Aeroelastic Analysis of Wing Structures Using Equivalent Plate Models

Abstract

In this paper we formulate the Reissner-Mindlin first order shear deformation model based governing equation for a non-isotropic plate. The governing equations are cast as a set of coupled Helmholtz equations which are then expressed as integral equations where the Green’s functions are expressed in terms of the traditional Hankel functions of the first kind. The integral equations are then solved to determine the static and dynamic influence coefficients which are inverted to generate the stiffness and dynamic matrices. In order to demonstrate the application of these computations we consider the aeroelastic analysis of a wing structure, modeled as an equivalent plate. The unsteady aerodynamic generalized loads are estimated by employing the Doublet-Lattice method which is coupled with the compatible numerical evaluation of the structure’s dynamic influence coefficient matrix without any need for independent vibration analysis. We have demonstrated that by employing appropriate equivalent anisotropic plate models, and a variant of the classical Nyquist plot to assess the relative stability of the system, it is possible to capture, simulate and predict all the instability features of real aircraft wings. These models are proving to be particularly useful in the synthesis of active controllers for smart structures.