TITLE:
Analysis of Dynamics and Vibration Characteristics of a Binary Wing Model
AUTHORS:
Jiaqi Liu, Liangqiang Zhou
KEYWORDS:
Aeroelasticity, Flutter, Binary Airfoil, Nonlinear Stiffness, Subcritical Hopf Bifurcation, Limit Cycle Oscillation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
15,
2026
ABSTRACT: This paper investigates the dynamics and flutter characteristics of a two-degree-of-freedom airfoil with cubic (third-order) structural stiffness nonlinearity, which captures the hardening behavior essential for predicting limit cycle oscillations and Hopf bifurcation in aeroelastic systems. Herein, the “binary wing” (or “binary airfoil”) specifically refers to the classic two-degree-of-freedom typical-section airfoil model, which idealizes the wing as a rigid profile undergoing plunge (heave) and pitch motions, capturing the fundamental aeroelastic coupling. The equations of motion are derived using Lagrange’s principle, and a state-space representation is formulated by incorporating an aerodynamic model. The variation of system eigenvalues with flow velocity is analyzed to determine the linear flutter critical speed. Numerical simulations are employed to verify the existence of subcritical flutter. The research demonstrates that the binary airfoil with nonlinear stiffness can exhibit stable limit cycle oscillations at subcritical speeds, with distinct patterns in modal coupling and flutter frequency evolution with velocity.