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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 174927, 8 pages
Research Article

Smolyak-Grid-Based Flutter Analysis with the Stochastic Aerodynamic Uncertainty

School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Received 6 January 2014; Accepted 14 February 2014; Published 23 March 2014

Academic Editor: Guanghui Wen

Copyright © 2014 Yuting Dai and Chao Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


How to estimate the stochastic aerodynamic parametric uncertainty on aeroelastic stability is studied in this current work. The aerodynamic uncertainty is more complicated than the structural one, and it takes more significant effect on the flutter boundary. First, the nominal unsteady aerodynamic influence coefficients were calculated with the doublet lattice method. Based on this nominal model, the stochastic uncertainty model for unsteady aerodynamic pressure coefficients was constructed with physical meaning. Afterwards, the methodology for flutter uncertainty quantification due to aerodynamic perturbation was developed, based on the nonintrusive polynomial chaos expansion theory. In order to enhance the computational efficiency, the integration algorithm, namely, Smolyak sparse grids, was employed to calculate the coefficients of the stochastic polynomial basis. Finally, the flutter uncertainty analysis methodology was applied to an aircraft's wing model. The influence of uncertainty with uniform distribution for aerodynamic pressure coefficients on flutter boundary was quantified. The numerical results indicate that, the influence of unsteady aerodynamic pressure due to the motion of coupling modes takes significant effect on flutter boundary. It is validated that the flutter uncertainty analysis based on Smolyak sparse grids integration is efficient and accurate for quantifying input uncertainty with high dimensions.