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Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures

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Abstract

In this paper, block circulant matrices and their properties are investigated. Basic concepts and the necessary theorems are presented and then their applications are discussed. It is shown that a circulant matrix can be considered as the sum of Kronecker products in which the first components have the commutativity property with respect to multiplication. The important fact is that the method for block diagonalization of these matrices is much simpler than the previously developed methods, and one does not need to find an additional matrix for orthogonalization. As it will be shown not only the matrices corresponding to domes in the form of Cartesian product, strong Cartesian product and direct product are circulant, but for other structures such as diamatic domes, pyramid domes, flat double layer grids, and some family of transmission towers these matrices are also block circulant.

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Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Mechanics, Iran University of Science and Technology, Narmak, Tehran-16, Iran

    Ali Kaveh

  2. Faculty of Engineering, University of Tehran, Tehran, Iran

    Hossein Rahami

Authors
  1. Ali Kaveh
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  2. Hossein Rahami
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Correspondence to Ali Kaveh.

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Kaveh, A., Rahami, H. Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures. Acta Mech 217, 51–62 (2011). https://doi.org/10.1007/s00707-010-0382-x

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  • DOI: https://doi.org/10.1007/s00707-010-0382-x

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