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
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，本文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。
【关键词】 张拉整体结构； 动力学等效； 降阶模型； 杆件屈曲； 软碰撞实验
Dynamic Equivalent Modeling of Tensegrity Structures and Experimental Verification
Zhankui Chen, Kai Luo, Qiang Tian
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 tensegrit.
Keyword:tensegrity structures;dynamics equivalence;reduced-order model;buckling of bars;soft impact experiments
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