Dynamic Characteristics Analysis And Stability Of Pipe Conveying Fluid With Follower Force

Pipeline is one of the classical problems of parametric dynamical systems.It has been widely used in practical engineering fields such as water conservancy,aerospace and petroleum transportation,and has important academic research value in the field of fluid-structure interaction mechanics.The study of the stability of the pipeline has indispensable guiding significance for the safety and durability issues in practical engineering applications.Mechanics analyses and numerical calculations of the fluid-structure interaction problems of the cantilevered and simply-supported pipelines under the action of the follower force and the axial force are carried out.The stability and dynamic characteristics of the problems are analyzed.Main contents and results are as follows:1.Based on Euler-Bernoulli beam model,the dynamic differentialequation for fluid-conveying pipes under co-action of end follower force and flowing fluid is established,which is then discretized with Galerkin method by choosing the beam modal functions as trial functions.2.Influences of different parameters to the vibration and stability of cantilever pipes conveying fluid and the relationship between dimensionless complex frequency and the critical flow velocity are studied by analyzing eigenvalues.Results show that the variation of the end follower force has great influence on the critical flow velocity.The types of instability of the system are related to the magnitude of the critical flow velocity.Divergence and single-model flutter are two prevailing types of instability of the system.3.The differential equations of motion for cantilevered pipes and simply-supported pipes end follower force and distributed follower force is established.Influences of the relationship between dimensionless complex frequency and the critical flow velocity are studied by analyzing eigenvalues,with which the dynamic characteristics of pipes conveying fluid with distributed follower force and end follower force are obtained.4.For simply-supported pipes,if the sum of the resultant force of the distributed follower force and 2 times of the end follower force keeps constant and the direction of the distributed follower force is changed,the real parts of the dimensionless complex frequencies keep the same but the signs of the imaginary parts are changed,i.e.,the critical flow velocity is the same but the stability characteristics are changed,and for cantilever pipes,if the resultantforce of the distributed follower force equals 2 times of the end follower force,the effects of these two loads are same,which is not affected by the mass-ratio.5.The dynamic differential equation for fluid-conveying pipes under co-action of distributed axial forces and flowing fluid is established.Influences of different parameters to the vibration and stability of cantilever pipes conveying fluid and the relationship between dimensionless complex frequency and the critical flow velocity are studied by analyzing eigenvalues.The effects of the distributed axial force on the instability of the cantilever pipe,the instability conditions,and the stability of cantilever pipes conveying fluid with the distributed axial force are obtained.