Dynamic Modelling And Nonlinear Flutter Analysis Of A Folding Fin

The freeplay nonlinearity is widespread in the structure of aviation vehicles,such as ailerons,flaps and elevators.Though as a kind of localized nonlinearity,the freeplay will cause the aircraft to have special dynamic phenomena during flight,such as limit cycle oscillation,buzzing,etc.;the large limit cycle oscillation of the wing and rudder will affect the aircraft's handling stability and may cause fatigue damage.In engineering applications,the simplified linear method is often used to ignore the freeplay for strength design and aerodynamic instability prediction,and the analysis results obtained are usually conservative.However,the existing manufacturing,installation errors and working wear will make the freeplay inevitably appear.Therefore,in order to improve the ultimate performance of the aircraft,accurately design the control law and put forward requirements for production accuracy,it is necessary to accurately model the structure with freeplay nonlinearity and discuss the influence of the freeplay parameters.This paper takes the folding control fin of a tactical missile as an object to study the influence of freeplay nonlinearity on the vibration characteristics and aeroelasticity of the fin.First,the ground vibration test and nonlinear modeling method are studied on the hinged folding fin with freeplays.By conducting a modal test on the pre-tightened linear fin,the modal parameters are obtained as the basis for judging modeling accuracy;then the freeplay and vibration level are adjusted,and the base excitation is performed through the shaking table to obtain the nonlinear dynamic characteristics of the folded fin.The ground vibration test shows that the introduction of the freeplay will cause many nonlinear phenomena in the structural response,such as the disappearance of the expected original first-order bending mode under random excitation,the difference between the forward and inverse sine frequency sweep experiment,and the jump in FRF.The effect of nonlinearity is mainly reflected in the change of the mode shape and frequency of the first-order bending mode.Increasing the excitation level and reducing the gyration freeplay will make the first-order resonance peak frequency and peak value increase and gradually approach the preloaded fin's first order' result.Next,a full finite element model of the folded fin is established where MPC is used for simulating hinge link,and the fin is dynamically condensed using the Craig-Bampton substructure modal synthesis method and the full model hybrid coordinate reduction method.The linear part is directly reducedand replaced with genearal coordinates,and the MPC contact part's degrees of freedom are retained as physical coordinates.Both methods can build accurate enough models,but the latter can greatly reduce the model size and simplify the process.For the hinge modelling part,this paper probed into the application of different contact theories to simulate the collision and contact during the movement of the actual structure,and finally selected the piecewise linear stiffness as the freeplay model in this research.Comparing the accuracy of Henon-RK4 and -Bathe algorithms for calculating non-smooth systems,Henon-RK4 has higher accuracy and computational efficiency,but it is only suitable for autonomous systems.The -Bathe two-step algorithm is used to calculate the dynamic response of the structure under base excitation,the phenomenon in the experiment is reproduced,thus the accuracy of this numerical model is verified;the effects of different contact stiffness,freeplay size parameters,and structural damping on the dynamic response of the structure are explored.The size of the freeplay in the model is identified based on the impulse response detection method,and the stiffness parameter is identified by using the Model Updating method for the pre-tightened fin modal parameters measured in the experiment.Then,based on an accurate stuctural dynamic model,the structure and aerodynamics are coupled for aeroelastic analysis.The aerodynamic calculation is carried out using the doublet lattice method based on linearized potential flow theory,and the transmission between structural deformation and aerodynamic force is carried out by infinite plate spline interpolation,ultimately the aeroelasticity equation of the folding fin considering freeplay nonlinearity and three-dimensional aerodynamic force is established.;The effects of freeplay size,contact stiffness,and structural damping on aerodynamic stability are analyzed.The results show that as the flight speed increases,the structure response will appear to decay,limit cycle ocsillation,and eventually diverge.The increase of the connection stiffness will cause the flutter speed to decrease,due to the closer flapping and torsing modes' frequency gap,and the introduction of the freeplay will increase the divergence speed,but it has an upper limit;the increase in the structural damping will increase the flutter boundary,and at the same time,the limit cycle will be introduced before the divergence speed.Under different initial disturbance conditions,the aeroelastic stability of the fin with freepay is different.