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.
Circulant Matrices and Their Application to Vibration Analysis
Manuscript received January 12, 2014; final manuscript received May 7, 2014; published online June 19, 2014. Editor: Harry Dankowicz.
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Olson, B. J., Shaw, S. W., Shi, C., Pierre, C., and Parker, R. G. (June 19, 2014). "Circulant Matrices and Their Application to Vibration Analysis." ASME. Appl. Mech. Rev. July 2014; 66(4): 040803. https://doi.org/10.1115/1.4027722
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