大型网架式可展开空间结构的非线性动力学与控制

胡海岩; 田强; 张伟; 金栋平; 胡更开; 宋燕平

doi:10.6052/1000-0992-13-045

大型网架式可展开空间结构的非线性动力学与控制

doi: 10.6052/1000-0992-13-045

1 北京理工大学飞行器动力学与控制教育部重点实验室, 北京100081
2 南京航空航天大学机械结构力学及控制国家重点实验室, 南京200016
3 北京工业大学机电学院, 北京100124
4 中国空间技术研究院西安分院, 西安710100

基金项目: 国家自然科学基金重大资助项目(11290150)

详细信息

作者简介:
胡海岩, 1956年出生, 1988年毕业于南京航空航天大学固体力学专业, 获工学博士. 现任北京理工大学校长、教授, 中国科学院院士, 发展中国家科学院院士；兼任中国科学院技术科学部副主任, 中国力学学会理事长, 中国宇航学会副理事长, 中国航空学会副理事长. 主要从事飞行器结构动力学与控制、非线性动力学与控制等领域的研究, 曾获国家自然科学奖二等奖, 国家科技进步奖二等奖, 何梁何利科学与技术进步奖(数学力学奖).

通讯作者:
胡海岩

中图分类号: O313, O322
计量
- 文章访问数: 3537
- HTML全文浏览量: 852
- PDF下载量: 2981
- 被引次数: 0
出版历程
- 收稿日期: 2013-06-19
- 修回日期: 2013-07-19
- 刊出日期: 2013-07-25

Nonlinear Dynamics and Control of Large Deployable Space Structures Composed of Trusses and Meshes

1 MOE Key Laboratory of Dynamics and Control of Flight Vehicles, Beijing Institute of Technology, Beijing 100081, China
2 State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 200016, China
3 College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
4 Xi’an Branch, China Academy of Space Technology, Xi’an 710100, China

More Information

Corresponding author: Hu Haiyan

摘要

摘要: 我国航天工业迫切需要掌握可入轨后展开的大型网架式空间结构技术，以便研制口径十几米、乃至数十米的大型星载天线。该技术的主要科学基础是这类空间结构展开和服役过程的非线性动力学建模、分析和控制。本文综述了与上述科学基础相关的研究进展，提出应重点关注的三个科学问题：一是大型网架式空间结构展开过程的多柔体系统动力学，尤其是如何对微重力环境下索网的接触和缠绕、运动副内碰撞、结构展开与航天器本体间的耦合等导致的非线性动力学进行建模和分析；二是大型网架式空间结构展开锁定后服役的动力学分析，尤其是如何揭示结构柔性、众多运动副间隙、交变热载荷等因素引起的复杂非线性振动机理；三是大型网架式空间结构展开锁定后服役的动力学控制，尤其是如何在欠驱动、低能耗条件下对非线性振动和波动传播提出有效的控制方法。
- 空间结构 /
- 展开 /
- 非线性动力学 /
- 多体系统动力学 /
- 振动控制 /
- 波动控制
Abstract: The space industry in China is eager to have the advanced technology of large space structures composed of trusses, cables and meshes. Such a large space structure, deployed on orbit, serves as the large antenna for different space missions. The important scientific basis of the technology is the nonlinear dynamic modeling, analysis and control of those space structures during their deployment and service. This review article surveys the advances in relevant researches and proposes three open problems as following. The first is the flexible multibody dynamics for the deployment of such a space structure, especially the nonlinear dynamic modeling and analysis for the contacts and wraps of mesh under microgravity, the internal impacts in clearance joints, and the coupling between structure deployment and spacecraft attitude. The second is the dynamic analysis of the space structures after deployment and during service, especially the complicated nonlinear vibrations of the flexible structure with numerous backlash joints under periodic thermal impacts. The third is the dynamic control of the space structures after deployment and during service, especially the under-actuated and lower-powered control for structure vibrations and waves.
- pace structure /
- deployment /
- nonlinear dynamics /
- multibody system dynamics /
- vibration control /
- wave control

HTML全文

参考文献(142)

[1]	Alijani F Bakhtiari-Nejad F, Amabili M. 2011. Nonlinear vibrations of FGM rectangular plates in thermal environments. Nonlinear Dynamics, 66: 251-270
[2]	Augusti G. 1968. Instability of struts subject to radiant heat. Mechanica, 3: 167-176
[3]	Bauchau O A, Rodriguez J. 2002. Modeling of joints with clearance in flexible multibody systems. International Journal of Solids and Structures, 39: 41-63
[4]	Bestsch P, Hesch C, S¨anger N, Uhlar S. 2010. Variational integrators and energy-momentum schemes for flexible multibody dynamics. Journal of Computational and Nonlinear Dynamics, 5(3): 031001
[5]	Boley B A. 1956. Thermally induced vibrations of beams. Journal of Aeronautical Science, 23(1): 179-181
[6]	Boley B A. 1972. Approximate analysis of thermally induced vibrations of beams and plates Journal of Applied Mechanics, 94: 212-216
[7]	Britvec S J. 1995. Stability and Optimization of Flexible Space Structures, Berlin: Birkhäuser
[8]	Brüls O, Duysinx P, Golinval J C. 2007. The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics. International Journal of Numerical Methods in Engineering, 69: 948-977
[9]	曹登庆, 初世明, 李郑发, 刘荣强. 2013. 空间可展机构非光滑力学模型和动力学研究. 力学学报, 45: 3-15 (Cao D Q, Chu S M, Li Z F, Liu Y Q. 2013. Study on the non-smooth mechanical models and dynamics for space deployable mechanisms. Chinese Journal of Theoretical and Applied Mechanics, 45: 3-15 (in Chinese))
[10]	Cao D X, Zhang W. 2009. Further studies on nonlinear responses of a string-beam coupled system with four-degrees-of-freedom and multiple parametric excitations. International Journal of Bifurcation and Chaos, 19: 225-243
[11]	Chamekh M, Aouadi S M, Moakher M. 2009. Modeling and numerical treatment of elastic rods with frictionless self-contact. Computer Methods in Applied Mechanics and Engineering, 198: 3751-3764
[12]	Chang Z, Hu J, Hu G K. 2010.Transformation method and wave control. Acta Mechanica Sinica, 26: 889-898 常正. 2013. 基于坐标变换的波场控制理论及应用. [博士论文]. 北京: 北京理工大学(Chang Z. Theory and Application of wavefield control based on coordinate transformation. [PhD Thesis]. Beijing: Beijing Institute of Technology (in Chinese))
[13]	Chiang R Y, Wang H G, Bender D J, Morgowicz B. 2003. Thermal snap disturbance identification via in-flight data AIAA-Paper 2003-5825
[14]	Chodimella1 S P, Moore J D, Otto J, Fang H F. 2006. Design evaluation of a large aperture deployable antenna. AIAA-Paper 2006-1603
[15]	Cottrell J A, Hughes T J R, Bazilevs Y. 2009. Isogeometric Analysis: Toward Integration of CAD and FEA. Chichester: John Wiley and Sons, Ltd
[16]	D´Iaz J J C, Nieto P J G, Fresno D C, Fernandez E B. 2009. Non-linear analysis of cable networks by FEM and experimental validation. International Journal of Com- putational Mathematics, 86: 301-313
[17]	董富祥, 洪嘉振. 2009. 多体系统动力学碰撞问题研究综述. 力学进展, 39: 352-359(Dong F X, Hong J Z. 2009. Review of impact problem for dynamics of multibody system. Advances in Mechanics, 39: 352-359 (in Chinese))
[18]	段宝岩. 2005. 柔性天线结构分析、优化与精密控制. 北京: 科学出版社(Duan B Y. 2005. Flexible Antenna Structure Analysis, Optimization and Control. Beijing: Science Press (in Chinese))
[19]	Duan J, Xiang Z H, Xue M D. 2008. Thermal-dynamic coupling analysis of large space structures considering geometric nonlinearity. International Journal of Structural Stability and Dynamics, 8: 569-596
[20]	Durville D. 2010. Simulation of the mechanical behavior of woven fabrics at the scale of fibers. International Journal of Material Forum, 3: S1241-1251
[21]	Durville D. 2012. Contact-friction modeling within elastic beam assemblies: an application to knot tightening. Computational Mechanics, 49: 687-707
[22]	Flores P, Ambr´osio J, Claro J C P, Lankarani H M. 2008. Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Berlin: Springer
[23]	Flores P, Leine R, Glocker C. 2009. Modeling and analysis of rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody System Dynamics, 23: 165-190
[24]	Flores P, Koshy C S, Lankarani H M, Ambrósio J, Claro J C P. 2011. Numerical and experimental investigation on multibody systems with revolute clearance joints. Non- linear Dynamics, 65: 383-398
[25]	Flores P, Leine R, Glocker C. 2012. Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems. Nonlin- ear Dynamics 69: 2117-2133
[26]	Galv˜ao A S, Silva A R D, Silveira R A M, Gon¸calves P B. 2010. Nonlinear dynamic behavior and instability of slender frames with semi-rigid connections. International Journal of Mechanical Science, 52: 1547-1562
[27]	Gao E W, Zhang X P, Yao Z Q. 2008. Simulation and analysis of flexible solar panels’ deployment and locking processes. Journal of Shanghai Jiaotong University (Sci- ence), 13: 275-279
[28]	高强, 姚伟岸, 吴锋, 张洪武, 林家浩, 钟万勰. 2011. 周期结构动力响应的高效数值方法. 力学学报, 43: 1181-1185 (Gao Q, Yao W A, Wu F, Zhang H W, Lin J H, Zhong W C. 2011. An efficient algorithm for dynamic response of periodic structures. Chinese Journal of Theoretical and Applied Mechanics, 43: 1181-1185 (in Chinese))
[29]	Gardonio P, Elliott S J. 1996. Active control of waves on a one-dimensional structure with a scattering termination. Journal of Sound and Vibration, 192: 701-730
[30]	葛建立, 杨国来, 吕加. 2012. 同几何分析研究进展. 力学进展42: 771-784 (Ge J L, Yang G L, L¨u J. 2012. Advances in isogeometric analysis. Advances in Mechanics, 42: 771784 (in Chinese))
[31]	Gerstmayr J, Sugiyama H, Mikkola A. 2013. Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. Journal of Compu- tational and Nonlinear Dynamics, 8: 031016
[32]	Goyal S, Perkins N C, Lee C L. 2005. Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables. Journal of Com- putational Physics, 209: 371-389
[33]	Goyal A, Dorfel M R, Simeon B, Vuong A V. 2013. Isogeometric shell discretizations for flexible multibody dynamics. Multibody System Dynamics, 30: 139-151
[34]	关富玲, 刘亮. 2010. 四面体构架式可展天线展开过程控制及测试. 工程设计学报, 17: 381-387 (Guan F L, Liu L. 2010. Deployment control and test of deployable tetrahedral truss antenna. Journal of Engineering Design, 17: 381-387 (in Chinese))
[35]	Han W, Hu H Y, Jin D P. 2007. Experimental study on dynamics of an oblique-impact vibrating system of two degrees of freedom. Nonlinear Dynamics, 50: 551-573
[36]	Haraguchi M., Hu H Y. 2008. Using a new discretization to design delayed LQG controllers. Journal of Sound and Vibration, 314: 558-570.
[37]	Hu H Y. 1995a. Simulation complexities in the dynamics of a continuously piecewise-linear oscillator. Chaos, Solitons and Fractals, 5: 2201-2212.
[38]	Hu H Y. 1995b. Detection of grazing orbits and incident bifurcations of a forced continuous, piecewise-linear oscillator. Journal of Sound and Vibration, 187: 485-493.
[39]	Hu H Y,Wang Z H. 2002. Dynamics of Controlled Mechanical Systems with Delayed Feedback. Berlin: Springer- Verlag
[40]	胡海岩, 程德林. 1986. 循环对称结构振动分析的广义模态综合法. 振动与冲击, 5: 1-7 (Hu H Y, Cheng D L. 1986. Generalized mode synthesis of cyclosymmetrical structures. Journal of Vibration and Shock, 5: 1-7 (in Chinese))
[41]	胡海岩, 程德林. 1988. 循环对称结构固有模态特征的探讨. 应用力学学报, 5: 1-8 (Hu H Y, Cheng D L. 1988. Investigation on modal characteristics of cyclosymmtrical structures. Chinese Journal of Applied Mechanics, 5: 1-8 (in Chinese))
[42]	胡海岩, 郭大蕾, 翁建生. 2001. 振动半主动控制技术的进展. 振动, 测试与诊断, 21: 235-244 (Hu H Y, Guo D L,Weng J S. 2001. Recent advances in semi-active control of vibration. Journal of Vibration, Measurement and Diagnosis, 21: 235-244 (in Chinese))
[43]	Hu J, Chang Z, Hu G K. 2011. Approximate method for controlling solid elastic waves by transformation media. Physical Review B, 84: 201101
[44]	Hughes T J R, Cottrell J A, Bazilevs Y. 2005. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Me- chanics and Engineering, 194: 4135-4195
[45]	Hyland D C, Junkins J L, Longman R W. 1993. Active control technology for large space structures. Journal of Guidance, Control and Dynamics, 16: 801-821
[46]	Ibrahim R A, Pettit C L. 2005. Uncertainties and dynamic problems of bolted joints and other fasteners. Journal of Sound and Vibration, 279: 857-936
[47]	Ingham M D, Kim YA, Crawley E F, McManus H L, Miller D W. 2000. Experimental characterization of thermal creak response of deployable space structures. Journal of Spacecraft and Rockets, 37: 342-349
[48]	Issa J, Mukherjee R, Shaw S W. 2010. Vibration suppression in structures using cable actuators. Journal of Vi- bration and Acoustics, 132: 013006
[49]	金栋平, 文浩, 胡海岩. 2004. 绳索系统的建模、动力学和控制. 力学进展, 34: 304-313 (Jin D P, Wen H, Hu H Y. 2004. Modeling, Dynamics and control of cable systems. Advances in Mechanics, 34: 304-313 (in Chinese))
[50]	金栋平, 胡海岩. 2005. 碰撞振动与控制. 北京: 科学出版社(Jin D P, Hu HY. 2005. Vibro-Impact Dynamics and Control, Beijing: Science Press, (in Chinese))
[51]	Kappaganthu K, Ntaraj C. 2011. Nonlinear modeling and analysis of a rolling element bearing with a clearance. Communication of Nonlinear Science and Numer- ical Simulation, 16: 4134-4145
[52]	Kim Y A. 1999. Thermal creak induced dynamics of space structures. [PhD Thesis]. Boston: Massachusetts Institute of Technology
[53]	Lan P, Shabana A A. 2010. Integration of B-spline geometry and ANCF finite element analysis. Nonlinear Dynamics, 61: 193-206
[54]	Lankarani H M, Nikravesh P E. 1990. A contact force model with hysteresis damping for impact analysis of multibody systems. Journal of Mechanical Design, 112: 369-376
[55]	Leine R I, Wouw N. 2008. Stability properties of equilibrium sets of nonlinear mechanical system with dry friction and impact. Nonlinear Dynamics, 51: 551-583
[56]	Lens E V, Cardona A. 2008. A nonlinear beam element formulation in the framework of an energy preserving time integration scheme for constrained multibody systems dynamics. Computers and Structures, 86: 47-63
[57]	Levine M B. 1998. The interferometry program experiments: IPEX I&II. in: Proceedings of SPIE. Astronautic Telescope and Instrumentation Conference, Kona Hawaii, 3350-14
[58]	Levine M B. 1999. Microdynamic behavior of a joint dominated structure on-orbit. AIAA-Paper 99-1267
[59]	李东旭. 2008. 大型挠性空间桁架结构动力学分析与模糊振动控制. 北京: 科学出版社(Li D X. 2008. Large Flexible Space Truss Structures Dynamic Analyses and Vibration Fuzzy Control. Beijing: Science Press (in Chinese))
[60]	李东旭. 2010. 挠性航天器结构动力学. 北京: 科学出版社. (Li D X. 2008. Structural Dynamics of Flexible Spacecraft. Beijing : Science Press (in Chinese))
[61]	Li P, Tian Q, Liu C, Hu H Y. 2012. Study on deployment dynamics of a large hoop truss satellite antenna based on the absolute coordinate method.in: Proceedings of the 6th Asian Conference on Multibody Dynamics, ID: 113000
[62]	Li T J, Wang Y. 2009. Deployment dynamic analysis of deployable antennas considering thermal effect. Aerospace Science and Technology, 13: 210-215
[63]	Li T J. 2012. Deployment analysis and control of deployable space antenna. Aerospace Science and Technology, 18: 42-47
[64]	李团结, 张琰, 段宝岩. 2008. 周边桁架可展天线展开过程仿真方法. 系统仿真学报, 20: 2081-2084 (Li T J, Zhang Y, Duan B Y. 2008. Approach to deployable process simulation of circular truss deployable antenna. Journal of System Simulation, 20: 2081-2084 (in Chinese))
[65]	李团结, 张琰, 李涛. 2009. 周边桁架可展天线展开过程动力学分析及控制. 航空学报, 30: 444-449 (Li T J, Zhang Y, Li T. 2009. Deployment dynamic analysis and control of hoop truss deployable antenna. Acta Aeronautica et Astronautica Sinica, 30: 444-449 (in Chinese))
[66]	Li W, Xiang Z H, Chen L J, Xue M D. 2007. Thermal flutter analysis of large-scale space structures based on finite element method. International Journal of Numer- ical Method in Engineering, 69: 887-907
[67]	Liu C, Li F, Huang W. 2010. Active vibration control of finite L-shaped beam with traveling wave approach. Acta Mechanica Solida Sinica, 23: 377-385
[68]	Liu C, Tian Q, Hu H Y. 2011. Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates. Multibody System Dynamics, 26: 283- 305
[69]	Liu C, Tian Q, Hu H Y. 2012a. New spatial curved beam and cylindrical shell elements of gradient deficient absolute nodal coordinate formulation. Nonlinear Dynamics, 70: 1903-1911
[70]	Liu C, Tian Q, Hu H Y. 2012b. Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mechanism and Machine Theory, 52: 106-129
[71]	Liu C, Tian Q, Yan D, Hu H Y. 2013. Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF. Computer Methods in Applied Mechanics and Engineer- ing, 258: 81-95
[72]	刘铖, 田强, 胡海岩. 2010. 基于绝对节点坐标的多柔体系统动力学高效计算方法, 力学学报, 42: 1197-1205 (Liu C, Tian Q, Hu H Y. 2010. Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Chinese Journal of Theoretical and Applied Mechanics, 42: 1197-1205 (in Chinese))
[73]	刘明治, 高桂芳. 2003. 可展开空间天线结构研究进展. 宇航学报, 24: 82-87 (Liu M Z, Gao G F. 2003. Advances in the study on structure for space deployable antenna. Journal of Astronautics, 24: 82-87 (in Chinese))
[74]	Liu X N, Huang G L, Hu G K. 2012. Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. Journal of the Mechanics and Physics of Solids, 60: 1907-1921
[75]	Luo G W, Zhang Y L, Xie J H. 2008. 1:3 resonance bifurcation of a three-degree-of-freedom vibratory system with symmetrical rigid stops. Physics Letter A, 372: 2026- 2031
[76]	Ma X F, Song Y P, Li Z J, Li T J, Wang Z W, Deng H Q. 2013. Mesh reflector antennas: forming-finding analysis review. AIAA Journal,1576
[77]	Mahapatra D R. 2006. Equivalent constitutive model-based design of wave-absorbing material system and controller. Journal of Sound and Vibration, 289: 509-528
[78]	Makihara K, Onoda J, Minesugi K. 2005. Low-energyconsumption hybrid vibration suppression based on an energy-recycling approach. AIAA Journal, 43: 1706- 1715
[79]	Meguro A, Harada S, Watanabe M. 2003. Key technologies for high- accuracy large mesh antenna reflectors. Acta Astronautica, 53: 899-908
[80]	Meguro A, Ishikawa H, Tsujihata A. 2006. Study on ground verification for large deployable modular structures. Journal of Spacecraft and Rockets, 43: 780-787
[81]	Meguro A, Shintate K, Usuib M, Tsujihata A. 2009. Inorbit deployment characteristics of large deployable antenna reflector onboard Engineering Test Satellite VIII. Acta Astronautica, 65: 1306-1316
[82]	Mikkola A, Shabana A A, Sanchez-Rebollo C, Jimenez- Octavio J R. 2013. Comparison between ANCF and Bspline surfaces. Multibody System Dynamics, 30: 119-138
[83]	Minghini F, Tullin N, Laudiero F. 2010. Vibration analysis of pultruded FRP frames with semi-rigid connections. Engineering Structures, 32: 3344-3354
[84]	Mitsugi J, Ando K, Senbokuya Y, Meguro A. 2000. Deployment analysis of large space antenna using flexible multibody dynamics simulation. Acta Astronautica, 47: 19-26
[85]	Moon F C, Li G X. 1990. Experimental study of chaotic vibrations in a pin-jointed space truss structure. AIAA Journal, 28: 915-921
[86]	Morterolle S, Maurin B, Quirant J, Dupuy C. 2012. Numerical form-finding of geotensoid tension truss for mesh reflector. Acta Astronautica, 76: 154-163
[87]	Murphy D M, McEachen M E, Macy B D, Gaspar J L. 2006. Demonstration of a 20-m solar sail system AIAA Journal, 2005-2126
[88]	Muvengei O, Kihiu J, Ikua B. 2012. Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints. Multibody System Dynamics, 28:369-393
[89]	Naets F, Heirman G H K, Vandepitte D, Desmet W. 2011. Inertial force term approximations for the use of Global Modal Parameterization for planar mechanisms. Inter- national Journal of Numerical Methods in Engineering, 85: 518-536
[90]	Naets F, Tamarozzi T, Heirman G H K, Desmet W. 2012. Real-time flexible multibody simulation with Global Modal Parameterization. Multibody System Dynamics, 27: 267-284
[91]	Negrut D, Tasora A, Mazhar H, Heyn T, Hahn P. Leveraging parallel computing in multibody dynamics. Multi- body System Dynamics, 27: 95117
[92]	Neto M A, Ambr´osio J A C, Leal R P. 2006. Composite materials in flexible multibody systems. Computer Methods in Applied Mechanics and Engineering, 195: 6860-6873
[93]	O’ Connor W J. 2011. Wave-like modeling of cascaded, lumped, flexible systems with an arbitrarily moving boundary. Journal of Sound and Vibration, 330: 3070- 3083
[94]	Oh K, Nayfeh A H. 1996. Nonlinear resonances in cantilever composite plates. Nonlinear Dynamics, 11: 143-169
[95]	Ojima H, Nagase K, Hayakawa Y. 2002. Wave-based analysis and wave control of damped mass-spring systems characterization from the propagation constants. Transac- tions of Society of Instrument and Control Engineering, 38: 239-246
[96]	Orden J C G. 2005. Analysis of joint clearances in multibody systems. Multibody System Dynamics, 13: 401-420
[97]	Pan J, Hansen C H. 1991. Active control of total vibratory power flow in a beam I: physical system analysis. Journal of Acoustical Society of America, 89: 200-209
[98]	Pfeiffer F, Glocker C. 2004. Multibody Dynamics with Unilateral Contact. New York: John Wiley.
[99]	Pfeiffer F, Foerg M. 2006. Numerical aspects of non-smooth multibody dynamics. Computer Methods in Applied Me- chanics and Engineering, 195: 6891-6908
[100]	Puig L, Barton A, Rando N. 2010. A review on large deployable structures for astrophysics missions. Acta As- tronautica, 67: 12-26
[101]	Reza Moheimani S O, Fleming A J. 2006. Piezoelectric Transducers for Vibration Control and Damping, London: Springer
[102]	Sakamoto H, Park K C. 2006. Localized vibration isolation strategy for low-frequency excitations in membrane space. Journal of Vibration and Acoustics, 128: 790-797
[103]	Salehiana A, Inman D. 2008. Dynamic analysis of a lattice structure by homogenization: experimental validation. Journal of Sound and Vibration, 316: 180-197
[104]	Salehiana A, Inman D. 2010. Micropolar continuous modeling and frequency response validation of a lattice structure. Journal of Vibration and Acoustics, 132: 011010
[105]	Scheuren J. 1985. Active control of bending waves in beams. in: Proceedings of Inter-Noise. 85, 591-595.
[106]	Schiehlen W. 2007. Research trends in multibody system dynamics. Multibody System Dynamics, 18: 3-13
[107]	Shabana A A. 1997. Flexible multi-body dynamics review of past and recent developments. Multibody System Dy- namics, 1: 189-222
[108]	Shen Z X, Tian Q, Liu X L, Hu G K. 2013a. Thermal induced vibration of flexible multibody system. Aerospace Science and Technology http://dx.doi.org/10.1016/j.ast.2013.04.009
[109]	Shen Z X, Hu G K. 2013b. Thermally induced vibrations of solar panel and their coupling with satellite. Interna- tional Journal of Applied Mechanics (in press)
[110]	Sirota L, Halevi Y. 2010. Free response and absolute vibration suppression of second-order flexible structuresthe traveling wave approach. Journal of Vibration and Acoustics, 132: 031008
[111]	Studer C. 2009. Numerics of Unilateral Contact and Friction, Berlin: Springer
[112]	Sun C T, Liebbet S W. 1990. Global-local approach to solving vibration of large truss structures. AIAA Jour- nal, 28: 303-308
[113]	Svensson J, Andersson P, Scheuren J, Kropp W. 2008. Active scattering control of flexural waves at beam junctions: the influence of beam properties on power flow and control effort. Journal of Sound and Vibration, 313: 418-432
[114]	Svensson J, Andersson P, Kropp W. 2010. On the design of structural junctions for the purpose of hybrid passiveactive vibration control. Journal of Sound and Vibra- tion, 329: 1274-1288
[115]	Tian Q, Zhang Y Q, Chen L P, Flores P. 2009. Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Computers and Structures 87: 913-929
[116]	Tian Q, Chen L P, Zhang Y Q, Yang J Z. 2010. Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dynamics, 60: 489-511
[117]	Tian Q, Liu C, Machado M, Flores P. 2011. A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dynamics, 64: 25-47
[118]	Tian Q, Sun Y L, Liu C, Hu H Y, Flores P. 2013. Elastohydrodynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Computers and Structures, 114: 106-120
[119]	田强, 张云清, 陈立平, 覃刚. 2010. 柔性多体系统动力学绝对节点坐标方法研究进展. 力学进展, 40: 189-202 (Tian Q, Zhang Y Q, Chen L P, Qing G. 2010. Advances in the absolute nodal coordinate method for the flexible multibody dynamics. Advance in Mechanics, 34: 304-313 (in Chinese))
[120]	Vaishya M, Singh R. 2003. Strategies for modeling friction in gear dynamics. Journal of Mechanical Design, 125: 383-393
[121]	Von Flotow A H. 1986. Traveling wave control for large space structures. Journal of Guidance, Control and Dy- namics, 9: 462-468
[122]	Von Flotow A, Schafer B. 1986. Wave-absorbing controller for flexible system. Journal of Guidance, Control and Dynamics, 9: 673-680
[123]	Walha L, Fakhfakh T, Haddar M. 2009. Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mechanism and Machine Theory, 44: 1058-1069
[124]	Wasfy T M, Noor A K. 2000. Multibody dynamic simulation of the next generation space telescope using finite elements and fuzzy sets. Computer Methods in Applied Mechanics and Engineering, 190: 803-824.
[125]	Wu J, Zhao Z H, Ren G X. 2012. Dynamic analysis of space structure deployment with transient thermal load. Advanced Materials Research, 479-481: 803-807
[126]	Xue M D, Ding Y. 2004. Two kinds of tube elements for transient thermal-structural analysis of large space structures. International Journal of Numerical Methods in Engineering, 59: 1335-1353
[127]	Xue M D, Duan J, Xiang Z H. 2007. Thermally induced bending-torsion coupling vibration of large scale space structures. Computational Mechanics, 40: 707-723
[128]	Yan D, Liu C, Tian Q, Zhang K, Liu X N, Hu G K. 2013. A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures. Nonlinear Dynamics, DOI:10.1007/s11071- 013-0955-z
[129]	Yang Y B, Yau J D, Leu L J. 2003. Recent developments in geometrically nonlinear and postbuckling analysis of framed structures. Applied Mechanics Review, 56: 431- 449
[130]	杨玉龙, 关富玲. 2009. 展开桁架天线热致振动数值分析. 空间科学学报, 29: 432-437 (Yang Y L, Guan F L. 2009. Numerical analysis of thermally induced vibration for deployable truss antenna. Chinese Journal of Space Sci- ence, 29: 432-437 (in Chinese))
[131]	Yousefi-Koma A, Vukovich G. 2000. Vibration suppression of flexible beams with bonded piezotransducers using wave-absorbing controllers. Journal of Guidance, Con- trol and Dynamics, 23: 347-357
[132]	Yu L, Zhao Z H, Tang J L, Ren G X. 2010. Integration of absolute nodal elements into multibody system. Nonlin- ear Dynamics, 62: 931-943
[133]	Yu Y Y. 1969. Thermally induced vibration and flutter of a flexible boom. Journal of Spacecraft and Rockets, 6: 902-910
[134]	占甫, 关富玲. 2009. 含三维间隙铰空间可展机构动力学数值分析. 浙江大学学报(工学版), 43: 177-182. (Zhan F, Guan F L. 2009. Dynamics numerical analysis of space deployable mechanism with three-dimensional clearance revolute joint. Journal of Zhejiang University (Engineering Science), 43: 177-182 (in Chinese))
[135]	Zhang J H, Zhang W. 2012. Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a honeycomb sandwich plate. Acta Mechanica, 223: 1047-1066.
[136]	Zhang W, Guo X Y. 2012. Periodic and chaotic oscillations of a composite laminated plate using the third-order shear deformation plate theory. International Journal of Bifurcation and Chaos, 22: 1250103
[137]	Zhang W, Hao Y X, Yang J. 2012. Nonlinear dynamics of FGM circular cylindrical shell with clamped–clamped edges. Computers and Structures, 94: 1075-1086.
[138]	Zhang W, Yao M H, Zhang J H. 2009. Using the extended Melnikov method to study the multi-pulse global bifurcations and chaos of a cantilever beam. Journal of Sound and Vibration, 319: 541-569.
[139]	张伟, 胡海岩. 2009. 非线性动力学理论与应用的新进展. 北京: 科学出版社. (Zhang W, Hu H Y. 2009. Advances in Theory and Application of Nonlinear Dynamics. Beijing: Science Press (in Chinese))
[140]	Zhao J, Tian Q, Hu H Y. 2013. Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method. Acta Mechanica Sinica, 29: 132-142.
[141]	赵国伟, 熊会宾, 黄海, 闫泽红. 2009. 柔性绳索体展开过程数值模拟及实验. 航空学报, 30: 1429-1434 (Zhao G W, Xiong H B, Huang H, Yan Z H. 2009. Simulation and experiment on deployment process of flexible rope. Acta Aeronautica et Astronautica Sinica, 30: 1429-1434 (in Chinese))
[142]	赵孟良, 关富玲. 2006. 考虑摩擦的周边桁架式可展天线展开动力学分析. 空间科学学报, 26: 220-227 (Zhao M N, Guan F L. 2006. Deployment dynamic analysis of circular truss deployable antenna with friction. Chinese Jour- nal of Space Science, 26: 220-227 (in Chinese))