Limit-cycle stability reversal via singular perturbation and wing-flap flutter

Abstract

A three-degree-of-freedom aeroelastic typical section with a trailing-edge control surface is theoretically modelled, including nonlinear springs for both the nonlinear description of the torsional stiffness and of the hinge elastic moment. Furthermore, augmented states for linear unsteady aerodynamic of 2-D incompressible potential flow, have been considered in the model. First, the system response is determined by numerically integrating the governing equations using a standard Runge–Kutta algorithm in conjunction with a ‘shooting method’. The numerical analysis has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. Consequently, the equations of motion are analysed by a singular perturbation technique based on the normal-form method. This method, originally introduced by strictly applying a resonance condition, is herein extended by applying a near-resonance condition in order to improve the semi-analytical description of the stability reversal behavior. Therefore, amplitudes and frequencies of limit cycles depending on the flow speed V are obtained from the normal-form equations, and the terms which are essentially responsible for the nonlinear system behavior are identified.