Nonlinear Stability Analysis of a Two-Dimensional Model of an Elastic Tube Conveying a Compressible Flow

Abstract

This paper examines the dynamic behavior of a two-dimensional channel whose upper and lower walls deform symmetrically with respect to the center line of the channel. Unsteady fluid dynamic forces acting on the internal wall are analytically evaluated on the basis of a linearized compressible potential flow theory. The effects of distributed springs outside the channel and an internal pressure on the stability characteristics are studied by considering small disturbances about flat and buckled equilibrium configurations of the wall. The analytic methods indicate that no flutter of the flat or buckled wall is predicted when the Mach number is small and the viscous damping coefficient is positive. Numerical results by the Runge-Kutta-Gill method suggest that nonlinear effect of flow should be taken into account to fully examine the dynamic characteristics of the channel conveying a flow.