基于有限元法的张拉整体系统动力学
Tensegrity system dynamics based on finite element method
摘要：
本文提出了一种以节点坐标矢量为广义坐标的拉格朗日法为基础的非线性和线性张拉整体动力学有限元分析方法。本文首先推导了有约束和无约束的非线性张拉整体动力学方程。给出了三种标准形式的平衡方程（节点坐标、力密度和力矢量）和协调方程。然后，我们提出了线性化的动力学和模态分析方程有约束和无约束。所开发的方法是能够进行以下全面的动力学研究的任何张拉整体结构准确：1。执行具有可接受误差的刚体动力学，这是通过在仿真中为杆设置相对较高的刚度来实现的。2.精确模拟FEM动力学，其中杆和弦可以有弹性或塑性形变。3.处理各种边界条件，例如，在任何方向的任何节点处固定或施加静/动载荷（即，重力、某些特定的力或任意的地震振动）。4.进行精确的模态分析，包括固有频率和相应的模态。选取了双摆、有外力作用的悬臂桁架和双棱柱张拉整体塔三个算例进行了研究。并将计算结果与刚体动力学和有限元软件ANSYS进行了比较。这项研究提供了一个深入的了解结构，材料，性能，以及接口集成控制理论。
英文摘要：
This study presents a finite element analysis approach to non-linear and linearized tensegrity dynamics based on the Lagrangian method with nodal coordinate vectors as the generalized coordinates. In this paper, nonlinear tensegrity dynamics with and without constraints are first derived. The equilibrium equations in three standard forms (in terms of nodal coordinate, force density, and force vectors) and the compatibility equation are also given. Then, we present the linearized dynamics and modal analysis equations with and without constraints. The developed approach is capable of conducting the following comprehensive dynamics studies for any tensegrity structures accurately: 1. Performing rigid body dynamics with acceptable errors, which is achieved by setting relatively high stiffness for bars in the simulation. 2. Simulating FEM dynamics accurately, where bars and strings can have elastic or plastic deformations. 3. Dealing with various kinds of boundary conditions, for example, fixing or applying static/dynamic loads at any nodes in any direction (i.e., gravitational force, some specified forces, or arbitrary seismic vibrations). 4. Conducting accurate modal analysis, including natural frequency and corresponding modes. Three examples, a double pendulum, a cantilever truss with external force, and a double prism tensegrity tower, are carefully selected and studied. The results are compared with rigid body dynamics and FEM software ANSYS. This study provides a deep insight into structures, materials, performances, as well as an interface towards integrating control theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
