Pre-Flutter Modes Analysis of Curved Panels Using Nonlinear Finite Elements

Abstract

In the widespread literature about supersonic panel flutter, natural mode shapes were heavily used to determine the deflection shape of a fluttering flat panel. The extension of panel flutter analysis to curved panels shed new lights to the concept of mode shapes. During the pre-flutter phase, the curved panel experiences a static deflection due to a static aerodynamic load (SAL) over the panel. This phenomenon prompted the introduction of a new generation of modes shapes called herein aero-static mode shapes. The purpose of this paper is to shed lights on this new generation of mode shapes and to investigate their properties. A finite element frequency domain method is developed to predict the curved panel pre-flutter aero-static mode shapes. The first-order shear deformation theory, the Marguerre curved plate theory, the von Karman large deflection theory, and the quasisteady first-order piston theory appended with SAL are used in the in the finite element formulation. The principle of virtual work is applied to develop the equations of motion of the fluttering curved panel in structural node degrees of freedom (DOF). The NewtonRaphson iteration method and an eigen-value solution are used to determine the aero-static modes for different panel’s curvatures. Intrinsic properties of sinusoidal, normal, and aerostatic mode shapes are thoroughly studied and compared. Amongst the found results a pre-flutter mode shape switching phenomenon has been found.