THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL

Based on the differential constitutive relationship of linear viscoelastic material,a solid-liquidcoupling vibration equation for viscoelastic pipe conveying fluid is derived by the D’Alembert’s principle.Thecritical flow velocities and natural frequencies of the cantilever pipe conveying fluid with the Kelvin model(flutter instability)are calculated with the modified finite difference method in the form of the recurrence for-mula.The curves between the complex frequencies of the first,second and third mode and flow velocity ofthe pipe are plotted.On the basis of the numerical calculation results,the dynamic behaviors and stability ofthe pipe are discussed.It should be pointed out that the delay time of viscoelastic material with the Kelvinmodel has a remarkable effect on the dynamic characteristics and stability behaviors of the cantilevered pipeconveying fluid,which is a gyroscopic non-conservative system.