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TECHNICAL PAPERS

Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams

[+] Author and Article Information
Sergio H. S. Carneiro

Instituto de Aeronáutica e Espaço, Centro Técnico Aeroespacial, CTA/IAE/ASA, S. J. Campos-SP 12228, Brazil

Daniel J. Inman

Center for Intelligent Material Systems and Structures, Virginia Polytechnic Institute and State University, 310 NEB, mail code 0261, Blacksburg, VA 24061

J. Vib. Acoust 124(2), 310-320 (Mar 26, 2002) (11 pages) doi:10.1115/1.1452744 History: Received August 01, 2000; Revised October 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Figures

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Typical geometry of a cracked beam
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Crack function for normal stress disturbance f1
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Crack function for shear stress disturbance f2
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Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.1.
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Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Curves normalized to the same element length. Crack depth ratio a/2d=0.5.
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Comparison of finite element model and beam theory results for the first three natural frequencies of a simply supported beam with a midspan crack. L/2d=20. FE results from Reference 10.
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Comparison of experimental and beam theory results for the first and third natural frequencies of a simply supported beam with a midspan crack. L/2d=25.64. Experimental results from Reference 9.
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Differences in natural frequencies estimated by Euler and Timoshenko models as a function of aspect ratio for a simply supported beam with a midspan crack
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Variation of normalized natural frequencies of simply supported beams with respect to crack depth. xc/L=0.5.
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Influence of crack depth on displacement mode shapes of a simply supported Timoshenko cracked beam. xc/L=0.5.
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Finite element model of a simply supported short beam, with detailed illustration of the mesh at the cracked region. L/2d=5.
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Variations of the normalized values of natural frequencies of a short simply supported beam with a midspan crack. L/2d=5. Left-hand-side plots: values normalized by the undamaged natural frequency from the corresponding model; right-hand-side plots: values normalized by the undamaged natural frequency from the 2-D FE model.
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Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.5.

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