Research On Nonlinear Vibration And Flutter Of The Floding Fin With Freeplay Under Thermal Environment

Freeplay is a kind of centralized nonlinearity,which widely exists in control systems,like ailerons,flaps and elevators.The existence of freeplay will not only cause a series of nonlinear dynamic problems of the structure,but also affect the aeroelasticity of the aircraft,thus reducing the maneuverability.In practical engineering,the influence of freeplay is often neglected and linear methods are deployed to analyze the structure,which undoubtedly puts forward higher requirements for manufacturing and installation accuracy,and the results are too conservative,which is not conducive to the further optimization of the aircraft structure design.Therefore,it is necessary take the freeplay nonlinearity in the modeling process into consideration.Furthermore,with the increase of the aircraft speed,the aerodynamic heating becomes more serious,which will reduce the structural stiffness and deteriorate the flutter stability.Therefore,it is necessary to introduce temperature field to the model.In this paper,the effect of the thermal field and the freeplay on ground vibration characteristics and the aeroelasticity of the missile's folding fin is studied.The influence of the freeplay on ground vibration and the nonlinear modelling of the freeplay,which exists in the joints connecting the inboard and the outboard fins,are studied in this paper.First,the linear modal characteristics of the structure are obtained by hammering test,which provides a validation support for subsequent theoretical modeling.Then,the nonlinear characteristics of the structure with freeplay are obtained by base excitation via shaking table.The experimental results show that the freeplay will lead to nonlinear responses of the structure,such as forward and backward sweep difference,jump,multi harmonics and frequency shift.The nonlinearity mainly affects the first bending mode.Both the increase of the excitation magnitude and the decrease of the freeplay will raise the fundamental frequency which gradually tends to the result of no freeplay,but they have little effects on the second torsional mode.The finite element model of the folding fin is established in the numerical simulation analysis and a method of nonlinear model reduction is proposed for folding mechanism with concentrated nonlinearity.Through twice coordinate transformations,the degree of freedom of the nonlinear connection is preserved as physical coordinates,while the linear part of the structure is reduced directly.Compared with the traditional fixed mode synthesis method,the model size can be greatly reduced.By introducing Hertz contact theory,a stiffness function of 3/2 order and linear combination is established to simulate the freeplay and the contact.Compared with the bilinear stiffness used in most literatures,it can better simulate the contact and collision of actual structures.The dynamic response of the structure under base excitation is calculated by Bathe's two-step implicit composite algorithm.The transfer functions obtained can simulate the nonlinear phenomena in the experiments.The rationality of the proposed modelling method is verified.The freeplay is identified through the restoring force surface method.The effect of aerodynamic heating on the aeroelasticity of the folding fin is studied.Before studying thermal flutter,thermal modal analysis is needed to verify the accuracy of the model in thermal environment and to obtain modal information of the structure.Through thermal stress calculation in thermal modal analysis,it can be found that the thermal stress in the all-movable folding fin with fixed root is very small,so only the influence of the change of material elastic modulus caused by heat on the frequency needs to be considered.This can not only save the computation time,but also make the nonlinear model reduction method proposed in this paper applicable to thermal environment.The above research has already provided an accurate structural model for flutter analysis,and it also requires the establishment of aerodynamic model.The modified first-order piston theory is used to calculate the aerodynamic forces in supersonic flight.The infinite plate spline method is used for data transfer between the structure and the aerodynamics.The nonlinear aeroelastic equation of the folding fin with freeplay considering thermal effects is established.The influence of heat on the nonlinear flutter is analyzed.The results show that the damping attenuation,periodic-three limit cycle oscillation,periodic-one limit cycle oscillation,multi-periodic motion and divergence occur successively in the process of increasing flight speed.The increase of temperature will reduce the divergence speed of the fin without freeplay,but it will increase the limit cycle speed and the divergence speed of the fin with freeplay.Therefore,the effect of freeplay and heat should be paid special attention to in the actual design of the missile's fin.