This paper is to determine vibrational eigensolutions of a three-dimensional, finite, linear, elastic solid C containing cracks in terms of crack configuration σc and eigensolutions of a perfect elastic solid P without the cracks. Use of Betti reciprocal theorem and the Green’s function of P expands in terms of an infinite series of . Substitution of the series representation into the Kamke quotient of C and stationarity of the quotient result in a Fredholm integral equation whose nontrivial solutions predict , and of C. Finally, natural frequencies and mode shapes of a circular shaft of finite length containing a circumferential crack under torsional vibration are predicted through a two-term Ritz approximation of the Fredholm integral equation. The results differ significantly from those predicted by the method of flexibility matrices, when the ratio of the shaft length to the shaft radius is small.
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June 1995
Technical Papers
Vibration of a Three-Dimensional, Finite Linear, Elastic Solid Containing Cracks
I. Y. Shen
I. Y. Shen
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195
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I. Y. Shen
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195
J. Appl. Mech. Jun 1995, 62(2): 282-288 (7 pages)
Published Online: June 1, 1995
Article history
Received:
February 2, 1993
Revised:
October 11, 1993
Online:
October 30, 2007
Citation
Shen, I. Y. (June 1, 1995). "Vibration of a Three-Dimensional, Finite Linear, Elastic Solid Containing Cracks." ASME. J. Appl. Mech. June 1995; 62(2): 282–288. https://doi.org/10.1115/1.2895929
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