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中心刚体-外Timoshenko梁系统的建模与分岔特性研究
引用本文:肖世富,陈滨.中心刚体-外Timoshenko梁系统的建模与分岔特性研究[J].应用数学和力学,1999,20(12):1286-1290.
作者姓名:肖世富  陈滨
作者单位:1. 西南结构力学研究所,成都,610003
2. 北京大学,力学与工程科学系,北京,100871
基金项目:国家自然科学基金!(19332022),863 高科技资助!(863_2_2_4_2)
摘    要:对于中心刚体固结悬臂梁系统,当不考虑梁剪应力( 即Euler_Bernoulli 梁) 影响时,匀速转动梁的平凡解是稳定的· 而对于深梁,有必要考虑剪应力( 即Timoshenko 梁) 的影响,此时其匀速转动平凡解将出现拉伸屈曲· 为此采用广义Hamilton 变分原理建立了中心刚体固结Timoshenko 梁这类刚_柔耦合系统的非线性动力学模型,应用数值方法研究了匀速转动Timoshenko 梁非线性系统的分岔特性,以及失稳的临界转速

关 键 词:刚_柔耦合系统  转动Timoshenko梁  拉伸失稳
文章编号:1000-0887(1999)12-1286-05
修稿时间:1997-06-17

Modeling and Bifurcation Analysis of the Centre Rigid-Body Mounted on an External Timoshenko Beam
Xiao Shifu,Chen Bin.Modeling and Bifurcation Analysis of the Centre Rigid-Body Mounted on an External Timoshenko Beam[J].Applied Mathematics and Mechanics,1999,20(12):1286-1290.
Authors:Xiao Shifu  Chen Bin
Abstract:For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler_Bernoulli type) is not considered. But for the deep beam, it is necessary to consider the effect of the shearing stress (i.e. the beam belongs to the Timoshenko type). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the general Hamilton Variation Principle, a nonlinear dynamic model of the rigid_flexible system with a centre rigid_body mounted on an external Timoshenko beam is established. The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods. Furthermore, the critical rotating velocity is also obtained.
Keywords:rigid_flexible coupling system  rotating Timoshenko beam  tension buckling
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