Dynamic Behavior Of Viscoelastic Cylinder In Axial Flow

With the development of the material science, more and more attention are received on the stability and vibration of the cylinder in axial flow . On the basis of the former research, the dynamic behavior of viscoelastic cylinder in axial flow is analyzed in this paper. The main research work is as follows:(1)By the analysis of force-balance of the cylinder element, the differential equation of viscoelastic cylinder is derived based on the D' Alemberf 's principle. And the operators of Kelvin model and three-parameter solid model are introduced into the differential equation respectively, then the differential equations and boundary conditions of viscoelastic cylinder with Kelvin model and three-parameter solid model are established. The differential equations of Kelvin and three-parameter viscoelastic cylinder are converted into dimensionless equations with introduction of dimensionless quantities.(2)By Differential Quadrature Method (DQM), The eigen-equations of Kelvin and three-parameter cylinder are obtained .The dynamic behavior of viscoelastic cylinder with Kelvin and three-parameter are discussed by the dimensionless frequency of the first three mode, which is obtained by Matlab program. And the effect of the supports at both ends mass ratio of cylinder, dimensionless velocity of fluid ,dimensionless delay time and the elasticity coefficient ratio on the dynamic behavior are analyzed.(3) The effects of elastic support on the viscoelastic cylinder are analyzed. The support point is regarded as the breakpoint, the differential equations are derived piecewise, and the continuous conditions at the spring support position are established. The effect of spring rigidity and the position of the spring on the dynamic behavior of viscoelastic cylinder are analyzed by the dimensionless frequency of the first three modes, which is obtained by Matlab program.