几何非线性空间梁的动力学建模与实验研究

摘要

建立了大变形细长空间梁的几何非线性动力学模型，并通过动力学实验验证建模理论的正确性。首先用曲梁中线上任意一点的3个绝对位置坐标和横截面的3个姿态角描述横截面的位置和姿态，建立了应变和曲率与位置坐标、姿态角的关系，在此基础上基于中线切线与横截面法线重合的假设，对节点广义坐标进行缩减，简化了动力学模型。用虚功原理建立了大变形细长空间梁的动力学方程，将该方法的计算时间与现有大型工程软件（LS －DYNA）进行比较，验证了方法的有效性。引入运动学约束方程，建立了气浮台和柔性空间梁系统的多体系统动力学方程。在大变形情况下，开展了气浮台和柔性空间梁系统的刚－柔耦合动力学实验，验证了几何非线性空间梁动力学模型的准确性。%Here,the geometric nonlinear dynamic model of a spatial slender beam with large deformation was established,and then dynamic tests were performed to verify the correctness of the dynamic model.Firstly,the position and the attitude of the cross-section of the beam were described with 3 absolute position coordinates and 3 rotational angles,and then based on the assumption of the coincidence of the tangent of the neutral axis and the normal vector of the cross-section,the number of the generalized coordinates of each node was reduced.Variational dynamic equations of the spatial slender beam were derived based on the virtual work principle.Comparing the simulation time of the geometric nonlinear model and that with LS-DYNA software verified the efficiency of the formulation.Introducing the kinematic constraint equations,the dynamic equations of the hub-beam multibody system were obtained.In case of large deformation,test for a rigid-flexible coupling system composed of an air-bearing test bed and a spatial beam were performed to verify the correctness of the geometric nonlinear model of a spatial beam.