LIMIT-CYCLE STABILITY REVERSAL NEAR A HOPF BIFURCATION WITH AEROELASTIC APPLICATIONS
✍ Scribed by D. DESSI; F. MASTRODDI; L. MORINO
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 382 KB
- Volume
- 256
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The objective of this paper is to present an analytical/numerical analysis of the phenomenon of limit-cycle stability reversal (from unstable to stable, and vice versa). A singular perturbation technique, the method of the normal form (in the asymptoticexpansion version), is utilized. The number of equations is then reduced to a &&minimal set'', for which the results are in good agreement with those from the original equations. This minimal set is determined by the amplitude of the K -points (a concept closely related to the small divisors in the KAM theory). This set is larger than that corresponding to the zero real-part eigenvalues (center-manifold theorem). The method is applied to a speci"c problem: an aeroelastic section with cubic free-play non-linearities where the parameter is the #ight speed. Numerical studies have been performed to show the dependence of the Hopf bifurcation characteristics upon the structural and geometric properties of the wing section. Plots depicting amplitudes and frequency versus #ight speed are presented.