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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

Rytter, A., 1993, “Vibration Based Inspection of Civil Engineering Structures;” Ph.D. thesis, Aalborg University, Denmark.
Dimarogonas,  A. D., 1996, “Vibration of Cracked Structures: a State-of-the-Art Review,” Eng. Fract. Mech., 55(5), pp. 831–857.
Gudmundson,  P., 1983, “The Dynamic Behavior of Slender Structures with Cross-Sectional Cracks,” J. Mech. Phys. Solids, 31(4), pp. 329–345.
Ostachowicz,  W. M., and Krawczuk,  M., 1990, “Vibration Analysis of a Cracked Beam,” Comput. Struct., 36(2), pp. 245–250.
Wauer,  J., 1990, “On the Dynamics of Cracked Rotors: a Literature Survey,” Appl. Mech. Rev., 43(1), pp. 13–17.
Abraham,  O. N. L., and Brandon,  J. A., 1995, “The Modelling of the Opening and Closure of a Crack,” ASME J. Vibr. Acoust., 117, pp. 370–377.
Brandon,  J. A., 1999, “Towards a Nonlinear Identification Methodology for Mechanical Signature Analysis,” Key Eng. Mater., pp. 167–168, pp. 265–272.
Christides,  S., and Barr,  A. D. S., 1984, “One-Dimensional Theory of Cracked Bernoulli-Euler Beams,” Int. J. Mech. Sci., 26(11/12), pp. 639–648.
Shen,  M-H. H., and Pierre,  C., 1990, “Natural Modes of Bernoulli-Euler Beams with Symmetric Cracks,” J. Sound Vib., 138(1), pp. 115–134.
Shen,  M-H. H., and Pierre,  C., 1994, “Free Vibrations of Beams with a Single Edge Crack,” J. Sound Vib., 170(2), pp. 237–259.
Chondros,  T. G., Dimarogonas,  A. D., and Yao,  J., 1998, “A Continuous Cracked Beam Vibration Theory,” J. Sound Vib., 215(1), pp. 17–34.
Barr,  A. D. S., 1966, “An Extension of the Hu-Washizu Variational Principle in Linear Elasticity for Dynamic Problems,” ASME J. Appl. Mech., 33(2), p. 465.
Armon,  D., Ben-Haim,  Y., and Braun,  S., 1994, “Crack Detection in Beams by Rank-Ordering of Eigenfrequency Shifts,” Mech. Syst. Signal Process., 8(1), pp. 81–91.
Banks,  H. T., Inman,  D. J., Leo,  D. J., and Wang,  Y., 1996, “An Experimentally Validated Damage Detection Theory in Smart Structures,” J. Sound Vib., 191(5), pp. 859–880.
Reddy, J. N., 1984, Energy and Variational Methods in Applied Mechanics, John Wiley & Sons, New York.
Carneiro, S. H. S., 2000, “Model-Based Vibration Diagnosis of Cracked Members in the Time Domain,” Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
Wang, Y., 1991, “Damping Modeling and Parameter Estimation in Timoshenko Beams,” Ph.D. thesis, Brown University, Providence, RI.

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. Crack depth ratio a/2d=0.5.
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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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