Analysis Of The Dynamics Of The Cylinder In Axial Flow

The dynamics of the flexible cylinder supported at both ends in axial flow is studied in this paper.The nonlinear equation of motion of the cylinder is derived by analyzing the forces acting on the cylinder. The additional longitudinal force arising from the transverse motion of the cylinder is considered as a nonlinear term in the equation which is different with that derived by Modarres-Sadeghi with Hamilton theory in 2005. The present equation is simpler than that derived by Modarres-Sadeghi in 2005. The purpose of the paper is to explain the flutter instability found by Paidoussis in experiment with this relatively simpler nonlinear equation.The non-dimensional equation of motion was discretized with two-mode Ritz-Galerkin method. Using the equation obtained, the existence region of the equilibria is determined and the stability of the equilibria is analyzed. The stability of the zero equilibria in the present result is the same with the result obtained by Paidoussis in 1973, but the stability of the non-zero equilibria is different with the result obtained by Modarres-Sadeghi in 2005. The reason is analyzed from three aspects: (1) the influence of the other nonlinear terms (2) the influence of the coupled motion (3) the influence of the discrete mode of Ritz-Galerkin method. After research, it is found that the influence of the other nonlinear terms and the coupled motion is small to the dynamics of the cylinder, but the influence of the discrete mode is large. After numerically simulating the equation of motion discretized to six-mode, it is found that the system would develop flutter at u = 14.28, the position of the non-zero equilibria is x₁ = 0.0946 and the main frequencyis 14(HZ). The present result is in agreement with the result obtained by Modarres-Sadeghi in 2005. Exceptionally, the equation of motion discretized to three-mode, four-mode and five-mode is numerically simulated too. It is found that the system discretized to three-mode wouldn't develop to flutter, the system discretized to five-mode would develop to flutter at u = 14.84, the dynamics of the system discretized to four-mode is very complex, it needs to be studied further.