Natural Frequencies and Global Mode Functions for Flexible Jointed-Panel Structures

Abstract

Deployable solar arrays play an important role in the realization of various spacecraft missions. Taking the flexible spacecraft as an application background, the natural characteristics of a jointed-panel structure is investigated in this paper. Based on the energy conservation principle and Rayleigh-Ritz method, an analytical approach for obtaining the natural frequencies and extracting global mode functions of the flexible jointed-panel structure was developed. Considering the solar panel as an isotropic rectangular plate and the connection at each hinge as a joint with an additional linear rotational spring, the natural frequencies and the corresponding global mode functions were obtained theoretically for the transverse vibration of the solar array. Simulation results for a typical solar array with two panels are given and were used to validate the proposed approach by comparing the obtained natural frequencies and those calculated from the finite-element method. The discussion for the effect of the rotational spring stiffness on the accuracy of the natural frequencies obtained by the proposed approach was conducted. It is shown that the natural frequencies obtained are matched very well with those from the finite-element method for a moderate stiffness of the rotational spring. The proposed approach can provide a theoretical basis for the preliminary design, the nonlinear dynamic analysis, and the design of active vibration controller for the solar array.