输流管道的超临界固有频率分析

Analysis of natural frequency of fluid-conveying pipeline in the supercritical regime

本文基于Kelvin粘弹性模型的横向非线性振动微分控制方程,推导了两端支承输流管道的后屈曲微分方程。得到出两端铰支输流管道的屈曲构型表达式。当输流管道内的流体流速加快,并且超过临界流速时,输流管道的零平衡构型发生屈曲变形。对于超临界状态下输流管道系统的扰动方程,利用伽辽金(Galerkin)方法,得到了输流管道在超临界状态下的非线性振动的第一阶固有频率的解析表达式。

In this study, the post-buckling differential equation of fluid-conveying pipelines supported at both ends is derived from the differential goveming equation for the nonlinear transverse vibration of Kelvin viscoelastic model. The expression of buckling configurations for hinged-hinged fluid-conveying pipeline is obtained. It is found thatthe straight equilibrium configuration turns into the unstable and buckling deformation as the flow speed of fluid exceeds the critical value. For the perturbation equation for the supercritical piping system,, the analytic expression of the first supercritical natural frequency for the nonlinear vibration of supercritical fluid-conveying pipelines is obtainedin Galerkin method.