非线性变形的平面柔性梁在非惯性系下的动力学分析
Dynamics Analysis of Planar Flexible Beam of Nonlinear Deformation in Non-inertial Frame

针对大范围运动已知的平面柔性梁结构建立了动力学方程。经过分析，提出了非线性精确模型，采用有限元方法对梁结构进行离散，利用Lagrange方法建立了系统的精确动力学方程。与原有一次耦合模型相比，该模型中各项矩阵新增了两类耦合项：基点速度和角速度耦合项和变形耦合项。通过仿真计算，比较其动力学特性与零次、一次耦合模型的差异，确定各种耦合项的作用，并进行了定性分析。
The dynamics equation is established for a planar flexible beam and girder structure with known large overall motion. After analysis, the accurate nonlinear equations is put forward. The finite element method is used for the system discretization and the coupling dynamics equations of flexible beams and girders are obtained by the Lagrange multipliers. Compared with the one-order coupling model, each matrix of our model adds two kinds of coupling: the velocity and the angular velocity coupling terms of basic point and the deformation coupling term. Compared the zero-order coupling model and the one-order coupling model with the accurate nonlinear model through simulation in dynamic response. The roles of various coupling terms is determined and qualitative analysis is carried out