Reexamination of Stability of a Two-Dimensional Finite Panel Exposed to an Incompressible Flow

Abstract

Stability of a flat or buckled panel exposed to an incompressible flow has been reanalyzed as the analyses on this problem by other investigators have errors in the fluid forces used. The deflection of the panel in an oscillatory motion is assumed in such a way that there occurs no change in the fluid volume in a control surface enclosing the panel. The nonlinear equation of motion of the panel on a continuous elastic spring is solved by using the Galerkin method and the generalized fluid forces which are derived in the author’s previous paper. The stability of the flat and buckled configuration in static equilibrium is examined against small disturbances. Existence of the limit cycle oscillation is studied by applying the harmonic balance method. Numerical results are compared with those of the analysis on a two-dimensional finite elastic channel conveying an almost incompressible flow.