Eigensolution of symmetric frames using graph factorization

In this paper, decomposition of matrices of special patterns to submatrices of smaller dimensions is briefly described. The graph models of frame structures with different symmetries are decomposed and appropriate processes are designed for their healing in order to form the corresponding factors. The eigenvalues and eigenvectors of the entire structure are then obtained by evaluating those of its factors. The methods developed in this article, simplifies the calculation of the natural frequencies and natural modes of the planar frames with different types of symmetry.