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Dynamic Modeling and Simulations of Rigid-Flexible Coupled Systems Using Quaternion Dynamics.

机译：基于四元数动力学的刚柔耦合系统动力学建模和仿真。

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摘要

In this study, a three-dimensional dynamic modeling and simulation of a satellite that consists of coupled rigid-flexible bodies is presented. In the modeling of this coupled system, the satellite is assumed to be a rigid body; and solar arrays, antennas or booms are assumed to be flexible bodies. Coupling the equations of motions of the rigid body and the flexible bodies is accomplished by using the finite element method (FEM). Since the satellite rotates in space, the conventional FEM has a singularity problem caused by rotational sequences of Euler angles. To solve this problem, quaternion-based FEM is used in this study. Quaternion is well known as its singularity-free representation of bodies in three-dimensional motions. The governing equations of motions are derived from Lagrange equation, and derivatives in the equations are explicitly solved for accurate results.;Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to an unbounded response of a quaternion-based model. In this study, theorems on the conditions of torque-induced singularity in four coordinate systems -- inertial frame, body frame, Euler basis, and dual Euler basis -- are derived. According to the theorems, torques applied in an inertial frame or a body frame or an Euler basis will never cause unbounded motion. Torques applied in a dual Euler basis, however, may lead to unbounded motion.;Numerical simulations of free and forced vibrations are conducted for the quaternion-based dynamic models of one rigid body and rigid-flexible coupled bodies. For the dynamic model of one rigid body, the simulation results show that there is no singularity in free vibrations, but when external torque is applied in dual Euler bases, singularity occurs. However, when the torque is applied in the other coordinate systems, there is no singularity. For the dynamic model of rigid-flexible coupled bodies, torque is applied only in the body frame in this simulation, so both free and forced vibrations have no singularity.
机译：在这项研究中，提出了由刚性刚柔体耦合组成的人造卫星的三维动态建模和仿真。在此耦合系统的建模中，卫星被假定为刚体。太阳能电池板，天线或吊杆被假定为柔性体。通过使用有限元方法（FEM）将刚体和挠性体的运动方程耦合起来。由于卫星在空间中旋转，因此传统的有限元法存在由欧拉角的旋转序列引起的奇异性问题。为了解决这个问题，本研究中使用了基于四元数的有限元方法。四元数是众所周知的三维运动中物体的无奇异表示。运动的控制方程式是从拉格朗日方程式导出的，并且明确求解了方程式的导数以得到准确的结果。尽管四元数在三维运动的刚体建模和分析中没有奇点，但是转矩的描述可能会导致基于四元数的模型的无穷响应。在这项研究中，推导了四个坐标系（惯性系，车身架，欧拉基和对偶欧拉基）中扭矩引起的奇点条件的定理。根据定理，施加在惯性框架或车身框架或欧拉基础上的扭矩将永远不会引起无限制的运动。但是，在双重Euler基础上施加的扭矩可能会导致运动无限制。对一个刚体和刚柔耦合体的基于四元数的动力学模型进行了自由振动和强制振动的数值模拟。对于一个刚体的动力学模型，仿真结果表明自由振动不存在奇异性，但是当在双重Euler基体上施加外部扭矩时，会出现奇异性。但是，当在其他坐标系中施加扭矩时，则没有奇异之处。对于刚柔耦合体的动力学模型，在此模拟中，扭矩仅施加在车体框架中，因此自由振动和强制振动都没有奇异之处。

著录项

  • 作者

    Choi, Homin.;

  • 作者单位

    University of Southern California.;

  • 授予单位 University of Southern California.;
  • 学科 Mechanical engineering.
  • 学位 Ph.D.
  • 年度 2014
  • 页码 111 p.
  • 总页数 111
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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