Dynamics And Stability Analysis Of Flexible Spinning Flight Vehicles

With the rapid development of modern rocket technology, range and precision demands have become higher and higher. To achieve better tactical and technical index, rockets have been made more and more slender, which means the elastic deformation of rocket structures can not be neglected any longer. Instead of the rigid model, the flexible model should be adopted to analyze the characteristics of rockets. Meanwhile movement of rockets undertaking spinning fight mode becomes extremely complicated because of the coupling effect of small elastic deformation, large-scale rigid motion and axial spinning. Therefor, the unique dynamic characteristics, aerodynamic elasticity and stability, resulting from spinning and flexibility, should be fully considered during the overall design of this type of rockets.The research on dynamics of flexible spinning vehicles and vibration of spinning rockets can reveal the mechanism of resonance and instability during free flight, and possess a very important value in scientific research of theoretical and practical engineering.In this dissertation, considering the influence of many factors with flexible spinning vehicles as the research object, equations of motion are established during free flight. Then taking the follower thrust into account, the gyroscopic effect caused by spinning on structural dynamic characteristics of rockets is studied in passive flight phase. Aerodynamic elasticity stability and dynamic response of flexible spinning vehicles in a general condition are analyzed and summarized during free flight.By integrating the basic ideas of rotor dynamics into flight dynamics and external ballistics, flexible vehicles are simplified as non-uniform beam axis rotor model under free boundary and discretized by the assumed model method. Then with a consideration of several affecting factors like the gyroscopic effect, shear deformation, the follower thrust and aerodynamic elasticity, equations of motion including differential equations of the elastic vibration, angular rate equations and equations of Angle of attack are deduced by Lagrange equations of the non-conservative system. Thus the comprehensive dynamic model for flexible spinning vehicles is established.Ignoring the rigid motion and aerodynamic force, research on the natural vibration of rocket structures during free time includes the analysis of elastic vibration characteristics with effects of the gyroscopic effect, moment of inertia and shear deformation. Based on the finite element method, equations of the transverse vibration and frequency for spinning vehicles are established to verify the feasibility of the transverse vibration problem of spinning vehicles and to analyze the precession frequency by using the rotor dynamics method and unbalance response of vehicle body with the change of speed of rotation through numerical simulations.On the basis of the research on natural vibration characteristics, considering the follower thrust effect, the element stiffness matrix resulting from thrust and the axial force is deduced. The finite element method is adopted to establish equations of the transverse vibration and frequency for spinning vehicles under the follower thrust effect. Then the structural transverse vibration of flexible vehicles with effect of spinning and the follower thrust is studied, which contains the analysis of the critical thrust and stability under different conditions and numerical simulations of unbalance responses under the action of the follower thrust. Finally conditions of instability are analyzed and summarized.Considering the large-scale rigid motion and aerodynamic force, equations of motion for flexible spinning vehicles during flight are reasonably simplified and transformed to obtain aerodynamic elasticity stability equations and differential equations of motion which can be used in practical engineering. For typical appearance of spinning vehicles, aeroelastic static stability and dynamic stability are studied with the influence of different speed of rotation, follower thrust, structural damping and whether under Magnus effect. Meanwhile dynamic responses are simulated under different aerodynamic force and eccentric mass force. Results show that factors affecting the stability of flexible spinning vehicles are not single and each factor on the aeroelastic stability of vehicles has different impact. To put it in another way, main influence factors need to be comprehensively considered and analyzed.Aiming at above theories and derived formulations, the corresponding numerical computation program has been developed. Comparison between numerical results and results of other studies verifies the effectiveness and accuracy of the proposed method and numerical program.Research results from this paper can provide relevant support of fundamental theoretical foundations for the practical design of rockets, realize the reasonable design of the overall structure, optimize the outside ballistic characteristics, and improve the development level of rockets.