Stochastic Flutter Analysis Of 3-DOF Wing In Two-dimensional Flow Field Under Stochastic Disturbance

Any accidental disturbance may cause flutter behavior when the aircraft flight speed exceeds a certain critical speed.The occurrence of flutter can cause changes in the additional aerodynamic forces near the wing structure,resulting in elastic deformation of the wing structure under aerodynamic forces and catastrophic damage to the wing structure.Therefore,studying flutter issues is of great significance for the design of aircraft.Considering the nonlinearity of higher-order structures,this paper takes 3-DOF wings with control surfaces as the research object to study the nonlinear and stochastic flutter problems of wings.In the two-dimensional flow field,based on the inviscid unsteady aerodynamic model,higher-order structural nonlinearity is introduced into the mechanical model of the 3-DOF wing with control surfaces.The Lagrange equation is used to establish the motion equation of the 3-DOF wing.The aerodynamic force and moment expressions of the unit span wing are derived from the Theodorsen theory and the Wanger’s and Küssner’s functions,and the mathematical model of the wing flutter problem is obtained.The improved averaging method is used to reduce the dimensions of the mathematical model of the wing stochastic flutter problem,draw the quadratic bifurcation diagram of the deterministic system,obtain Ito stochastic differential equation and FPK equation by using the stochastic averaging method,and analyze the influence of the critical speed parameters of the system’s large stochastic flutter;The steady-state response probability density function is solved,and the theoretical calculation results are compared by using Monte Carlo numerical simulation.Considering the influence of stochastic disturbances in two-dimensional flow fields on the stochastic flutter behavior of wings,the effects of system parameters and nonlinear stiffness coefficient changes on the critical flutter speed were studied;Subsequently,based on the topological structure of the steady-state response probability density curve,the influence of stochastic disturbance intensity and inflow speed of the aeroelastic system on stochastic P-bifurcation and wing stochastic flutter behavior is discussed;Draw PDF curves,time history curves,and joint probability density curves of the steady-state response of 2-DOF wings under different parameters,and study the variation of critical flutter speed with longitudinal inflow speed and stochastic disturbance intensity.