Flow Angle Effects on Supersonic Flutter of Clamped Curved Panels

Abstract

A frequency domain non linear Finite Element formulation (FE) is presented herein to investigate the effects of arbitrary flow angle on the flutter structural response of simply supported and clamped isotropic curved skin panels under a supersonic flow. The first-order shear deformation theory, the Marguerre curved plate theory, the von Karman straindisplacement relations, and the quasi-steady first order piston theory appended with a Static Aerodynamic Load (SAL) are used as the theoretical backbones of the nonlinear finite element formulation. The triangular Mindlin MIN3 finite element with improved shear correction factor is used to develop the finite element formulation and is integrated in the developed source code. 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 curved panel linear stiffness, first-order non-linear stiffness, and second-order non-linear stiffness are accurately determined under the SAL for a specific range of dynamic pressure and arbitrary yaw flow angles. An eigen value solution is then utilized to determine the critical dynamic pressure of the curved panel. The flutter stability boundaries for different yaw flow angles and specific panel height rises are thoroughly investigated using the flutter mode coalescence eigen-value techniques. It has been determined that for a curved clamped panel with different height rise H/h, there is a preferential panel orientation at which the critical dynamic pressure is maximized.