中心刚体-变截面梁系统的动力学特性研究

对在平面内做大范围转动的中心刚体-变截面梁系统的动力学进行了研究. 考虑柔性梁横向弯曲变形和纵向伸长变形, 且在纵向位移中计及由于横向变形而引起的纵向 缩短项, 即非线性耦合变形项. 采用假设模态法描述变形, 运用第二类Lagrange方程推导得 到系统刚柔耦合动力学方程. 在此基础上对做大范围旋转运动的中心刚体-楔形梁以及中心刚 体-梯形梁模型的动力学进行了详细研究. 研究表明: 梁宽比、梁高比以及梯形梁变截面位置 都对系统的动力学特性有很大影响.

DYNAMICS OF HUB-VARIABLE SECTION BEAM SYSTEMS

The dynamics of a hub-variable section beam system which is rotating in a plane is investigated，where the beam is a flexible one. Both the transversal deformation and the longitudinal deformation of the flexible beam are considered. And in the total longitudinal deformation the non-linear coupling term, also known as the longitudinal shortening caused by transversal deformation, is considered here. The approach of assumed modes is used to describe the deformation of the flexible beam. The rigid-flexible coupling dynamic equations of the system are established via employing the second kind of Lagrange’s equation. Then dynamic characteristics of both of the hub-tapered beam system and the hub-trapezium beam system undergoing large overall motions are investigated in details by using numerical simulation. The results obtained in the investigation indicate that: The ratio in width, the ratio in height, the variable section position of the trapezium beam will have a larger impact to the dynamic response and the chord-wise bending natural frequencies.