Abstract
AbstractIn this paper, the method recently developed for the free vibration of symmetric frames using canonical forms of stiffness matrices is extended to the flexibility matrices. Weighted graphs are associated with the flexibility and mass matrices of the frame structures. Using graph symmetry, the models are decomposed into submodels and a healing process is employed, such that the union of the eigenvalue of the matrices corresponding to the healed submodels contains the eigenvalues of the entire model. This two‐step process is termed as the factorization of a weighted graph. The presented method is illustrated through simple examples having different symmetries. Copyright © 2009 John Wiley & Sons, Ltd.
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