Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》
Abstract： In the study of dynamic problems of flexible spacecraft , the problem of rigid and flexible cou-pling of flexible spacecraft system is concerned , that is , the vibration of flexible appendage of spacecraftmay cause instability of spacecraft motion.A beam simplified model of the spacecraft panel structure isproposed for a spinning flexible spacecraft with a central rigid body and bilateral large flexible structureand an unconstrained modal dynamics model is established. In this paper , the unconstrained modal dynam-ics modeling and characteristics of a spinning flexible spacecraft are discussed considering the action of u-niversal gravitation.Firstly , the dynamic equation of the spinning flexible spacecraft is established by usingEuler equation and Hamiltonian principle , which explains the coupling between rigid and elastic modes.Then the modal discretization is carried out ,the eigenvalue problems of the constrained mode and uncon-strained mode are discussed respectively , and the frequency and relevant modes of vibration are quantita-tively compared.Finally , numerical simulation is carried out to solve the unconstrained mode eigenvalue problem of the spinning flexible spacecraft.The differences between the constrained mode and the uncon-strained mode are compared and verified with the finite element method.The conclusion is that with the in-crease of the length of the beam , that is , with the decrease of the ratio of inertia and mass , the uncon-strained mode is more accurate than the constrained mode.
Subjects: Mechanics >> Basic Mechanics submitted time 2022-12-21 Cooperative journals: 《应用力学学报》
Abstract：
A dynamical model was derived by using Lagrange equation for a spacecraft with a center rigid body and a single large flexible structure,and then the unconstrained modal dynamic equation was developed by modal expansion.The relevant theoretical knowledge of modal cost analysis criterion and internal balance technique was introduced to solve model reduction.Modal cost analysis approximation formula to solve a weak damping and sufficiently separated from natural frequency in system was given in this paper.Modal cost analysis criterion could show the share of each modal in the total value of the system,and the reduced order system was composed of the modes with more contributions.Internal balance technique meaning the state space system was converted to internal balance system by non-singular linear transformation.The reduced order system was constructed according to discard the modes corresponding to the values on the diagonal Gram matrixes of the internal balance system.Finally,numerical simulation was applied to reduce the order of the unconstrained modal dynamics model of the spacecraft with central rigid body and a single flexible beam.The numerical calculation of the reduction of the system model by two criteria shows that the original system is effectively reduced.
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