Engineering Transactions, 47, 1, pp. 39–55, 1999

A Certain Approximate Solutions of Nonlinear Flutter Equation

J. Grzędziński
Polish Academy of Sciences

A nonlinear integro-differential flutter equation of a thin airfoil placed in an incompressible flow is solved by two different methods. The first method involves the center-manifold reduction and gives the asymptotic limit cycle amplitude and frequency in terms of power series expansions. The second method replaces the integro-differential equation by an approximate set of first-order ordinary differential equations which are solved by using bifurcation and continuation software package. A comparison of these two methods shows that the domain of a good agreement between them varies significantly depending on the parameters of the problem.
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B.D. HASSARD, N.D. KAZARINOFF, and Y.-H. WAN, Theory and applications of Hopf bifurcation, Cambridge University Press, 1981.

J. GRZĘDZIŃSKI, Calculation of coefficients of a power series approximation of a center manifold for nonlinear integro-differential equations, Arch. Mech., 45, 2, 235–250, 1993.

J. GRZĘDZIŃSKI, Flutter analysis of a two-dimensional airfoil with nonlinear springs based on center-manifold reduction, Arch. Mech., 46, 5, 735–755, 1994.

J. GRZĘDZIŃSKI, Subsonic flutter calculation of an aircraft with nonlinear control system based on center-manifold reduction, Arch. Mech., 49, 1, 3–26, 1997.

Y.C. FUNG, An Introduction to the theory of aeroelasticity, John Wiley & Sons, New York, 1955.

C. J. HALE, Theory of functional differential equations, Springer Verlag, New York Heidelberg Berlin, 1977.

S.-N. CHOW, J.K. HALE, Methods of bifurcation theory, Gründlehren der mathematischen Wissenschaften 251, Springer-Verlag, 1982.

R.T. JONES, The unsteady lift of a wing of finite aspect ratio, NACA Report 681, 1940.

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