Structurally Nonlinear Fluttering of a Three-Degree-Freedom Wing with Random Disturbances

Abstract

The differential equations of motion are established for a three-degree-freedom wing dynamic model subjected to unsteady aerodynamic loads and random perturbations. The system is dimensionally reduced by the improved average method to obtain the standard equations. Flutter problems of the deterministic wing system with high-order structural nonlinearity are studied using Hopf bifurcation theory and numerical simulation, the critical flutter speed is obtained and the effectiveness of the improved average method in the process of dimensionality reduction is verified. The stochastic P-bifurcation behaviors of the system are analyzed considering the effects of random perturbations of the longitudinal airflow by examining the qualitative variations of the probability density function curves. The results show that the deterministic wing system has a secondary bifurcation, a bistable phenomenon in which the equilibrium and the limit cycle oscillations coexist. The random disturbances significantly increases the critical flutter speed of the wing system, and the amplitude of limit cycle oscillations increases after including random perturbations for the same incoming flow speed.