Flutter analysis of periodically supported curved panels

Abstract

This paper presents the one-dimensional axial wave propagation in an infinitely long periodically supported cylindrically curved panel subjected to supersonic airflow. The aerodynamic forces are based on piston theory. For this study the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element. A high precision triangular finite element with certain wave boundary conditions (Floquet's principle) is introduced in flutter problems of the proposed structure for the first time. The airflow is assumed in the direction of the straight edges of the panel. It is assumed that the deflection function accounts for a phase lag term only and does not consider any attenuation terms. Aerodynamic damping has been neglected for brevity. For a given geometry a three-dimensional plot related to the phase constant, flutter frequency and pressure parameter has been obtained corresponding to the optimum periodic angle. The “flutter line”(line of instability) has been identified. The limiting values of flutter frequencies and pressure parameters of the “flutter line” are compared with the critical flutter condition of a single curved panel, using two methods—an exact approach and a finite element method. The critical flutter results for multi-supported (1-span, 2-span and 3-span) curved panels are obtained using the band discretization principle.