Asymptotics of aeroelastic modes and basis property of mode shapes for aircraft wing model

In this paper, we announce our recent results on the asymptotic and spectral analysis of the model of an ail crafting in a subsonic air flow. This model has been developed in the Flight Systems Research Center of UCLA and is presented in the works by Balakrishnan. The model is governed by a system of two coupled integro-differential equations and a two-parameter family of boundary conditions modeling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic sg stem: the integral parts are: of the convolution type. We provide the spectral asymptotics for the eigenfrequencies of the system (or aeroelastic modes) and the asymptotical approximations for the corresponding eigenfunctions (or the mode shapes). Based on the asymptotical results, we (a) state that the set of the mode shapes in complete in the energy space; (b) construct a system which is biorthogonal to the set of the mode shapes in the case when there might be multiple aeroelastic modest and (c) show that the mode shapes from a Riesz basis in the energy space. (C) 2001 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.