Vibration Characteristics Of Non-uniform Cantilevered Pipes Conveying Fluid

The vibration characteristics and stability of non-uniform cantilevered pipes conveying fluid,which includes axially functionally graded(AFG)pipes,locally reinforced pipes and locally rigid pipes,are investigated through theoretical analysis and numerical calculation in this thesis.Based on numerical calculation,the effects of different parameters on the critical flow velocity for flutter instability are analyzed.The main research contents of this paper are as follows:1.Both the elastic modulus and the density of pipe are assumed to be varied from the clamped to the free ends.Based on this,the model of AFG cantilevered pipe has been built.The differential equation of motion is derived in this paper,and discretized by the differential quadrature method(DQM).The article focuses on the influence of elastic modulus gradient and density gradient.And the results show that,compared with uniform pipes,the decrease of density along the pipe length leads to a more stable system,while the opposite result may be obtained for the decrease of elastic modulus for small values of mass ratio.Furthermore,the phenomenon of instability mode exchange appeared with the increase of density gradient or elastic modulus gradient within a certain range of mass ratio.2.The locally reinforced cantilevered pipes are made up of basic material and reinforced material,and the reinforced segment changes from the clamped to the free ends.The differential equation of motion is derived,and solved by the finite element method(FEM).The position and length of reinforced segment are as the focus of research.Moreover,the effects of stiffness ratio and total mass ratio on the stability are investigated.The calculation results show that,compared with uniform pipe,the system will be more stable when the reinforced segment located in the front half of pipe,while the system will be easier to lose stability when the reinforced segment located in the rear part of pipe.Besides,the greater the stiffness ratio,the more stable the system is.3.The stability of locally rigid cantilevered pipes which be composed of flexible material and rigid material has been analyzed.It is found that the stability of system is greatly influenced by the position of the rigid segment.When the mass ratio is small and the rigid section is located in the front half of pipe,the critical velocity of system is higher than that of uniform cantilevered pipe under the same condition.However,as the rigid segment moves towards the free end of pipe,the critical velocity will be smaller.