Singular perturbations of the Paidoussis equation: A thin cylinder in an axial flow

This report examines, from the viewpoint of singular perturbation theory, a fourth order partial differential equation which was derived by Paidoussis as a model for the behavior of a thin cylinder in an axial flow. It is found that for sufficiently large form drag (c sub t < 1/2) and small flexural rigidity the influence of the higher order boundary conditions is restricted to the boundary; i.e., the reduced equation is a good approximation. Furthermore for small frequencies the downstream boundary conditions can be ignored in the sense that outside of the very end of the cylinder, their effect on the solution is negligible. Finally, an examination of the characteristics of the reduced PDE leads one to conjecture that this remains true in the case (c sub t < 1/2).