Nonlinear stochastic flutter analysis of a three-degree-of-freedom wing in a two-dimensional flow field under stochastic perturbations

Abstract

Based on the inviscid Theodorsen unsteady aerodynamic model, a stochastic nonlinear aerodynamic model of three-degree-of-freedom wing with high-order structural nonlinearity in longitudinal and vertical two-dimensional flow fields is established in this paper. The improved averaging method is applied to reduce the dimension of the high-dimensional stochastic nonlinear dynamic model, and the second bifurcation diagram of the system is obtained. The stochastic p-bifurcation analysis method of high-dimensional multi-stable system is applied to study the stochastic p-bifurcation phenomenon of the steady-state response of the system under longitudinal and vertical stochastic excitation, and the theoretical calculation results are compared and verified by Monte-Carlo numerical simulation. The effects of structural parameters, longitudinal flow, longitudinal and vertical stochastic disturbances on the stochastic flutter behavior of the system are analyzed and discussed. It is concluded that the nonlinear critical flutter velocity of the system increases with the increase of the high-order (third and fifth order) nonlinear stiffness of the pitch and control flap, and decreases with the increase of the high-order nonlinear coefficient stiffness of the plunging direction. Considering the high-order structural nonlinearity, there is a bistable phenomenon that the equilibrium point and the limit cycle coexist. Considering the influence of stochastic disturbance, the flutter amplitude of large amplitude oscillation of the system steady-state response increases obviously, and limit-cycle oscillation (LCO) evolves into a diffusion limit cycle.