Analysis of Flutter in Compressible Flow of a Panel on Many Supports

Abstract

Two-dimensional linearized compressible flow theory is used, together with elementary beam theory, to analyze the dynamic stability of an infinitely long panel on equally spaced supports, having an air stream of arbitrary speed on one side and dead air on the other. I t is assumed that the flutter mode has a spatial periodicity of two bays. Longitudinal stresses in the panel are taken into account. An exact solution for the condition of neutral stability yields two independent equations in the form of rapidly converging infinite series. The results of some numerical calculations made on the basis of the first few terms of one of the series are shown, and states of stability and instability on either side of a flutter boundary are carefully distinguished. The implications of the numerical results are discussed.