STUDY OF THE DYNAMIC STABILITY OF A CANTILEVER FLEXIBLE TUBE ASPIRATING INTERNAL FLUID
This dissertation aims to analyze the dynamic stability of a flexible cantilever pipe in the vertical configuration, aspirating internal fluid at its free end. A mathematical model is developed considering simplifying assumptions, in which the equations of motion are derived and linearized around the equilibrium configuration using the Newtonian analytical approach, based on the method of equilibrium of forces and moments. The differential equation describing the motion was discretized using the Galerkin method, obtaining a set of second-order ordinary differential equations. These equations are expressed in matrix form considering that the fluid velocity is gradually increased, and the complex natural frequencies are numerically solved at each velocity increase. Then, the Argand diagram is presented to identify the critical velocity at which the system becomes unstable by Hopf bifurcation or beginning of flutter. The results show that the onset of instability occurs at the first frequency associated with the first mode at very small fluid velocities compared to the pipe discharge fluid. Finally, a sensitivity analysis is presented considering the effect of the viscoelastic coefficient of the pipe in relation to the critical velocity of the system for the different fluids tested.