Supercritical and Subcritical Bifurcation in Typical Aeroelastic Section with Structural Nonlinearities
Daniel de Almeida Pereira1; Flávio Donizeti Marques1
1 Engineering School of São Carlos, University of São Paulo
doi:10.20906/CPS/COB-2015-0339
Resumo
Aeroelasticity studies the mutual interaction between aerodynamic and structural dynamics loading. This relationship often behaves nonlinearly, causing various problems such as instabilities, limit cycle oscillations, bifurcations and chaos. Those phenomena are difficult to diagnose and may cause serious problems to the aircraft structure, affecting their operations. The objective of this work is to analyse and identify the dynamic response of a three degree of freedom airfoil section with hardening nonlinearity in the pitching stiffness and free-play nonlinearity in the control surface stiffness using the bifurcation analysis. The effect of hardening corresponds to a nonlinear increasing in restoring structural loading for a given displacement, typically modeled by polynomial functions of odd order. The free-play is modeled here by hyperbolic functions combination. All aeroelastic responses will be analysed with computational and experimental results. The study of the phenomena associated with the hardening, free-play and their intensity variation effects provide ways to mitigate or circumvent any undesired responses to those behaviours. This contributes to determine safety margins for aircraft even with these nonlinearities, as fully linear systems represent major challenges to achieve, and results in very high costs.
Palavras-chave: Subcritical bifurcation; Supercritical bifurcation; Aeroelasticity; Structural nonlinearity; Hardening; Free-play