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SUMMARYIn this paper, decomposition of matrices of special patterns to submatrices of smaller dimensions is brie y described. The graph models of frame structures with di erent 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, simpliÿes the calculation of the natural frequencies and natural modes of the planar frames with di erent types of symmetry.

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