Vibration of Elastic Structures With Cracks

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

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

J. Appl. Mech 60(2), 414-421 (Jun 01, 1993) (8 pages) doi:10.1115/1.2900809 History: Received January 09, 1992; Revised June 08, 1992; Online March 31, 2008


An analytical algorithm is proposed to represent eigensolutions [λm 2 , ψm (r )]m=1 ∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn 2 , φn (r )]n=1 ∞ of a perfect structured without P the cracks. To illustrate this algorithm on mechanical systems governed by the two-dimensional Helmholtz operator, the Green’s identity and Green’sfunction of P are used to represent ψm (r ) in terms of an infinite series of φn (r ) . Substitution of the ψn (r ) representation into the Kamke quotient of C and stationarity of the quotient result in a matrix Fredholm integral equation. The eigensolutions of the Fredholm integral equation then predict λm 2 and ψm (r ) of C . Finally, eigensolutions of two rectangular elastic solids under antiplane strain vibration, one with a boundary crack and the other with an oblique internal crack, are calculated numerically.

Copyright © 1993 by The American Society of Mechanical Engineers
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