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1 APL - Johns Hopkins University Applied Physics Laboratory Laurel, MD 2 Department of Mechanical Engineering 3 Department of Mechanical Engineering 4 Department of Mechanical Science and Engineering Urbana 5 Department of Mechanical Engineering

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.

Autor: Brian Olson - Steven Shaw - Chengzhi Shi - Christophe Pierre - Robert Parker -



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