2005,25(3):205~209
    118 C. J. Gantes, M. E. Lemonis. Influence of Equivalent Bolt Length in Finte Element Modeling of T-stub Steel Connection. Computers and Structures. 2003,81:595~604

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700