计及变形耦合项的平面柔性梁动力学建模及频率分析

Dynamics modeling and frequency analysis for a planar flexible beam with coupling deformation terms

考虑了变形产生的几何非线性效应对作大范围运动的平面柔性梁的影响,在其纵向、横向的变形位移中均考虑了变形的二次耦合变量,从非线性应变-变形位移的原理出发,说明增加耦合变量后,使得剪应变近似为零,由此得出的变形模式更符合工程实际和简化需要。考虑两个方向的变形耦合后,采用有限元离散,通过L agrange方程导出系统的动力学方程。最后对一作旋转运动的平面柔性梁进行仿真计算,并对其固有频率进行分析研究。将本文模型所得的结论,与一次耦合动力学模型、零次近似模型进行比较,说明了三种模型的差异,得到了作旋转运动的平面柔性梁的一些新特点。

A moving planar flexible beam, which incorporates the effect of the geometrically non-linear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transversal deflections, the exact none-linear strain-displacement relations for a beam element is described. The shearing strains formulated are nearly zero, So, it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange＇s equations are employed for deriving the coupling dynamical formulations. A model of a rotating planar flexible beam is presented and a frequency analysis is given in the end. The frequency resulting from the dynamic model is compared with that of one-order coupling dynamic model and zero-order approximate model ,and the difference among them is demonstrated, then some new characters of the rotating planar flexible beam are obtained.