Dynamics of rotationally periodic large space structures

Abstract

The dynamic analysis of large area space structures is restricted by cost and utter size of the computer analysis. An efficient analysis must take advantage of construction periodicity inherent in many structures. In the analysis described here a finite element transfer matrix method is employed to eliminate internal degrees of freedom from the basic unit of a rotationally periodic space structure. Eigenfunctions of the resulting periodic unit transfer matrix are used to obtain frequency responses of the complete structure without increasing the analysis variables. Interpolation procedures are developed which significantly reduce the required computations, the dimension of the transfer matrix, and the number of eigenvalues/eigenvectors extractions required in a given frequency range. A substantial saving in the resulting computer analysis is obtained. For a 100 m parabolic dish structure with 3642 structural members contained in 44 units, the periodic analysis involves less than 5% of the variables of a finite element analysis. The frequency response functions obtained are used to compare added coatings, gyroscopic, and tuned damping devices for reducing the responses of large area structures. Transient response can be obtained by an inverse Fourier transform of the frequency response. The analysis also provides modal information for the periodic structure.