The effect of inertial inhomogeneity on the flutter of a cantilevered flexible plate

Abstract

We study the two-dimensional fluid-structure interaction between a fluid flow and a thin flexible plate held at its leading edge. This fundamental system may be considered representative of many engineered or natural systems in which a plate or membrane experiences spontaneous, and often sustained, vibration. As the plate moves, its changing shape means that the lift it generates - the sum of the pressure forces that drive the plate motion - also changes and this effect underlies the instability of the plate when the applied flow speed reaches a threshold value. In this paper we apply and further develop a computational model of the system to study the effect of inertial inhomogeneity by way of a point mass adhered to the otherwise homogeneous plate. Our results show that the effect of adding a point mass to the plate can be either stabilising or destabilising. This counter-intuitive finding is explained using the classification of the flutter types that can exist in the system. In particular, this explanation shows how and why the system stability is sensitive to the location of the added mass and the plate length. Finally, we briefly present the results of a preliminary experimental investigation for short plates that qualitatively confirms the theoretical predictions.