Residue harmonic balance for two-degree-of-freedom airfoils with cubic structural nonlinearity

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Author(s)

  • A. Y T Leung
  • Zhongjin Guo

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)2607-2615
Journal / PublicationAIAA Journal
Volume49
Issue number12
Publication statusPublished - Dec 2011

Abstract

A residue harmonic balance method is extended to determine the approximations and bifurcations for a coupled airfoil system with cubic structural nonlinearity analytically. The approximate solutions to any desired accuracy can be obtained easily by solving a set of linear algebraic equations in each step. The strongly cubic nonlinear pitching and plunging stiffness terms in the two-degree-of-freedom self-excited equations of airfoil motions are considered. The approximations to the angular frequency and limit cycle are analytically found. The results show that the secondorder approximations obtained by the proposed technique are in excellent agreement with the numerical integration results. The existence of cubic nonlinearity in the stiffness term does not affect the linear flutter speed of airfoil motion a great deal. However, the responses are different not only after supercritical bifurcation flutter, but also before the linear flutter speed in the subcritical bifurcation. Furthermore, the supercritical and subcritical Hopf bifurcations of three nonlinear cases of airfoil motions are analyzed taking the flow speed as the bifurcation parameter. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc.

Citation Format(s)

Residue harmonic balance for two-degree-of-freedom airfoils with cubic structural nonlinearity. / Leung, A. Y T; Guo, Zhongjin.

In: AIAA Journal, Vol. 49, No. 12, 12.2011, p. 2607-2615.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal