Circulant matrices and their application to vibration analysis

Brian J. Olson, Steven W. Shaw, Chengzhi Shi, Christophe Pierre, Robert G. Parker

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number040803
JournalApplied Mechanics Reviews
Volume66
Issue number4
DOIs
StatePublished - Jan 1 2014

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Olson, Brian J. ; Shaw, Steven W. ; Shi, Chengzhi ; Pierre, Christophe ; Parker, Robert G. / Circulant matrices and their application to vibration analysis. In: Applied Mechanics Reviews. 2014 ; Vol. 66, No. 4.
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Circulant matrices and their application to vibration analysis. / Olson, Brian J.; Shaw, Steven W.; Shi, Chengzhi; Pierre, Christophe; Parker, Robert G.

In: Applied Mechanics Reviews, Vol. 66, No. 4, 040803, 01.01.2014.

Research output: Contribution to journalArticle

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