Nonlinear Flutter of Cylindrical Shell Panels Under Yawed Supersonic Flow Using FE

Abstract

In the extensive published literature about panel flutter, a large number of papers were dedicated to investigate flat plates with supersonic or hypersonic flow regimes. Very few authors have extended their work to flutter of shallow shell panels. The curved geometry generates a pre-flutter behavior due to a static aerodynamic pressure load over the panel, and resulting in the presence of a static deflection. The purpose of this paper is to provide additional insights in the area of flutter of stream-wise shallow shell panels. A finite element frequency domain method, and a multi-modal finite element time domain method are developed and presented to predict the flutter onset and the non-linear flutter response of shallow shell panels. The principle of virtual work is applied to develop the equations of motion of the fluttering system. The von Karman non-linear strain-displacement relations are used to account for large deflections, and the quasisteady first-order piston theory appended with a static aerodynamic load due to the panel geometry is employed. System equations of motion in structural degrees of freedom are obtained and reduced into the modal coordinates. The reduced non-linear finite element multi-modal equations account for pre-flutter and flutter behavior with curvature effect. In the frequency domain procedure, the Newton-Raphson method coupled with and eigen-value problem is used to determine the flutter critical dynamic pressure for different shallow shell panel height-rises. Through the time domain procedure, non-linear flutter bifurcation diagrams, time responses, phase plots and power spectrum densities were investigated for various shallow shell panel height-rises. The results showed that the flutter response of the shallow shell panel is quite similar to the one associated with flat plates for very low panel’s height-rises. As the panel’s height-rises increase, the shallow shell panel flutter response reveals a new variety of dynamic behaviors.