Equivalent circular ring model for the radial vibration analysis of hoop truss structures

Abstract

In large deployable mesh antenna, the dynamic property of hoop truss is vital to the working performance of the whole antenna. For large space truss structures, the model simplification of these structures with simple elastic continuum model is always the focus of dynamics research. By regarding the hoop truss as a hoop periodic structure composed of repetitive planar truss elements, and based on the equivalent beam model of the repeated truss element, an equivalent circular ring model for the radial vibration analysis of the hoop truss structure is presented. By variable substitution, the fourth-order partial differential equations (PDEs) for the radial vibration of the circular ring are reduced to first-order PDEs, then the reduced PDEs are transform to ordinary differential equations via Laplace transform, Green's function method is utilized to solve the dynamic response of the circular ring in complex frequency domain. Furthermore the characteristic equations for natural vibration and the expression of transfer function of the equivalent ring model were derived. At last, a numerical example is used to compare the natural frequencies, mode shapes and transfer functions of the finite element model and the equivalent ring model of the hoop truss. The results verifies the feasibility of using equivalent circular ring model for radial vibration analysis of hoop truss structure.