Nonlinear Aeroelastic Analysis For Slender Wing With Store

The slender wing with store is widely adopted in the high-altitude long-endurance uninhabited air vehicle.With the large aspect ratio for the slender wings,the structural nonlinearity cannot be neglected in the deformation.Except this,the motion of the store,and the junction between the wing and store will also introduce nonlinear factors for the wing-store system.In addition,when the state of the wing is in the stall regime,the aerodynamic loads on the wing will become nonlinear,and this nonlinearity also should be considered in the system.The interactions between these nonlinearities will lead the dynamic characteristics of the wing-store system to become very complex.For better understanding the wing-store characteristics,and guiding the design of this system,it is necessary to study the nonlinear aeroelastic properties of the slender wing with store.To the slender wing with store,through completely considering the structural nonlinearities about the wing and store,the nonlinear dynamic equations are constructed for three typical wing-store systems,which are the wing with rigid-mounted store,wing with flexible-mounted store,and wing with store which includes a free-play gap in the junction.On the other hand,the frequently used unsteady aerodynamic model in the aeroelastic analyses of slender wing are discussed,which are the linear unsteady aerodynamic model based on Wagner function,the nonlinear ONERA(Office National d'Etudes et de Recherches Aérospatiales)aerodynamic model where the effects of stall are considered.For the cases of using ONERA aerodynamic model,the total number of states are very large when the classical method is adopted.To solve this problem,a new method is proposed for the ONERA model.For the new method,by using the Duhamel integral method,the aerodynamic coefficients associated with the circulatory part of the ONERA model are solved and directly presented in terms of the system motion state.Through introducing two additional variables,the linear parts of the ONERA model can be presented in the model space of the wing without using the aerodynamic elements.Through the aeroelastic analysis about the slender wing,the effectiveness of the new method is validated.Using the new method for the ONERA model can reduce the total number of the states without damaging accuracy.Based on the dynamic equations of wing-store system and the unsteady aerodynamic models,the aeroelasitc equations of the three typical wing-store systems are established.The nonlinear aeroelasitc responses of the wing-store systems are simulated by using the time marching procedure.From the analyses about the wing-store systems,it is found that the nonlinear characteristics obtained for the cases of using the linear unsteady aerodynamic model based on Wagner function are different from those for the cases of using the ONERA aerodynamic model.And the reasons for these phenomena are explored.For the slender wing with rigid-mounted store,the effects of the spanwise position of the store,the distance between the store mass center and the wing elastic center on the system nonlinear characteristics are studied.It is found that when the vertical distance between the store mass center and the wing elastic center is not zero,the nonlinear factors about the store will lead the wing bending motion equilibrium position to deviate zero.In addition,the absolute value of the response peak of the system decreases with the increase of the horizontal distance between the store mass center and wing elastic center,but these phenomena are insignificant when the store is mounted near the wing root.For the slender wing with flexible-mounted store,when the junction stiffness is small,the wing bending motion changes insignificantly with the change of the horizontal distance between the store mass center and the wing elastic center.The deviation between the equilibrium position of wing bending motion and zero is small.The response peak of the system torsional motion is insensitive to the horizontal distance between the store mass center and the wing elastic center,but the store motion changes violently with the change of this distance.When the store mass center is under the wing elastic center,the response peak of store motion can be located in an appropriate region.In addition,for the slender wing with flexible-mouted store,when the junction stiffness is large,the characteristics about the system bending motion will vary with the horizontal distance between the store mass center and the wing elastic center.The store motion will be very complex.The absolute value of the response peak about the wing bending motion,torsional motion,and the store motion all will decrease with the increase of the horizontal distance between the store mass center and the wing elastic center.For the slender wing with store including a free-play gap in the junction,the store mounted on the pylon including a free-play gap will induce the occurrence of sub-critical Hopf bifurcation for the wing-store system.Additionally,for this system,when the equilibrium position becomes unstable,the system will directly go into the chaos region.With the increase of free-stream velocity,the motion of the system will transfer to the single periodic motion from chaotic motion.