基于非约束模态的中心刚体-Timoshenko梁动力学建模与分析  

Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes

作　　者：关玉铭 戈新生[1] GUAN Yuming;GE Xinsheng(College of Mechanical and Electrical Engineering,Beijing Information Science and Technology University,Beijing 100192,P.R.China)

机构地区：[1]北京信息科技大学机电工程学院,北京100192

出　　处：《应用数学和力学》2022年第2期156-165,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重点项目)(11732005)。

摘　　要：梁的横向变形会导致梁纵向缩短,建模过程中考虑梁横纵变形二次耦合项则存在动力刚化现象,这说明梁的纵向变形会对模型的广义刚度造成影响.对于做旋转运动的梁结构,旋转运动时还会受到离心力的作用而产生轴向拉力,轴向拉力同样也会引起梁的轴向变形,这种影响对粗短梁更加明显.以大范围运动中心刚体-Timoshenko梁模型为研究对象:首先,运用Timoshenko梁理论以及Hamilton原理建立含离心力的动力学模型;其次,引入非约束模态概念,采用Frobenius方法求解非约束模态振型函数以及固有频率;最后,通过数值仿真探究不同恒定转速时非约束模态与约束模态广义刚度的差异和非约束模态条件下离心力对模型的影响.The transverse deformation of the beam will lead to the longitudinal shortening deformation, and this transverselongitudinal deformation coupling will bring the dynamic stiffening effect term on the generalized rigidity of the beam model. For the rotating beam structure, the centrifugal force will cause axial tension, with coupling axial and transverse deformation of the beam and bring additional geometric stiffness, which is more obvious for the thick short beam. The central rigid body-Timoshenko beam model with a large-range-motion center was investigated. Firstly, the dynamic model with centrifugal forces was established by means of the Timoshenko beam theory and the Hamilton principle. Secondly, the unconstrained mode concept was introduced, and the unconstrained mode shape functions and natural frequencies were solved with the Frobenius method. Finally, numerical simulations were carried out to explore the difference of generalized stiffness between the unconstrained mode and the constrained mode at different constant speeds, and the effects of centrifugal forces on the model under unconstrained mode condition were discussed.

关 键 词：刚柔耦合 动力刚化 TIMOSHENKO梁 非约束模态 

分 类 号：V231.92[航空宇航科学与技术—航空宇航推进理论与工程] O342[理学—固体力学]