基于改进伽辽金法解释简支输流管颤振误判  

An explanation for the flutter paradox in the supercritical region of a simply‑supported fluid‑conveying pipe based on modified Galerkin method

作　　者：丁明 范祖相 孟帅[1] DING Ming;FAN Zu-xiang;MENG Shuai(State Key Laboratory of Marine Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Shanghai MicroPowers Co.,Ltd.,Shanghai 201203,China)

机构地区：[1]上海交通大学海洋工程国家重点实验室,上海200240 [2]上海齐耀动力技术有限公司,上海201203

出　　处：《振动工程学报》2023年第6期1564-1571,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51879161)。

摘　　要：两端简支输流管系统内流效应保守,即系统不会从内流中获取或损失能量。基于传统伽辽金法线性分析,在内流超临界区可预测到模态耦合颤振现象,但是系统没有能量输入以维持该振动。该悖论已困扰学者多年,通过非线性分析已证明模态耦合颤振不可能发生,但发生耦合颤振误判的机理尚未可知。内流主要引入离心力、科氏力和惯性力,其中科氏力项为反对称矩阵。基于加权残值法,采用一组新的加权函数提出了改进伽辽金法,利用权函数和基函数的正交性可使科氏力项消失,从而实现系统结构动力方程全解耦。基于改进伽辽金法预测某柔性输流管系统固有频率,在亚临界区与文献数据吻合较好,在超临界区未发生颤振误判。同时发现,基于传统伽辽金法可能高估了输流管系统高阶固有频率,且随着模态阶数的增加和内流速度的加快更加显著。The internal flow effect of a simply-supported pipe is conservative,since the system does not gain or lose energy in the course of vibration.Based on linear analysis via traditional Galerkin method,when the internal flow velocity exceeds a critical value,a coupled-mode flutter occurs,which constitutes a paradox as there is no energy to sustain the oscillation.Although it has demonstrated that the flutter does not exist adopting nonlinear analysis method,the paradox remains to be clarified.From linear analysis viewpoint,internal flow introduces centrifugal force,Coriolis force and initial force.Coriolis matrix is skew-symmetric(antisymmetric).A modified Galerkin method is proposed based on the weighted residual approach.The Coriolis force term disappears by using the orthogonality of the weighting functions and base functions and the dynamic equation can be fully decoupled.The natural frequencies of a flexible pipe system are predicted via the modified method.The predictions in the subcritical region fit well with literature and the flutter phenomenon does not appear.An explanation is given for the paradox.Moreover,it has demonstrated that the predictions by traditional Galerkin method overestimate the natural frequencies,and it becomes more obvious in higher-order modes at larger internal flow velocities.

关 键 词：简支输流管 内流效应 颤振悖论 加权残值法 改进伽辽金法 

分 类 号：O353.1[理学—流体力学]