Analysis of stochastic P-bifurcation and critical flutter velocity parameter effects on a 3 degree of freedom wing

In this study, we develop a stochastic nonlinear aerodynamic model for a three degree of freedom (3-DOF) wing with higher-order substructural nonlinearity in a two-dimensional flow field, applying high-dimensional and multi-stable system dimensionality reduction analysis methods to reduce system dimensionality. We obtain linear and nonlinear critical flutter velocities for the system to experience significant oscillations. We discuss the influence law of the nonlinear stiffness coefficient and stochastic disturbance parameters on the large critical flutter velocity of the system. We derive the probability density function of the steady-state response in three directions, that is, plunge, pitch, and control surface angle, by applying the stochastic averaging method, and analyze the influence law of structural parameters and stochastic airflow disturbance on the stochastic flutter behavior of the system in a two-dimensional flow field. We apply the stochastic P-bifurcation analysis method for high-dimensional multidimensional systems to study the stochastic P-bifurcation phenomenon of the steady-state response of a 3-DOF wing flutter system under stochastic disturbances.