Mathematical Analysis of Aircraft Wing Models and Application to Flutter Control

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The primary goal of this proposal is to develop the spectral, asymptotic, and stability analysis for three increasingly more complete models of an aircraft wing in a surrounding airflow, which are governed by complicated systems of evolution-type integro -differential equations. The first two of these models (1-dim and 2-dim respectively) have been developed at the Flight Systems Research Center at UCLA in collaboration with NASA Dryden Flight Research Center. The designing of the 3-dim model is in progress. The 1-dim model has recently been tested in a series of four flight experiments at Edwards Airforce Base. The results have shown an excellent agreement with theoretical predictions of the model, at least, for lower frequency aeroelastic modes. The ultimate goal of the entire wing modeling projects is to give specific practical recommendations to aircraft industry engineers working on flutter suppression in aircraft wings. The objective of this project include completion of the analysis of 1-dim model, i.e., obtaining the asymptotics for the eigenfunctions of the continuous spectrum and deriving the space-time domain representation for the solution of the main equations; b) applying the results to the flutter suppression problem; c) extension of the analysis to 2-dim and forthcoming 3-dim models (the most challenging part of the project); d) developing of a new graduate program on mathematical methods in aircraft engineering for both mathematics and engineering students