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 spectra l analysis of the model of an ail crafting in a subsonic air flow. This mod el 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 o f two coupled integro-differential equations and a two-parameter family of boundary conditions modeling the action of the self-straining actuators. Th e differential parts of the above equations form a coupled linear hyperboli c 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 eigenfunc tions (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) const ruct a system which is biorthogonal to the set of the mode shapes in the ca se when there might be multiple aeroelastic modest and (c) show that the mo de shapes from a Riesz basis in the energy space. (C) 2001 The Franklin Ins titute. Published by Elsevier Science Ltd. All rights reserved.