Dynamic Analysis Of A Slender Rope Towing A Space Flexible Beam

Flexible beams are the basic components in flexible spacecraft;during long-term orbital motion of space flexible beams,the lateral vibration caused by gravity gradients and other factors will have a significant impact on its plane motion.At the same time,the weak damping effect of the flexible beam itself will cause the attenuation of the lateral vibration,so that the track-posture of the flexible beam tends to be stable.Based on the variational principle,this thesis studies the vibration characteristics of spatial flexible beams,with the main contents in the following.First,based on the theory of space flexible beam mechanics,the coupling of lateral vibration and space motion generated when it is running on orbit is considered.The slender space structure is simplified as a flexible beam model;Lagrangian function is constructed through kinetic energy and potential energy,with the dynamic equations established by the Hamiltonian principle of minimum action.Second,for the dynamic equations of the above-mentioned spatial flexible beams,this thesis mainly considers two theoretical models:the rigid rod model that ignores the lateral vibration,and the lateral vibration model of the flexible beam that is considered.The variable separation method is used to separate the variables of the kinetic equation,the fourth-order Runge-Kutta method is used to solve the differential equations,and numerical calculations are carried out through MATLAB programming.Thirdly,the influences of different drag force,drag angle,and grab point position on the height of the track during the towing process are analyzed separately.For the rigid rod model,if a larger drag force is selected,it will cause a larger energy loss during the operation of the entire system.Comparing different drag angles to drag the target,it is found that increasing the drag angle can make the target reduce the orbit height in a short time.In both cases,the energy required to control the movement of the rigid rod on the rail is correspondingly increased.By comparing the positions of different grab points,it is found that when grabbing them close to the end of the rigid rod,the track height has a downward trend;dragging near the center of mass of the rigid rod will cause the orbit radius to increase,and the entire system will be in an unstable state.For the spatial flexible beam considering the lateral vibration,the influence of the grabbing point from the center of mass of the flexible beam on the height of the beam’s running track is analyzed.At the same time,the motion state and energy dissipation of its on-orbit operation are also analyzed.The results show that the different positions of the gripping points cause the track radius of the flexible beam to decrease,and that the closer to the end of the flexible beam,the faster the decrease.In addition,selecting polyethylene fiber composites graphite fiber composites and aluminum alloy material by comparing the relationship between the orbit radius and the orbital angular velocity over time,it is found that the work done by the drag force is transformed into the kinetic energy of the plane motion of the flexible beam in space,and that the drag force makes the orbit height of the flexible beam significantly down.