张拉整体结构的动力学等效建模与实验验证

陈占魁; 罗凯; 田强

doi:10.6052/0459-1879-21-056

张拉整体结构的动力学等效建模与实验验证

doi: 10.6052/0459-1879-21-056

北京理工大学宇航学院力学系, 北京 100081

基金项目: 1)国家自然科学基金资助项目(11902028);国家自然科学基金资助项目(11722216);国家自然科学基金资助项目(11832005)

详细信息

作者简介:
2)罗凯, 助理教授, 主要研究方向: 软机器动力学与控制. E-mail: kailuo@bit.edu.cn

通讯作者:
罗凯

中图分类号: O313
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出版历程
- 收稿日期: 2021-02-02
- 刊出日期: 2021-06-01

DYNAMIC EQUIVALENT MODELING OF TENSEGRITY STRUCTURES AND EXPERIMENTAL VERIFICATION

Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 为了实现张拉整体结构高效动力学计算, 并考虑其大范围运动中柔性杆局部动态屈曲, 提出了一种受压细长杆动力学降阶模型, 采用五节点弹/扭簧集中质量离散模型等效连续杆的静力学和动力学特性. 首先, 通过静力学等效分析推导了弹簧拉压刚度和扭簧弯曲刚度表达式, 可准确预测杆件受压屈曲和近似预测其后屈曲行为. 第二, 通过动能等效分析推导了集中质量表达式, 可准确预测杆在线速度场下的运动. 第三, 通过弯曲振动固有模态等效分析确定弯曲刚度和节点质量的分布参数, 合适的分布参数取值组合可将降阶模型前两阶固有频率相对误差均降低至1%以内. 第四, 在全局坐标系下建立张拉整体结构瞬态动力学方程, 并利用静力凝聚法实现方程高效迭代求解. 最后, 分别对球形张拉整体结构准静态压缩、模态分析和碰撞动力学进行仿真和实验对比分析, 证明了提出的动力学降阶模型可有效预测张拉整体结构的静力学行为、固有振动特性及瞬态动力学响应, 并分析了结构参数变化对其力学特性的影响规律. 本文提出的动力学等效建模与计算方法, 可望用于软着陆行星探测器、大型可展开空间结构及点阵材料等复杂张拉整体系统的动力学分析与控制.
- 张拉整体结构 /
- 动力学等效 /
- 降阶模型 /
- 杆件屈曲 /
- 软碰撞实验
Abstract: To perform efficient dynamic computation of a tensegrity structure and to consider local dynamic buckling of the flexible bars during large overall motions of the structure, the reduced-order dynamic model of a slender bar under compression is proposed in this research. The model is a five-node discrete one with lumped parameters of axial stiffnesses, torsional stiffnesses and lumped masses that are achieved by the equivalent analysis of the static and dynamic characteristics of the continuous bar. First, the expressions of the axial and torsional stiffnesses are deduced by the equivalent analysis of the static behaviors such that the discrete model can predict accurately the pre-buckling and buckling of the bar and approximate its post-buckling. Second, the expressions of the lumped masses are deduced by the equivalent analysis of the kinetic energy such that the linear motion of the bar can be accurately described. Third, the distributed parameters of the torsional stiffnesses and lumped massed are determined by the equivalent analysis of the natural modes of transverse vibration. The appropriate combination of their values can largely reduce the relative errors of the first two natural frequencies up to less than 1%. Fourth, the transient dynamics equations of tensegrity structures are established in the frame of global coordinates, and the method of static condensation is used to enhance the computational efficiency of the iterative solution. Last, the simulation and experimental tests are carried out and the results are compared for the quasi-static compression, modal analysis and impact dynamics of a spherical tensegrity structure. The effectiveness of the proposed reduced-order dynamic model is verified for modeling statics, natural vibration and transient dynamics of tensegrity structures. And the influence of the variation of structural parameters on the mechanics of tensegrity structures is analyzed. The proposed modeling and computation method is expected to be applied for dynamic analysis and control of complex tensegrity systems, such as planetary probes with soft landing, large-scale deployable space structures and lattice materials.
- tensegrity structures /
- dynamics equivalence /
- reduced-order model /
- buckling of bars /
- soft impact experiments

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参考文献(34)

[1]	Fuller RB. Synergetics: Explorations in the Geometry of Thinking. Sebaftopol: Estate of R. Buckminster Fuller, 1982
[2]	Snelson KD. Continuous tension, discontinuous compression structures: Google Patents, 1965
[3]	Pellegrino S. Analysis of prestressed mechanisms. International Journal of Solids & Structures, 1990, 26(12): 1329-1350
[4]	Pellegrino S. A class of tensegrity domes. International Journal of Space Structures, 1992, 7(2): 127-142
[5]	Connelly R, Whiteley W. The stability of tensegrity frameworks. International Journal of Space Structures, 1992, 7(2): 153-163
[6]	Tibert AG, Pellegrino S. Deployable tensegrity reflectors for small satellites. Journal of Spacecraft and Rockets, 2002, 39(5): 701-709
[7]	SunSpiral V, Gorospe G, Bruce J, et al. Tensegrity based probes for planetary exploration: Entry, descent and landing (EDL) and surface mobility analysis//Proc. 10th Int. Planetary Probe Workshop, San Jose, CA, 2013: 17-21
[8]	Caluwaerts K, Despraz J, I??en A, et al. Design and control of compliant tensegrity robots through simulation and hardware validation. Journal of the Royal Society Interface, 2014, 11(98): 20140520
[9]	Iscen A, Caluwaerts K, Bruce J, et al. Learning tensegrity locomotion using open-loop control signals and coevolutionary algorithms. Artificial Life, 2015, 21(2): 119-140
[10]	Ingber DE. Tensegrity: The architectural basis of cellular mechanotransduction. Annual Review of Physiology, 1997, 59: 575-599
[11]	Ingber DE. Tensegrity I. Cell structure and hierarchical systems biology. Journal of Cell Science, 2003, 116: 1157-1173
[12]	Rovira AG, Tur JMM. Control and simulation of a tensegrity-based mobile robot. Robotics and Autonomous Systems, 2008, 57(5): 526-535
[13]	陈竑希. 四杆张拉整体机器人动力学分析. [硕士论文]. 哈尔滨: 哈尔滨工程大学, 2018 (Chen Hongxi. Kinetics analysis for four-bar tensegrity robot. [Master Thesis]. Harbin: Harbin Engineering University, 2018 (in Chinese))
[14]	Tietz BR, Carnahan RW, Bachmann RJ, et al. Tetraspine: Robust terrain handling on a tensegrity robot using central pattern generators//International Conference on Advanced Intelligent Mechatronics, 2013: 261-267
[15]	Barnes MR. Form finding and analysis of tension structures by dynamic relaxation. International Journal of Space Structures, 1999, 14(2): 89-104
[16]	Vassart N, Motro R. Multiparametered formfinding method: Application to tensegrity systems. International Journal of Space Structures, 1999, 14(2): 147-154
[17]	Koohestani K. Form-finding of tensegrity structures via genetic algorithm. International Journal of Solids and Structures, 2012, 49(5): 739-747
[18]	Chen Y, Feng J, Wu Y, et al. Novel form-finding of tensegrity structures using ant colony systems. Journal of Mechanisms and Robotics, 2011, 4(3): 031001
[19]	Lee S, Lee J. A novel method for topology design of tensegrity structures. Composite Structures, 2016, 152: 11-19
[20]	Wang Y, Xu X, Luo Y. Topology design of general tensegrity with rigid bodies. International Journal of Solids and Structures, 2020, 202: 278-298
[21]	Liu K, Paulino G H. Tensegrity topology optimization by force maximization on arbitrary ground structures. Structural and Multidisciplinary Optimization, 2019, 59(6): 2041-2062
[22]	Goyal R, Skelton RE. Tensegrity system dynamics with rigid bars and massive strings. Multibody System Dynamics, 2019, 46(3): 203-228
[23]	Goyal R, Skelton RE, Peraza Hernandez EA. Efficient design of lightweight reinforced tensegrities under local and global failure constraints. Journal of Applied Mechanics, 2020, 87: 111005
[24]	朱世新, 张立元, 李松雪等. 数字状张拉整体结构的构型设计与力学性能模拟. 力学学报, 2018, 50(4): 798-809 (Zhu Shixin, Zhang Liyuan, Li Songxue, et al. Number-shaped tensegrity structures: Configuration design and mechanical properties analysis. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 798-809 (in Chinese))
[25]	沈黎元, 李国强, 罗永峰 . 预应力索结构位移控制. 同济大学学报(自然科学版), 2006, 34(3): 291-295 (Shen Liyuan, Li Guoqiang, Luo Yongfeng. Displacement control of prestressed cable structures. Journal of Tongji University (Natural Science), 2006, 34(3): 291-295 (in Chinese))
[26]	(Shea K, Fest E, Smith IFC. Developing intelligent tensegrity structures with stochastic search. Advanced Engineering Informatics, 2002, 16: 21-40
[27]	Begey J, Vedrines M, Andreff N, et al. Selection of actuation mode for tensegrity mechanisms: The case study of the actuated Snelson cross. Mechanism and Machine Theory, 2020, 152: 103881
[28]	Kebiche K, Kaziaoual MN, Motro R. Geometrical non-linear analysis of tensegrity systems. Engineering Structures, 1999, 21: 864-876
[29]	Kahla NB, Kebiche K. Nonlinear elastoplastic analysis of tensegrity systems. Engineering Structures, 2000, 23: 1552-1566
[30]	Zhang L, Lu MK, Zhang HW, et al. Geometrically nonlinear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach. International Journal of Mechanical Sciences, 2015, 93: 154-165
[31]	Rimoli JJ. A reduced-order model for the dynamic and post-buckling behavior of tensegrity structures. Mechanics of Materials, 2018, 116: 146-157
[32]	Rimoli JJ, Pal RK. Mechanical response of 3-dimensional tensegrity lattices. Composites Part B, 2017, 115: 30-42
[33]	Li P, Liu C, Tian Q, et al. Dynamics of a deployable mesh reflector of satellite antenna: Parallel computation and deployment simulation. Journal of Computational and Nonlinear Dynamics, 2016, 11(6): 061005
[34]	Wilson EL. The static condensation algorithm. International Journal for Numerical Methods in Engineering, 2010, 8(1): 198-203