轴向受压中间支承梁的横向振动和稳定性

Stability analysis of the beam with intermediate support subjected to axial force

研究了一端固支且自由端轴向受压具有中间支承梁的横向振动和稳定性。利用边界条件推导了此种梁频率方程及分段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截断方法,采用梁的前四阶振型对梁的运动微分方程进行离散化处理,讨论了梁在各个中间支承位置处的失稳形式。发现了在梁上存在一个特殊的中间支承位置ξl,当中间支承位置ξb<ξl时,随着压力p从零开始增加,梁先发生颤振失稳,当中间支承位置ξb>ξl时,则梁先发生发散失稳,而在中间支承位置ξl处,梁由颤振失稳跳跃到发散失稳。

Transversal vibrations of a beam,clampedly supported at one end,resting on a support at some intermediate location,and subjected to axial force at the other end were studied.The characteristic equations and the eigenfunctions of the beam were derived in accordance with the corresponding boundary conditions.Using the characteristic equation,the effect of the location of intermediate support on the frequencies was discussed.The differential equation of the beam's motion was discretized by applying Ritz-Galerkin method with the first four eigenfunctions as its trial functions and the instability mechanism corresponding to different location of intermediate support was discussed.It is shown that there exists a special location of intermediate support ξ1;as the axial pressure p increases from zero,for the location of intermediate support ξb<ξf,the beam becomes unstable due to flutter,and for ξb>ξf,it loses stability due to divergence.At ξb=ξf the critical force undergoes a jump,implying the transition of instability mode from flutter to divergence.