Dynamic Model And Vibration Suppression Of A Segmented Space Elevator System

The space elevator system is a space tether system to achieve low-cost space transportation.Although there are no materials that meet the needs of the space elevator system and can be manufactured industrially,it is the most promising space transportation system for large-scale development and utilization of space due to its high efficiency,large load capacity,and reusability.However,the current space elevator system model is based on the gradient cross section model.This model has the disadvantages of difficult control of the bearing cross-sectional area and single function.It is necessary to develop a multifunctional and reasonable structure elevator system model.At the same time,the elevator system will be affected by various factors and produce vibrations.In particular,the safe operation of the elevator system is greatly threatened by the gravitational forces of the sun and the moon,which cannot be avoided.In order to reduce the vibration amplitude of the space elevator system,some methods are required.In this paper,a mechanical model of segmented space elevator system is established based on the traditional equal cross-section and gradient cross-section space elevator model.Through analytical analysis and numerical simulation,the design method of key parameters of segmented space elevator system is given.The stability and dynamic characteristics of the segmented space elevator system are analyzed,and the influence of solar and lunar gravity on the elevator system is analyzed.According to the different characteristics of the elevator system inside and outside the equatorial plane,the oscillation suppression scheme is designed,which provides basic and technical support for the research of space elevator system in China.Based on the segmented design idea,a segmented space elevator system model is established.The modified numerical calculation method of the stress distribution of the segmented space elevator model is derived,and the dynamic model of the segmented space elevator system based on the ANCF(Absolute Nodal Coordinate Formulation)method is established,which verifies the correctness of the model.The numerical simulation shows that the dynamic model based on the ANCF method is consistent with the calculation results of the finite element model and the traditional lumped mass model in loading,and has better flexible reflection ability and calculation speed.The design method of the segmentation parameters of the segmented space elevator system was given.According to the stress distribution characteristics of the segmented space elevator system,the key structural parameters of the stress distribution characteristics were summarized,and the optimization problem is formulated.By using the complex method to search for the best segmentation parameters of the segmented space elevator system in the design space,and by analyzing the maximum stress and mass scale of the space elevator model with different segments,it is found that a better stress and scale level can be achieved by taking 5 to 6 segments of the space elevator ropes within GEO.The stability of the segmented space elevator system oscillating in and out of the Earth’s equator was demonstrated.According to the deformation characteristics of the segmented space elevator system under lateral loading,the segmented space elevator model was simplified to a rigid rod model,and the stability of the system at the equilibrium point was analyzed by using the Lyapunov stability theory,which shows that the segmented space elevator system is stable at the equilibrium point.The maximum deflection angle of the system in and out of the equatorial plane was analyzed with the criterion that the recovery moment of the system and the tension of the rope at the ground anchorage end must be greater than 0.The maximum deflection angle of the system in and out of the equatorial plane was analyzed with the criterion that the recovery moment and the tension of the rope at the ground anchorage end must be greater than 0.It was found that the maximum deflection angle of the segmented space elevator system is positively correlated with the tension of the rope at the ground anchorage end,whether in or out of the equatorial plane.The modal analysis method of the segmented space elevator system was derived,and the effect of the gravitational force of the sun and moon on the space elevator system was analyzed.The modal calculation method of the segmented space elevator system was derived based on the dynamics model established by the ANCF method,and compared with the bead point model and the finite element beam model to verify the correctness of the ANCF beam cell-based space elevator system model.The effect of different structural parameters on the natural frequency of the segmental space elevator system was analyzed by modal analysis of the segmental space elevator model established with different structural parameters.By introducing the solar and lunar gravity into the dynamic model of the segmented space elevator system for simulation,it is found that the influence of the solar and lunar gravity on the segmented space elevator system comes mainly from the moon,causing oscillations with periods around 24 h outside the equatorial plane and 12 h inside the plane.The frequency domain analysis of the solar-lunar gravitational excitation of the space elevator system shows that the steady-state vibration amplitude of the space elevator system in the equatorial plane is easily affected by the dynamic characteristics of the system,while the steady-state vibration amplitude outside the equatorial plane is mainly affected by the damping ratio.In order to reduce the steady-state oscillation amplitude of the space elevator system in the equatorial plane,a double pendulum model of the segmented elevator system is constructed based on the dynamic characteristics of the double tuned mass damper.By analyzing the influence of the position and mass of the inner pendulum on the vibration characteristics of the elevator system,the system parameters of the double pendulum model of the segmented elevator system are determined.By comparison,it is found that the in-plane steady-state response of the double pendulum model of the space elevator system is reduced by 18.9 %,but there is no significant effect on the suppression of the pendulum vibration outside the equatorial plane.