摘要
研究了一端简支另一端轴向受压具有中间支承梁的振动.推导了此梁弯曲振动的频率方程及振型函数的解析表达式.根据频率方程讨论了中间支承位置变化对梁固有频率的影响.应用Ritz-Galerkin方法,采用梁的前三阶振型对梁的运动微分方程进行离散化处理,得到了梁在不同中间支承位置处的失稳临界压力.发现了在梁上存在一个特殊的中间支承位置lξ,随着压力P从零开始增加,当中间支承位置ξb<lξ时,梁先发生颤振失稳,当中间支承位置bξ>lξ时,则梁先发生发散失稳.
The vibration of a beam which is simply supported at one end, resting on a support at some intermediate location, and has the other end subjected to an axial force is studied. The characteristic equation of the beam is derived, as well as an analytic expression of its eigenfunction. Then based on the characteristic equation, the effect of the position of intermediate support on the natural frequencies of the beam is discussed. The differential equation of the beam＇s motion is discretized applying the first three eigenfunctions by Ritz-Galerkin method, thus getting the critical axial force for the beam destabilization when the intermediate support is positioned differently. It is found that there is a special position of intermediate support ξl, as the axial load P increases, for location of intermediate support ξb〈ξl, the beam becomes unstable by flutter, and for ξbξ1, it loses stability by divergence.
出处
《东北大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2008年第10期1463-1466,共4页
Journal of Northeastern University(Natural Science)
基金
国家自然科学基金资助项目(50535010)
关键词
中间支承梁
固有频率
振型函数
发散
颤振
beam with intermediate support
natural frequency
eigenfunction
divergence
flutter
