On the Mode Splitting of Degenerate Mechanical Systems Containing Cracks

[+] Author and Article Information
I. Y. Shen

Department of Engineering Mechanics, University of Nebraska-Lincoln, Lincoln, NE 68588-0347

C. D. Mote

University of California, Berkeley, CA 94720

J. Appl. Mech 60(4), 929-935 (Dec 01, 1993) (7 pages) doi:10.1115/1.2901003 History: Received January 22, 1992; Revised January 20, 1993; Online March 31, 2008


This paper presents sufficient conditions governing mode splitting in a two-dimensional, degenerate, mechanical system whose eigensolutions satisfy the Helmholtz equation. When cracks are introduced into such systems, a pair of repeated vibration modes may remain repeated or become distinct (termed split modes) depending on the location and geometry of the cracks. Two types of split modes can occur. Split modes of the first kind are a pair of split modes in which one mode undergoes a frequency shift but the other does not. In contrast, split modes of the second kind are a pair of split modes in which both modes undergo frequency shifts. A sufficient condition for split modes of the first kind is derived through an orthogonal transformation of repeated eigenmodes of the perfect system. Sufficient conditions for repeated modes and split modes of the second kind are derived through an asymptotic analysis. Numerical examples on square and circular domains illustrate the analytical predictions on mode splitting.

Copyright © 1993 by The American Society of Mechanical Engineers
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