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Eigensolution for free vibration of planar frames by weighted graph symmetry
Author(s) -
Kaveh A.,
Dadfar B.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1818
Subject(s) - eigenvalues and eigenvectors , vibration , simple (philosophy) , symmetry (geometry) , planar , graph , mathematics , graph theory , computer science , combinatorics , geometry , physics , acoustics , quantum mechanics , computer graphics (images) , philosophy , epistemology
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 © 2006 John Wiley & Sons, Ltd.