摘要
针对梁的弯曲振动问题,研究了具有弹性支承输流管道的稳定性.以相同支承条件下梁的固有频率和振型函数作为输流管道的近似固有频率和振型函数,利用李兹-伽辽金方法对具有弹性支承输流管道的运动微分方程进行离散化处理,经过适当的变换得到一阶状态方程组.根据特征方程分析和讨论弹性支承刚度、质量比和流体压力等主要物理参数对失稳临界流速的影响.研究结果表明,随着流体的流速从零缓慢增加,输流管道先发生动态颤振失稳,静态失稳的临界流速随弹性支承刚度增加而上升,随流体压力的增加而下降,但不随质量比变化.动态失稳的临界流速随弹性支承刚度的增加而上升,随流体压力的增加而下降,但随质量比的增加而先上升后下降.该结论可以为工程实际中所出现的相同边界条件的输流管道振动稳定性分析提供理论依据.
In order to study the bending vibration of a beam, the stability of a pipeline with elastic support was investigated. The differential equation of the pipeline＇s motion with elastic support was diseretized by the Ritz-Galerkin method based on the natural frequency and eigenfunctions of a pipeline, which were regarded to be similar to the natural frequency and eigenfunctions of a beam with the same boundary conditions, thus achieving the first-order state equations after the appropriate transformation. The effect of main physical parameters such as stiffness of elastic support, mass ratio, and fluid pressure on critical instability flow velocity was analyzed and discussed based on the eigenequation. The results showed that the fluid-conveying pipeline became unstable by dynamic flutter as the fluid velocity increased slowly from zero. The critical flow velocity of static instability increased with the increase of stiffness in the elastic support, and it decreased following the increase of fluid pressure, but it did not change following mass ratio. The critical flow velocity of dynamic flutter instability increased following the increase of stiffness in the elastic support, and it decreased following the increase of fluid pressure, but it first increased and then decreased with the increase of mass ratio. The conclusions may provide a theoretical basis for analyzing vibration stability of a pipeline appearing with the same boundary conditions in engineering practice.
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
2010年第11期1509-1513,共5页
Journal of Harbin Engineering University
基金
中央高校基本科研业务费专项资金资助项目(HEUCF101703)
哈尔滨工程大学基础研究基金资助项目(HEUFT08015)
关键词
弹性支承
输流管道
稳定性
临界流速
elastic support
fluid-conveying pipeline
stability
critical flow velocity
