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International Journal of Aerospace Engineering
Volume 2017, Article ID 2571253, 17 pages
Research Article

Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Correspondence should be addressed to Yuting Dai; nc.ude.aaub@iadgnituy

Received 18 October 2016; Revised 14 December 2016; Accepted 19 December 2016; Published 16 February 2017

Academic Editor: Enrico Cestino

Copyright © 2017 Linpeng Wang et al. 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.


An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF) and the modified Leishman–Beddoes (LB) model were built and validated. The nonintrusive polynomial chaos expansion (PCE) based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO) and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS) is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.