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2 Journal of Theoretical and Applied Mechanics

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Stochastic P-bifurcation of a 3-DOF airfoil with structural nonlinearity

Hao Ying, Du Xuewen, Hu Yuda, Wu Zhiqiang

Journal of Theoretical and Applied Mechanics

2021

Vol. 59 nr 2

307--317

In this paper, the stochastic-aeroelastic nonlinear response of a three-degree-of-freedom (3-DOF) structural nonlinear airfoil with a control flap is presented. The critical parameter conditions of stochastic P-bifurcation are solved by using the improved average method, the stochastic average method combined with the singularity theory. The results show that the periodic solution produced by Hopf bifurcation has involved a second bifurcation, the nonlinear critical speed of saddle node bifurcation points is advanced, and the airfoil appears bi-stable. The stochastic singularity analysis shows that the increasing stochastic disturbance intensity will cause a greater probability for a large amplitude stochastic flutter.

Stochastic flutter of multi-stable non-linear airfoil in turbulent flow

Hao Ying, Wu Zhi-Qiang

Journal of Theoretical and Applied Mechanics

2020

Vol. 58 nr 1

155--168

Stochastic airfoil flutter in an unsteady flow is discussed using the stochastic P-bifurcation method, taking into account potential effects of the longitudinal and vertical turbulent flow. The critical conditions of stochastic P-bifurcation are deduced by stochastic singularity analysis in order to discuss stochastic P-bifurcation phenomena. The results of parameter analysis show that as the turbulent intensity increases, the critical flutter velocity for sharp stochastic airfoil flutter decreases. And the large amplitude vibration comes earlier; an increase in the turbulent scale causes an earlier appearance of the critical velocity for large amplitude stochastic flutter.