Abstract Summary
In this paper, the nonlinear aeroelastic system behaviour of a typical section airfoil with two degrees of freedom is investigated. The aim of this work is to characterize the nonlinear dynamics and mapping the regions of limit cycle oscillations (LCO). Firstly, a previous numerical model [1] is simulated and analysed the time histories and phase portrait as function of initial conditions. Also, the bifurcation diagram and section of Poincaré are used to determine the behavior of the attractors. The experimental device consists of a typical section airfoil mounted on elastic structure. The translational motion or plunge motion 'h' is obtained by means of four vertical flexible beams with a linear stiffness 'k_h' and the rotational motion or pitch motion α is obtained by a torsional spring implemented with a horizontal beam, assuming a quadratic representation of a nonlinear dynamic stiffness 'k_α (α)' to represent the structural nonlinearity and to evaluate its effect on flutter phenomena. Further work, the model parameters will be updated and the experimental apparatus will also be characterized. The governing equations of motion of the aeroelastic system is presented in [2] [3]. The influence of a nonlinear aerodynamic lift and moment on the airfoil is considered under free stream velocity 'V∞' and the model includes the angular position of the control surface β. The quasi steady aerodynamic lift and moment are evaluated as [4] including the control surface effect in aerodynamic. In this work, a bifurcation diagram associated with the pitch degree of freedom was plotted and the diagram was obtained with a free stream velocity range between 0 and 110 m/s. It indicates the existence of a limit cycles for free stream velocity around 15m/s. Additionally, this work investigates the effect the elastic axis position in the bifurcation diagram, using the same procedure as above. Also, it can be observed that the nonlinearity affects the ocurrency of limit cycle by observation of Jacobian matrix that is directly dependent of the angular displacement. Thus, the nonlinearitties lead to limit cycle oscillations that cause the flutter phenomenon is aeroelastic sytem as obtained in the phase planes. Therefore, a bifurcation diagram was obtained and it reveals an existence of LCO in which its amplitude depend upon the free stream velocity and also the initial conditions. [1] R. C. M. Barbosa, L. C. S. Góes, A. Nabarrete, J. M. Balthazar, D. F. C. Zúniga, Nonlinear identification using polynomial NARMAX model and a stability analysis of an aeroelastic system, Proceedings of the XVII DINAME, 2017. [2] T., O’Neil, H., Gilliatt, T. W., Strganac, Investigations of aeroelastic response for a system with continuous structural nonlinearities, AIAA Meeting Papers on Disc, Paper 96 1390, 1996. [3] S. L., Kukreja. Nonlinear system identification for aeroelastic systems with application to experimental data, NASA, 2008. [4] D. Li, S. Guo, J. Xiang, Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities, Journal of Sound and Vibration, Vol. 329, pp. 4756, 2010.
