Stability Of Cracked Fluid-conveying Pipeline On Elastic Foundation Under Distributed Follower Forces

Based on two different supporting conditions: both sides are clamped and simply supported, under the distributed follower force, Winkler foundation model and circumferential crack comprehensive influence, the paper establishes the fluid-solid coupling theory and numerical calculation model is enabled to the theory. The paper study pipelines dynamic properties under factors and the rich and colorful stability characterization deeply. Main results as follows:(1) On Winkler foundation, the pipe containing circumferential crack both sides are clamped(simply supported).Beam vibration mode function is trial function at this time. When considered distributed follower force and elastic foundation stiffness, the pipeline conveying fluid differential equation is discrete by Galerkin method.(2) Combined with the boundary condition, the pipeline conveying fluid containing circumferential crack mode function and frequency characteristic value are solved by the transfer matrix method.(3) During the process of solving eigenvalues value, on Winkler foundation, the pipe containing circumferential crack relationship between the dimensionless current Speed and the dimensionless distributed follower force can be received. The paper receive the corresponding frequency characteristic value when crack position and depth are changed.(4) Considering the influence of distributed follower force, Winkler foundation, velocity comprehensive and the mass ratio, it shows the relationship between dimensionless velocity and complex frequency and the instability critical velocity of system; When the crack position and depth of pipeline were changed, under the distributed follower force it can be received the change of pipeline conveying fluid instability form.