Stability Analysis of Straight and Buckled Two-Dimensional Channels Conveying an Incompressible Flow

Abstract

This paper analyzes the stability of a two-dimensional flexible channel of finite length by evaluating the fluid dynamic pressure analytically, and solving a plate equation with the aid of a two-term Galerkin approach. The walls of the channel are collapsible, flat plates supported laterally by a set of uniformly distributed springs and at the ends by pins. The nonlinear relationship between axial and lateral displacement is taken into account in order to examine the behavior of the walls when they deviate from the flat configuration after an onset of aerodynamic buckling or classical buckling due to the fluid force or endshortening, respectively. As the flow is increased from zero the walls become statically unstable at a certain flow speed and start to collapse in the first axial mode when there are no distributed springs. With further increase in flow speed the deflection of the buckled walls increases continuously. The analysis of limit cycle oscillations indicates that no flutter of the flat and buckled walls is predicted when damping exists.