TY - JOUR
T1 - Circulant matrices and their application to vibration analysis
AU - Olson, Brian J.
AU - Shaw, Steven W.
AU - Shi, Chengzhi
AU - Pierre, Christophe
AU - Parker, Robert G.
PY - 2014/7
Y1 - 2014/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84903181357&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903181357&partnerID=8YFLogxK
U2 - 10.1115/1.4027722
DO - 10.1115/1.4027722
M3 - Article
AN - SCOPUS:84903181357
SN - 0003-6900
VL - 66
JO - Applied Mechanics Reviews
JF - Applied Mechanics Reviews
IS - 4
M1 - 040803
ER -