基于绝对坐标法的柔性旋转梁的动力学研究

发布时间：2018-06-03 04:06

本文选题：Euler梁 + Rayleigh梁　；参考：《大连理工大学》2011年硕士论文

【摘要】：随着科技的发展和实际的需求,航天器的长机械臂、太空发动机的曲轴系等众多的轻质柔性、高速运动的多体系统被应用到各个领域。当这些机构工作时,系统的大范围刚性运动将会与柔体变形运动产生强烈的耦合效应。研究表明,基于小变形、小转动假设的传统柔性多体系统建模方法已经不能得出这些问题的精确解。绝对节点坐标方法的出现可以很好地解决此类问题。近年来,该方法已成为柔性多体动力学中一个非常活跃的研究领域。本文基于绝对节点坐标法建立了一维Euler梁和平面Rayleigh梁单元模型。在全局坐标系下定义了两模型的单元节点坐标,采用全局绝对斜率矢量代替传统有限元方法中的转动坐标矢量来描述梁单元的运动。基于几何非线性理论,运用虚功原理和拉格朗日运动方程等推导出大变形、大旋转柔性Euler梁和Rayleigh梁的动力学运动方程。该动力学微分代数方程具有质量矩阵为常数阵、科氏力和离心力项均为零等优良特点。研究证明,绝对节点坐标法即使在大转动、大变形情况下也可以精确的建模,同时还大大降低了动力学方程的非线性度。本文采用变步长Runge-Kutta法对Euler梁模型的动力学运动方程进行求解,研究了该柔性梁模型大范围旋转运动下的动力学特性,并通过能量守恒定律去验证了Euler柔性梁单元模型的正确性。随后,分别分析比较了不同弹性模量和单元数目下的Euler梁模型的位形图以及相应的动力学特性。然后,使用转换矩阵将绝对坐标系下的位移和速度转化为随体坐标系下的变形和变形速度,研究比较了随体坐标系下各种情况的Euler梁的动力学特性,并给出相应的柔性Euler梁端点和中间节点处绝对坐标系下的相平面图。作为比较,文中还计算了分布质量的刚性单摆仅在自身重力作用下自水平位置做自由下落运动的理论解和自由端在绝对坐标系下的相平面图,并与本文的柔性Euler梁模型下的计算结果进行对比。最后,本文还研究了计及剪切效应的平面Rayleigh梁模型的仿真计算,对其进行动力学分析,并相应地与Euler梁进行了比较研究。
[Abstract]:With the development of science and technology and the actual demand, the long manipulator of spacecraft, the crankshaft system of space engine, and so on, many light flexible and high-speed multi-body systems have been applied to various fields. When these mechanisms work, the large range of rigid motion of the system will have a strong coupling effect with the deformation of flexible body. The research shows that the traditional modeling method of flexible multi-body system based on small deformation and small rotation assumption can not get the exact solution of these problems. The emergence of absolute node coordinate method can solve this kind of problem well. In recent years, this method has become a very active research field in flexible multibody dynamics. In this paper, one dimensional Euler beam and plane Rayleigh beam element model are established based on the absolute node coordinate method. The element node coordinates of the two models are defined in the global coordinate system. The global absolute slope vector is used to replace the rotational coordinate vector in the traditional finite element method to describe the motion of the beam element. Based on the theory of geometric nonlinearity, the dynamic equations of motion of large deformation, large rotating flexible Euler beams and Rayleigh beams are derived by using the principle of virtual work and Lagrange equation of motion. The differential algebraic equation is characterized by constant mass matrix and zero Coriolis force and centrifugal force. It is proved that the absolute nodal coordinate method can be used to model the dynamic equations accurately even in the case of large rotation and large deformation. At the same time, the nonlinear degree of the dynamic equations is greatly reduced. In this paper, the variable step Runge-Kutta method is used to solve the dynamic equations of the Euler beam model, and the dynamic characteristics of the flexible beam model under the large-scale rotation motion are studied. The correctness of the Euler flexible beam element model is verified by the conservation law of energy. Then, the configuration diagram of the Euler beam model with different elastic modulus and the number of elements are analyzed and compared respectively, and the corresponding dynamic characteristics are compared. Then, the displacement and velocity in the absolute coordinate system are transformed into the deformation and deformation velocities in the body coordinate system by using the transformation matrix, and the dynamic characteristics of the Euler beam under various conditions in the accompanying body coordinate system are studied and compared. The phase plane diagram in the absolute coordinate system between the end point and the middle node of the flexible Euler beam is given. For comparison, the theoretical solution of the free falling motion of a rigid pendulum with distributed mass only under its own gravity is calculated, and the phase plane diagram of the free end in absolute coordinate system is also calculated. The results are compared with the calculated results under the flexible Euler beam model in this paper. Finally, the simulation calculation of the plane Rayleigh beam model with shear effect is studied, and the dynamic analysis is carried out, and the results are compared with that of the Euler beam.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH113

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