A unified approach to dynamic analysis of tensegrity structures with arbitrary rigid bodies and rigid bars

IF 2.6 2区 工程技术 Q2 MECHANICS Multibody System Dynamics Pub Date : 2024-07-25 DOI:10.1007/s11044-024-10007-3
Jiahui Luo, Xiaoming Xu, Zhigang Wu, Shunan Wu
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Abstract

We propose a unified approach to dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a nonminimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in the three-dimensional space. This leads to a set of differential-algebraic equations with constant mass matrix free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme that yields realistic results for long-time simulations and accommodates nonconservative forces and boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-\(k\) general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multifunctional structures.

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对带有任意刚体和刚杆的张弦结构进行动态分析的统一方法
我们提出了一种统一的方法,用于对带有任意形状的刚杆和刚体的一般张拉整体结构进行动态建模和模拟。采用自然坐标作为基本点和基向量不同组合的非最小描述,以解决三维空间中刚体和刚杆之间的异质性。这导致了一组不含三角函数的质量矩阵恒定的微分代数方程。推导出线性化动力学公式,从而可以围绕静态平衡进行模态分析。对于非线性动力学的数值分析,我们推导出了一种改进的交映积分方案,该方案可为长时间模拟提供真实结果,并能适应非保守力和边界条件。数值实例证明了所提出的方法在复杂情况下(包括动态外部负载、基于缆线的部署和移动边界)对 Class-1-to-\(k\) 一般张弦结构进行动态模拟的有效性。新颖的张拉整体结构还体现了创建多功能结构的新方法。
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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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