Nonlinear Dynamics Of Pipe Conveying Pulsating Fluid With Lumped Mass

Pipes conveying fluid are widely used in marine transportation,West-East natural gas transmission project,water conservancy project and biological engineering.The dynamics of pipe structures conveying fluid have been one of the hottest topics attracted by many researchers.Based on previous studies,the planar and non-planar nonlinear dynamics of pipes conveying pulsating fluid with lumped mass are investigated in this dissertation.Considering two different boundary conditions of cantilevered and simply supported pipes,the effects of pulsating flow and lumped mass,as well as the comparison between twodimensional model and three-dimensional model are analyzed and discussed.The results in this work provide a theoretical basis for the dynamic analysis and optimization design of pipe structures,and have certain guiding significance.The main contents of this study are listed as follows:1.The two-dimensional(2D)model and governing equation of a cantilevered pipe conveying pulsating fluid with lumped mass at the free end are established.Discretizing and solving the equation by means of Galerkin method numerically,the parametric response of the pipe system is mainly discussed.Results show that the pulsating frequency leads to a parametric resonance and different types of nonlinear dynamic responses,such as quasiperiodic and chaotic motions.The increase of the pulsating amplitude can cause wider unstable frequency region,and more asymmetric feature of the bifurcation curve.The lumped mass at the free end can reduce the critical flow velocity of the pipe.2.The three-dimensional(3D)model of a cantilevered pipe conveying pulsating fluid with lumped mass at the free end is developed and solved by numerical methods.The influence of pulsating flow and lumped mass on the planar and non-planar motions of the pipe are compared and analyzed.Results show that the effects of pulsating flow and lumped mass on the motion state of the 3D pipe model is similar to that of the 2D pipe model.The only difference is that there may be a spatial movement of the pipe under the 3D model.By comparing the results of four groups of different initial conditions and the two models,it is found that under a set of planar initial conditions,the 2D model has more computational advantages than the 3D pipe model due to its smaller calculation amount.When selecting non-planar initial conditions,the 3D model has more advantages than the 2D model because it can describe the real space motion state of the pipe better.3.The two-dimensional(2D)model of a simply-supported pipe conveying pulsating flow with lumped mass is established,and the nonlinear dynamics of the extensible pipe system is analyzed.Results show that compared with the cantilevered pipe,chaotic motions and jump phenomena in amplitude of the simply-supported pipe at both ends can be more easily excited,and the dynamics of the simply-supported pipe in high-frequency region can be affected by nonlinear factors more easily.The closer the lumped mass is to the end of the pipe,the smaller influence on the nonlinear dynamics of the pipe.4.The three-dimensional(3D)model of a simply-supported pipe conveying pulsating flow with lumped mass is established.Under the influence of pulsating flow and lumped mass,the similarity and difference of the dynamic responses between 2D and 3D models are analyzed.Results show that the planar and non-planar motions of the 3D pipe model appear alternately under different pulsating frequencies.The influence of the location of the lumped mass is quite different from that of 2D model.By comparing the calculation results of the small-disturbance initial conditions and the non-planar initial conditions under the boundary conditions of the cantilever and the simply supported ends,it is expected that the approximate pulsating frequency range of the non-planar motions can be quickly determined by the small disturbance method.