Introduction to Symmetry and Regularity

Kaveh, A.

doi:10.1007/978-3-7091-1565-7_1

Cited by 2 publications

(3 citation statements)

References 60 publications

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“…A structure is called repetitive if it consists of a number of identical units, which are connected to each other in a regular form (Kaveh, 2013). The repetitive structure in Figure 1 has n identical units.…”

Section: Repetitive Structuresmentioning

confidence: 99%

“…In the above equation, the sign ⊗ denotes the Kronecker product of two matrices. This sign is used for efficient representation of this product, and there are many theorems on this product as discussed by Kaveh (2013), Bellman (1974) and Brewer (1987).…”

Section: New Circulant Matrixmentioning

confidence: 99%

“…The symmetry and regularity of structure are examples of such characteristics. Symmetry has been widely studied in engineering science (Gould, 1967; Topping et al , 1998; Godsil and Royle, 2001; Kaveh and Rahami, 2005; Kaveh, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of repetitive and near-repetitive structures by transformation to equivalent circulant structures

Kaveh

Rahami

Jodaki

2017

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Purpose There are many structures that have a repetitive pattern. If a relationship can be established between a repetitive structure and a circulant structure, then the repetitive structure can be analyzed by using the properties of the corresponding circulant structure. The purpose of this paper is to develop such a transformation. Design/methodology/approach A circulant matrix has certain properties that can be used to reduce the complexity of the analysis. In this paper, repetitive and near-repetitive structures are transformed to circulant structures by adding and/or eliminating some elements of the structure. Numerical examples are provided to show the efficiency of the present method. Findings A transformation is established between a repetitive structure and a circulant structure, and the analysis of the repetitive structure is performed by using the properties of the corresponding circulant structure. Originality/value Repetitive and near-repetitive structures are transformed to circulant structures, and the complexity of the analysis of the former structures is reduced by analyzing the latter structures.

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Section: Repetitive Structuresmentioning

confidence: 99%

Section: New Circulant Matrixmentioning

confidence: 99%

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Analysis of repetitive and near-repetitive structures by transformation to equivalent circulant structures

Kaveh

Rahami

Jodaki

2017

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Circulant Matrices and Their Application to Vibration Analysis

Olson

Shaw

Shi

et al. 2014

Applied Mechanics Reviews

106

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This paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. Our presentation of the basic theory is distilled from the classic book of Davis (1979, Circulant Matrices, 2nd ed., Wiley, New York) with results, proofs, and examples geared specifically to vibration applications. Our aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications, and generalizations of the theory.

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Introduction to Symmetry and Regularity

Cited by 2 publications

References 60 publications

Analysis of repetitive and near-repetitive structures by transformation to equivalent circulant structures

Analysis of repetitive and near-repetitive structures by transformation to equivalent circulant structures

Circulant Matrices and Their Application to Vibration Analysis

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