Coupled vibration analysis for equivalent dynamic model of the space antenna truss

Abstract

A novel equivalent dynamic model is developed for coupled vibration analysis of the space antenna truss to enhance the design capacity of vibration controllers. Based on energy equivalence principle, the space antenna truss with two important features of rigid joints and complicated configuration is equivalent to a spatial anisotropy Timoshenko beam model. According to the kinematic assumptions, strain and kinetic energy expressions of the spatial periodic element can be obtained in accordance with displacement components at its center. Hamilton's principle is carried out to formulate the governing partial differential equations of motion for the equivalent beam model (EBM) which is divided into two sets of PDEs. Each set of PDEs includes three degrees of freedom and describes bending-torsion and bending-extension couplings respectively, due to the asymmetry of the antenna truss. An exact analytical method is developed to solve the two sets of coupled motion equations. The natural characteristics of the EBM are shown to be in excellent agreement with those of the finite element method, which demonstrates that the proposed EBM can provide a satisfactory accuracy for the antenna truss. In addition, since the mode shapes of the EBM are expressed as analytical functions of the spatial coordinate, such an approach may lead the investigations of dynamic property and the design of vibration control law to become convenient for the space antenna truss.