Eigensolution of Symmetric Space Frames by Factorization of Their Graph Models

Abstract

In this paper the graph models of space frames with different symmetries are factorized by decomposition followed by healing. The eigensolution of a structure is then obtained by evaluating the eigen values and eigenvectors of its factors. These methods simplify the calculation of the natural frequencies and natural modes of the space frames with different types of symmetry by reducing the size of the eigensolution problems involved. This is achieved by decomposing a symmetric model into smaller sub models followed by their healing to obtain the factors of the model. The methods of this paper provide a mathematical foundation and a logical means for dealing with symmetry, in place of looking for various boundary conditions to be imposed on symmetric structures, as in the traditional methods. Examples are provided to illustrate the simplicity and efficiency of the present method.