Characterization of a 3DOF aeroelastic system with freeplay and aerodynamic nonlinearities – Part II: Hilbert–Huang transform

The Hilbert–Huang Transform is used to analyze the nonlinear aeroelastic response of a 2D 3DOF aeroelastic airfoil system with control surface freeplay under transonic flow conditions. Both static and dynamic aerodynamic conditions, i.e., for accelerating freestream speed, are considered using a linearized aerodynamic model. The main aim of this paper is to provide an in-depth physical understanding of the observed transition between periodic and aperiodic behavior, and the presence of a stable periodic region well below the domain characterized by stable limit cycles. Physical insights towards the forward and backward abrupt transition between aperiodic/chaotic and periodic behavior types appear to be the result of an internal resonance (IR) phenomenon between linear modes followed by a lock-in between linear and nonlinear modes. More specifically, initially a 2:1 IR between linear modes leads to a shift in the frequency composition and dynamic behavior of the system. A secondary effect of the IR can be observed immediately after the exact point of 2:1 IR such that a nonlinear mode locks into a subharmonic of the linear mode which in-turn drives a finite stable periodic region.