Eigensolution for free vibration of planar frames by weighted graph symmetry

In this paper, the method recently developed for mass-spring systems is generalized to include the free vibration of frames. Here, the inter-relation for the mechanical properties of elements is established using weighted graphs, enabling the calculation of the eigenvalues involved. Using graph symmetry, the models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels results in the eigenvalues of the entire model. The present method is illustrated through many simple examples of different configurations. Copyright q 2006 John Wiley & Sons, Ltd.