On Degeneracy of Eigenvalues and Recursive Solution of Symmetrically Coupled Dynamic Systems

[+] Author and Article Information
Fan Y. Chen

Department of Mechanical Engineering, Ohio University, Athens, Ohio

J. Appl. Mech 37(4), 1180-1182 (Dec 01, 1970) (3 pages) doi:10.1115/1.3408689 History: Received November 24, 1969; Revised February 13, 1970; Online July 12, 2010


Based on mathematical induction, we can prove that the eigenvalues of a special nth order circulant matrix are degenerate. Hence the eigenvibration problem of an n degree-of-freedom symmetrically coupled system with equal masses and equal spring stiffnesses can be solved by direct inspection of the system schematic.

Copyright © 1970 by ASME
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