Example of a non-smooth Hopf bifurcation in an aero-elastic system

Abstract

We investigate a typical aerofoil section under dynamic stall conditions, the structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model are non-linear and non-smooth, therefore we have integrated the equation of motion using a Runge-Kutta-Fehlberg algorithm equipped with event detection. The main focus of the paper is on the interaction between the Hopf bifurcation typical of aero-elastic systems, which causes flutter oscillations, and the discontinuous definition of the stall model. The paper shows how the non-smooth definition of the dynamic stall model can generate a non-smooth Hopf bifurcation. The mechanisms for the appearance of limit cycle attractors are described by using standard tools of the theory of dynamical systems such as phase plots and bifurcation diagrams.Comment: 13 pages, 6 figure

Flutter of a two-dimensional wing with asymmetry at low Mach numbers

“…Consistent with Chantharsenawong, 19 Galvanetto et al. 20 and Magri and Galvanetto, 21 the asymmetrical parameter C m0 is applied to break the symmetry of the wing aeroelastic system. In order to investigate the influence of the asymmetry on the flutter behaviors of the wing aeroelastic system, some system parameters listed in Table 1 are adjusted and given as following: m = 6.31 kg/m, I θ = 0.0351 kg-m, K h = 604 N/m and K θ = 108.98 Nm/rad.…”

“…20 and Magri and Galvanetto. 21 However, the effects of the asymmetry defined by the asymmetrical parameter to the aeroelastic system are not analyzed.…”

Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

“…From condition (35) we find that equilibrium The admissible equilibria of system (17)- (21) in the (μ, α) plane are illustrated in Fig. 4 for the parameters of the NACA 0012 and NACA 0009 profiles (listed in Tables 1 and 2).…”

“…The phase space of piecewise linear systems consists of regions, each of which has linear dynamic equations of motion [34]. Magri et al [35] proved that a typical airfoil section applying nonsmooth definition of the dynamic stall model can generate a nonsmooth Hopf bifurcation, similar to a rapid bifurcation.…”

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

“…In [3], the airfoil flutter with multiple strong nonlinearities was investigated via the incremental harmonic balance method. Besides the researches of finding LCOs, the bifurcation analysis of LCOs is another important part of nonlinear aeroelastic investigations [4][5][6]. The bifurcation of an airfoil with both structural and aerodynamic nonlinearities in a supersonic flow field was investigated in [7] by using the center manifold theory and complex normal form method.…”