Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams

Sergio H. S. Carneiro; Daniel J. Inman

doi:10.1115/1.1452744

Journal of Vibration and Acoustics | Volume 124 | Issue 2 | TECHNICAL PAPERS

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TECHNICAL PAPERS

Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams

Sergio H. S. Carneiro and Daniel J. Inman

[+] 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

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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. x_c/L=0.5.

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Influence of crack depth on displacement mode shapes of a simply supported Timoshenko cracked beam. x_c/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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Carneiro SS, Inman DJ. Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams. ASME. J. Vib. Acoust. 2002;124(2):310-320. doi:10.1115/1.1452744.

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Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams

References

Figures

Typical geometry of a cracked beam

Crack function for normal stress disturbance f₁

Crack function for shear stress disturbance f₂

Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.1.

Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.5.

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.

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.

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.

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

Variation of normalized natural frequencies of simply supported beams with respect to crack depth. x_c/L=0.5.

Influence of crack depth on displacement mode shapes of a simply supported Timoshenko cracked beam. x_c/L=0.5.

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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Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams

References

Figures

Typical geometry of a cracked beam

Crack function for normal stress disturbance f1

Crack function for shear stress disturbance f2

Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.1.

Comparison of convergence characteristics of the Euler and Timoshenko cracked beam models. Crack depth ratio a/2d=0.5.

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.

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.

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.

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

Variation of normalized natural frequencies of simply supported beams with respect to crack depth. xc/L=0.5.

Influence of crack depth on displacement mode shapes of a simply supported Timoshenko cracked beam. xc/L=0.5.

Finite element model of a simply supported short beam, with detailed illustration of the mesh at the cracked region. L/2d=5.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

Crack function for normal stress disturbance f₁

Crack function for shear stress disturbance f₂

Variation of normalized natural frequencies of simply supported beams with respect to crack depth. x_c/L=0.5.

Influence of crack depth on displacement mode shapes of a simply supported Timoshenko cracked beam. x_c/L=0.5.