Dynamic Behavior And Stability Of Viscoelastic Pipes Conveying Fluid

In this paper, the dynamic behaviors and stabilities of viscoelastic pipes conveying fluid are analyzed. The main research work is as follows: Firstly, by the analysis of force-balance of fluid and pipes elements, the differential equations of motion for viscoelastic pipes conveying fluid on viscoelastic foundation are derived. The vibration differential equations of pipes conveying fluid are converted into dimensionless vibration mode equations with introduction of dimensionless quantities and assumption of main vibration form, which is a production between exponent function of time and vibration mode function. On the basis of studies above, the dynamic behaviors and stabilities of cantilevered elastic pipes and simply supported pipes conveying fluid with three-parameter solid model both on Kelvin model foundation are calculated. The effect of dimensionless delay time H , rigidity ratio a of foundation to pipes and mass ratio β on dimensionless excited complex frequency ω and critical flow velocity u0 is analyzed.Secondly, for curved pipes conveying fluid, a common method, Hamilton principle for system of changing mass, is used to derive the differential equation of motion for viscoelastic curved pipes conveying fluid. By use of normalized power series method, eigenvalue equations, included massratio, critical flow velocity and viscoelastic characteristics of material, are arrived at. The effect of dimensionless delay time H on real part and imaginary part of dimensionless excited complex frequency ω and critical flow velocity a0 of curved pipes conveying fluid is discussed.Lastly, based on the studies of (1) and (2) above, the dynamic stability problem of viscoelastic pipes conveying oscillational fluid is analyzed, and the figures, related to effect of dimensionless delay time H , rigidity ratio a and flow velocity on the dynamic unstable zones in (μ,ω) parameter plane, are given.