Equivalent Dynamic Model of the Space Antenna Truss with Initial Stress

Abstract

The equivalent modeling approach is one of the key technologies in the design of vibration controllers motivated by the large flexible space truss structure applications. Based on the energy equivalence principle and the classical Timoshenko beam theory, this study establishes a new equivalent dynamic model for the space antenna truss with initial stress by the static condensation method. Compared with previous truss structures of the triangular prism reported in equivalent modeling, the space antenna truss has a more complicated configuration and more members. Meanwhile, this truss structure is in a self-stress state and the connection of the adjacent members is a rigid-jointed. The equivalent anisotropic Timoshenko beam model of the complex space antenna truss with a rigid joints is proposed for the spatial repeating element composed of the beam and cable members in the initial stress state and the joints. According to the kinematic assumptions, displacement expressions of the spatial repeating element are derived using the Taylor series expansion at the center of the spatial repeating element. Then, the stiffness and mass matrices of the equivalent beam model are obtained. The natural vibration characteristics of the equivalent beam model are proved to be in good agreement with those of the original space antenna truss, which indicates that the equivalent beam model has a satisfactory accuracy. As a result, the equivalent dynamic model may serve for the vibration control of the space antenna truss.