Investigation of bifurcation behavior in aeroelastic system with linear and nonlinear damping under stall condition

Abstract

This study investigates the nonlinear dynamic behavior of a stall-induced aeroelastic system, focusing on the influence of both linear and nonlinear damping on bifurcation characteristics and response dynamics. The unsteady aerodynamic loads are modeled using the Leishman Beddoes dynamic stall model, which captures essential post-stall phenomena such as flow separation and vortex shedding. The aeroelastic system is modeled with two degrees of freedom (pitch and plunge) and incorporates damping through both linear and nonlinear (quadratic) velocity-dependent terms. A comprehensive parametric study is conducted by varying the damping coefficients both individually and collectively, and the bifurcation analysis reveals that small linear damping values provide limited stabilization, with only partial suppression of aperiodic oscillations. As the damping levels increase, the system transitions toward periodic behavior and ultimately stable limit-cycle oscillations. In contrast, quadratic damping, which becomes increasingly dominant at higher oscillation amplitudes, shows a pronounced stabilizing effect by significantly reducing oscillation magnitudes and eliminating aperiodic dynamics. These results highlight the importance of considering both linear and nonlinear damping effects to improve the modeling accuracy and understanding of stall-induced aeroelastic responses. The findings provide valuable insights for the passive control and design of flexible aerodynamic structures such as wings, rotorcraft blades, and other lifting surfaces operating in highly nonlinear aerodynamic environments.