APPLICATION OF THE CENTRE MANIFOLD THEORY IN NON-LINEAR AEROELASTICITY

✍ Scribed by L. LIU; Y.S. WONG; B.H.K. LEE

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 198 KB
• Volume: 234
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2895

✦ Synopsis

In this study, a frequency relation for limit cycle oscillations of a two-degree-of-freedom aeroelastic system with structural non-linearities represented by cubic restoring spring forces is derived. The centre manifold theory is applied to reduce the original system of nine-dimensional "rst order ordinary di!erential equations to a governing system in two dimensions near the bifurcation point. The principle of normal form is used to simplify the non-linear terms of the lower dimensional system. Using the frequency relation and the amplitude}frequency relationships derived from a previous study, limit cycle oscillations (LCOs) for self-excited systems can be predicted analytically. The mathematical technique proposed here has been applied to investigate LCO near a Hopf-bifurcation for an aeroelastic system with cubic restoring forces. Not only that an excellent agreement is obtained compared to the numerical results from solving the original system of eight non-linear di!erential equations by Runge}Kutta time integration scheme, but we also demonstrate that the use of a mathematical approach leads to a better understanding of non-linear aeroelasticity.