旋转Timoshenko输流管道的固有频率和稳定性分析  

Natural Frequency and Stability Analysis of Rotating Timoshenko Pipe Conveying Fluid

作　　者：杨佳丽 杨虹[1] 李伟 Yang Jiali;Yang Hong;Li Wei(School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《动力学与控制学报》2023年第2期58-65,共8页Journal of Dynamics and Control

基　　金：北京信息科技大学校科研基金资助项目(2021XJJ65);国家自然科学基金资助项目(11772063,11972050)。

摘　　要：基于Timoshenko梁模型,本文研究了旋转输流管道在自由振动状态下的流固耦合振动特性.考虑流体压力、重力、初始轴应力作用,基于Hamilton原理和欧拉角转换,推导得到了旋转Timoshenko输流管道的偏微分方程.根据Galerkin截断法将运动方程进行离散,通过求解系统的特征方程即得到输流管一阶复频率的实部和虚部,实部代表固有频率,虚部代表能量变化.在流速较高时,研究发现必须考虑4阶及以上Galerkin截断,才能得到稳定的结果.通过与Euler-Bernoulli梁模型对比,验证了本文结果的正确性.研究发现针对短粗型管道,Timoshenko梁模型更加精确.此外研究了多种参数对旋转Timoshenko输流管道固有频率和振动稳定性的影响.研究结果表明质量比、流速、剪切系数对Timoshenko输流管道流固耦合振动的稳定性影响显著,而转动惯量、重力、流体压力和初始轴应力在一定程度上也会影响管道振动的频率和稳定性.转速的出现将管道频率分为两个量值,但转速并不影响系统能量变化.Based on the Timoshenko beam model,the fluid structure coupling vibration characteristics of rotating pipe conveying fluid under free vibration is studied.Considering fluid pressure,gravity and initial axial stress,the partial differential equation of rotating Timoshenko pipe conveying fluid is derived by using Hamilton principle and Euler angle transformation.The partial differential equations of motion are discretized according to Galerkin truncation method.By solving the characteristic equation of the system,the real part and the imaginary part of the first order complex frequency of the pipe conveying fluid are obtained,the real part represents the natural frequency and the imaginary part denotes the energy change.When the fluid velocity is high,it is found that the fourth order and above Galerkin truncation must be considered in order to obtain stable results.By comparing with the Euler-Bernoulli beam model,the correctness of the results in this paper is verified,and it is found that the Timoshenko beam model is more accurate in the study of short and thick pipes.In addition,the effects of various parameters on the natural frequency and vibration stability of the rotating Timoshenko pipe conveying fluid are studied.The results show that the mass ratio,flow velocity and shear coefficient have significant effects on the stability of fluid structure coupling vibration of Timoshenko pipe conveying fluid.To a certain extent,the moment of inertia,gravity,fluid pressure and initial axial stress also affect the frequency and stability of the pipe conveying fluid.The frequency of the pipe is divided into two values when the rotating speed appears,and the rotating speed does not affect the energy change of the system.

关 键 词：Timoshenko梁模型 输流管道 Galerkin截断法 固有频率 稳定性分析 

分 类 号：O321[理学—一般力学与力学基础]