Analysis Of Stability And Divergence Critical Velocity Of A Cylinder In Axial Flow

The stability and divergence critical velocity of a pinned-pinned and a clamped-pinnedcylinder in the axial flow is studied with three different methods in this paper.The model of a cell in a cylinder placed in the vertical direction is used in this paper, andthe linear differential equation of motion is set up with D′Alembert′s principle after the forceanalysis. Within seting up the dimensionless differential equation, three methods as followedfor the study of this subject are used:Garlerkin method: Garlerkin method is applied to discretize the differential equation ofmotion with the two-mode expansions to obtain a first-order differential equation of state. Thedivergence critical velocity of a cylinder is ascertained by judging the sign of the real part andthe imaginary part of the eigenvalues which are calculated by the numerical analysis andchanging with the flow velocity.Differential quadrature method: the dimensionless differential equation and boundaryconditions are solved with homogenous nodes to obtain the simulation equation, boundaryconditions and the divergence critical velocities in different boundary conditions throughnumerical analysis.Experimental method: the experimental method is used to analyse the stability of aclamped-pinned cylinder. The experiments are performed with several different sizes of thecylinder with some different flow velocities,to obtain the experimental data of parameters ofthe first mode divergence. The results of the experiment are good agreement with theoreticalresults. Some reasons that may lead to quantitative error are analyzed.Through the analysis in this article, some conclusions are found: the divergence criticalvelocity of a pinned-pinned and a clamped-pinned cylinder in the axial flow is u=3.14andu=4.59by the study of Garlerkin method; the divergence critical velocity of apinned-pinned and a clamped-pinned cylinder in the axial flow is u=3.3828andu=4.7881by the study of DQM method. The qualitative identity of the results found by the three methods was obtained; the theoretical results are perfectly confirmed by the experiment.