ARTICLE
Stochastic P-bifurcation of a 3-DOF airfoil with structural nonlinearity
Ying Hao 1  
,   Xuewen Du 1,   Yuda Hu 1,   Zhiqiang Wu 2
 
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1
College of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China
2
School of Mechanical Engineering, Tianjin University, Tianjin, China
CORRESPONDING AUTHOR
Ying Hao   

School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China
Submission date: 2020-09-22
Final revision date: 2021-02-26
Acceptance date: 2021-02-26
Online publication date: 2021-04-11
Publication date: 2021-04-15
 
Journal of Theoretical and Applied Mechanics 2021;59(2):307–317
 
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ABSTRACT
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.
 
REFERENCES (20)
1.
Chassaing J.C., Lucor D., Trégon J., 2012, Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method, Journal of Sound and Vibration, 331, 2, 394-411.
 
2.
Christiansen L.E., Lehn-Schiøler T., Mosekilde E., Gránásy P., Matsushita H., 2002, Nonlinear characteristics of randomly excited transonic flutter, Mathematics and Computers in Simulation, 58, 4-6, 385-405.
 
3.
Conner M.D., Tang D., Dowell E., Virgin L., 1997, Nonlinear behavior of a typical airfoil section with control surface freeplay: a numerical and experimental study, Journal of Fluids and Structures, 11, 1, 89-109.
 
4.
Dowell E.H., Thomas J.P., Hall K.C., 2004, Transonic limit cycle oscillation analysis using reduced order aerodynamic models, Journal of Fluids and Structures, 19, 1, 17-27.
 
5.
Dribusch C., Missoum S., Beran P., 2010, A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity, Structural and Multidisciplinary Optimization, 42, 5, 693-705.
 
6.
Hao Y., Wu Z.Q., 2019, Random flutter of multi-stable airfoils excited parametrically in steady flows, Journal of Mechanics, 35, 3, 419-426.
 
7.
Hao Y., Wu Z., 2020, Stochastic flutter of multi-stable non-linear airfoil in turbulent flow, Journal of Theoretical and Applied Mechanics, 58, 1, 155-168.
 
8.
Irani S., Sarrafzadeh H., Amoozgar M.R., 2011, Bifurcation in a 3-DoF airfoil with cubic structural nonlinearity, Chinese Journal of Aeronautics, 24, 3, 265-278.
 
9.
Lee B.H.K., Price S.J., Wong Y.S., 1999, Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos, Progress in Aerospace Sciences, 35, 3, 205-334.
 
10.
Missoum S., Dribusch C., Beran P., 2010, Reliability-based design optimization of nonlinear aeroelasticity problems, Journal of Aircraft, 47, 3, 992-998.
 
11.
Poirel D., Dunn S., Porter J., 2005, Flutter-margin method accounting for modal parameters uncertainties, Journal of Aircraft, 42, 5, 1236-1243.
 
12.
Poirel D.C., Price S.J., 1997, Post-instability behavior of a structurally nonlinear airfoil in longitudinal turbulence, Journal of Aircraft, 34, 5, 619-626.
 
13.
Poirel D.C., Price S.J., 2003a, Random binary (coalescence) flutter of a two-dimensional linear airfoil, Journal of Fluids and Structures, 18, 1, 23-42.
 
14.
Poirel D.C., Price S.J., 2003b, Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow, Probabilistic Engineering Mechanics, 18, 2, 185-202.
 
15.
Poirel D., Price S.J., 2007, Bifurcation characteristics of a two-dimensional structurally nonlinear airfoil in turbulent flow, Nonlinear Dynamics, 48, 4, 423-435.
 
16.
Poirel D.C., Price S.J., 2012, Structurally nonlinear fluttering airfoil in turbulent flow, AIAA Journal, 39, 10, 1960-1968.
 
17.
Theodorsen T., 1935, General theory of aerodynamic instability and the mechanism of flutter, NACA Report, 496, 413-433.
 
18.
Virgin L., Dowell E.H., 1992, Nonlinear aeroelasticity and chaos, Computational Nonlinear Mechanics in Aerospace Engineering, 1, 531-546.
 
19.
Yang Y.R., 1995, KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with a wind-tunnel test, Journal of Sound and Vibration, 187, 2, 271-280.
 
20.
Zheng G., Yang Y., 2006, Analysis of bifurcation of an airfoil with an external store in incompressible flow, Science Technology and Engineering, 6, 8, 1018-1021.
 
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