旋转运动中弹性梁耦合振动的辛方法  

A symplectic method for the coupling vibration of elastic beams in the revolution system

作　　者：马国军[1] 徐新生[1] 郭杏林[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《计算力学学报》2004年第6期671-677,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(19902014;10272024)资助项目.

摘　　要：研究旋转梁结构的弹性耦合振动问题。通过引入对偶体系,建立了解决该类问题的辛方法。在辛体系中描述旋转梁纵向和横向耦合振动控制方程,即哈密顿正则方程。进一步求解得到结构的固有振动频率及相应的振动模态,发现固有振动频率随转动角速度先升后降以及模态之间的某种转化规律。The problem of the coupling vibration of elastic beams in the revolution system is studied in the present paper. A symplectic method is established by introducing a duality system. In symplectic system, coupling control equations of longitudinal and transverse vibrations, i.e. Hamiltonian duality equations, are described. The intrinsic frequency and correlated model are obtained. Some phenomena and rules of the coupling vibration of the rotating beams are revealed between transformations of the mode shapes of various orders. It is also found that natural frequencies are firstly increased then decreased concerning the angular velocities.

关 键 词：对偶体系 辛几何 耦合振动 旋转梁 

分 类 号：O316[理学—一般力学与力学基础] O326[理学—力学]