热环境中超临界黏弹性输流管道自由振动分析  

Free Vibration Analysis on Supercritical Viscoelastic Pipes Conveying Fluid in Thermal Environment

作　　者：高思禹 毛晓晔 丁虎[1] 陈立群[1] Gao Siyu;Mao Xiaoye;Ding Hu;Chen Liqun(School of Mechanics and Engineering Science,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学力学与工程科学学院,上海200444

出　　处：《动力学与控制学报》2023年第6期39-46,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金青年基金项目(12002195);国家自然科学基金杰出青年基金(12025204);上海市教育委员会科研创新计划项目(2019-01-07-00-09-E00018);上海市科学技术委员会浦江人才计划(A类20PJ1404000)。

摘　　要：基于Euler-Bernoulli梁模型,本文研究了热环境中输流管道在超临界范围内流固耦合自由振动特性.考虑温度增量以及初始轴向拉力作用,在两端简支边界条件下,利用广义Hamilton原理建立输流管道横向振动偏微分-积分控制方程.通过解析方法得到输流管道非平凡静平衡位形及临界流速精确表达式,与微分求积单元法(DQEM)数值结果吻合较好.基于复模态法,结合伽辽金(Galerkin)法离散系统偏微分-积分控制方程,得到热环境下超临界输流管道的模态函数和固有频率.结果表明,温度增量越大,临界流速越小,此时的管道越容易屈曲,但相同流速下超临界管道固有频率越大;初始拉力越大,临界流速越大,相同流速下超临界固有频率越小.该研究可以为热环境中超临界状态下的管道系统振动设计提供理论指导.Based on the Euler-Bernoulli beam theory,the current work investigates the free vibration of a supercritical pipe conveying fluid in the thermal environment.Considering the temperature increment and the initial axial force,the partial-differential-integral governing equation for the transverse vibration of the simply supported pipe is established by the generalized Hamilton’s principle.The non-trivial equilibrium configurations and corresponding critical flow velocities are obtained analytically,and verified by the differential quadrature element method(DQEM).Based on the complex mode method and the Galerkin method,the natural frequencies of the supercritical pipe conveying fluid in the thermal environment are obtained.The results show that the larger the temperature increment is,the smaller the critical flow velocity will be,which also makes the pipe buckled more easily.But the supercritical natural frequencies become bigger at the same fluid velocity.The discussion also finds that the larger the initial tension is,the larger the critical flow velocity will be.Under this condition,the natural frequencies in the super critical region become smaller at the same flow velocity.This study provides guidance for the vibration design of pipes conveying fluid in the supercritical region under the thermal environment.

关 键 词：热环境 输流管道 超临界流速 非平凡静平衡位形 

分 类 号：O322[理学—一般力学与力学基础]