This paper develops a unified framework to study the dynamics of tensegrity systems with any arbitrary rigid bodies and rigid bars. The natural coordinates are adopted as a completely non-minimal modeling approach to describe both rigid bodies and rigid bars in terms of different combinations of basic points and base vectors. Various coordinate combinations are then unified into polymorphic expressions that succinctly encompass Class-1-to-$k$ tensegrities. Then, the Lagrange-d'Alembert principle is employed to derive the dynamic equation, which has a constant mass matrix and is free from trigonometric functions as well as centrifugal and Coriolis terms. For numerical analysis of nonlinear dynamics, a modified symplectic integration scheme is derived, accommodating non-conservative forces and boundary conditions. Additionally, formulations for statics and linearized dynamics around static equilibrium states are derived to help determine cable actuation values and calculate natural frequencies and mode shapes, which are commonly needed for structural analyses. Numerical examples are given to demonstrate the proposed approach's abilities in modeling tensegrity structures composed of Class-1-to-$k$ modules and conducting dynamic simulations with complex conditions, including slack cables, gravity loads, seismic grounds, and cable-based deployments. Finally, two novel designs of tensegrity structures exemplify new ways to create multi-functional composite structures.
翻译:本文开发了一个统一的框架, 以任意的僵硬体和硬条形来研究时态系统的动态。 自然坐标被作为一种完全非最小的建模方法, 以描述基本点和基矢量的不同组合来描述僵硬体和硬条形。 各种坐标组合随后被统一成多色表达式, 简洁地包含1至1美元之间的时态。 然后, Lagrange- d'Alember 原则被用来得出动态方程式, 该方程式具有恒定质量矩阵, 并且没有三角测量功能以及离心和 Coriolis 术语。 对于非线性动态的数值分析, 将产生一个经过修改的静态组合和边界条件。 此外, 将静态平衡状态周围的静态和线性动态配方, 帮助确定电缆动能值, 计算自然频率和模式形状, 这是结构分析通常需要的。 数字示例用来显示拟议的方法在模拟时的时态度结构结构模型性结构, 由级一至级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级- 级