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On the Accuracy of the Timoshenko Beam Theory Above the Critical Frequency: Best Shear Coefficient

Published online by Cambridge University Press:  21 January 2016

J. A. Franco-Villafañe  and
R. A. Méndez-Sánchez
J. A. Franco-Villafañe*
Affiliation:
Instituto de Ciencias FísicasUniversidad Nacional Autónoma de MéxicoMorelos, México
R. A. Méndez-Sánchez
Affiliation:
Instituto de Ciencias FísicasUniversidad Nacional Autónoma de MéxicoMorelos, México
*
*Corresponding author (jofravil@fis.unam.mx)
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Abstract

We obtain values for the shear coefficient both below and above the critical frequency by comparing the results of the Timoshenko beam theory with experimental data published recently. The best results are obtained, by a least-square fitting, when different values of the shear coefficient are used below and above the critical frequency.

Keywords

Timoshenko beam theoryTimoshenko shear coefficientCritical frequency
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 515 - 518
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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References

1. Wang, X. Q. and So, R. M. C., “Timoshenko Beam Theory: A Perspective Based on the Wave-Mechanics Approach,” Wave Motion, 57, pp. 64–87 (2015).CrossRefGoogle Scholar
2. Jun, Z., Zhushi, R. and Na, T., “Energy Flow, Energy Density of Timoshenko Beam and Wave Mode Incoherence,” Journal of Sound and Vibration, 354, pp. 104–117 (2015).Google Scholar
3. Eslami, M. R., Finite Elements Methods in Mechanics, Springer International Publishing, Switzerland (2014).Google Scholar
4. Chen, W. R., “Parametric Studies on Bending of Twisted Timoshenko Beams Under Complex Loadings,” Journal of Mechanics, 28, pp. N1–N6 (2012).Google Scholar
5. Kaneko, T., “On Timoshenko's Correction for Shear In Vibrating Beams,” Journal of Physics D: Applied Physics, 8, pp. 1927–1936 (1975).Google Scholar
6. Cowper, G. R., “The Shear Coefficient in Timoshenko Beam Theory,” Journal of Applied Mechanics, 33, pp. 335–340 (1966).Google Scholar
7. Stephen, N. G. and Levinson, M., “A Second Order Beam Theory,” Journal of Sound and Vibration, 67, pp. 293–305 (1979).Google Scholar
8. Renton, J. D., “A Check on the Accuracy of Timoshenko's Beam Theory,” Journal of Sound and Vibration, 245, pp. 559–561 (2001).CrossRefGoogle Scholar
9. Hutchinson, J. R., “Shear Coefficients for Timoshenko Beam Theory,” Journal of Applied Mechanics, 68, pp. 87–92 (2001).Google Scholar
10. Stephen, N. G., “On a Check on the Accuracy of Timoshenko's Beam Theory,” Journal of Sound and Vibration, 257, pp. 809–812 (2002).CrossRefGoogle Scholar
11. Chan, K. T., Lai, K. F., Stephen, N. G. and Young, K., “A New Method to Determine the Shear Coefficient of Timoshenko Beam Theory,” Journal of Sound and Vibration, 330, pp. 3488–3497 (2011).Google Scholar
12. Hearmon, R. F. S., “The Influence of Shear and Rotatory Inertia on the Free Flexural Vibration of Wooden Beams,” British Journal of Applied Physics, 9, pp. 381–388 (1958).Google Scholar
13. Rosinger, H. E. and Ritchie, I. G., “On Timoshenko's Correction for Shear in Vibrating Isotropic Beams,” Journal of Physics D: Applied Physics, 10, pp. 1461–1466 (1977).Google Scholar
14. Méndez-Sánchez, R. A., Morales, A. and Flores, J., “Experimental Check on the Accuracy of Timoshenko's Beam Theory,” Journal of Sound and Vibration, 279, pp. 508–512 (2005).Google Scholar
15. Gruttmann, F. and Wagner, W., “Shear Correction factors in Timoshenko's Beam Theory for Arbitrary Shaped Cross-Sections,” Computational Mechanics, 27, pp. 199–207 (2001).Google Scholar
16. Graff, K. F., Wave Motion in Elastic Solids, Dover, New York (1991).Google Scholar
17. Díaz-de-Anda, A., Flores, J., Gutiérrez, L., Méndez-Sánchez, R. A., Monsivais, G. and Morales, A., “Experimental Study of the Timoshenko Beam Theory Predictions,” Journal of Sound and Vibration, 331, pp. 5732–5744 (2012).CrossRefGoogle Scholar
18. Stephen, N. G., “The Second Frequency Spectrum of Timoshenko Beams,” Journal of Sound and Vibration, 80, pp. 578–582 (1982).Google Scholar
19. Bhashyam, G. R. and Prathap, G., “The Second Frequency Spectrum of Timoshenko Beams,” Journal of Sound and Vibration, 76, pp. 407–420 (1981).Google Scholar
20. Levinson, M. and Cooke, D. W., “On the Two Frequency Spectra of Timoshenko Beams,” Journal of Sound and Vibration, 84, pp. 319–326 (1982).CrossRefGoogle Scholar
21. Nesterenko, V. V., “A Theory of Transverse Vibration of the Timoshenko Beam,” Journal of Applied Mathematics and Mechanics, 57, pp. 669–677 (1993).Google Scholar
22. Geist, B. and McLaughlin, J. R., “Double Eigenvalues for the Uniform Timoshenko Beam,” Applied Mathematical Letters, 10, pp. 129–134 (1997).CrossRefGoogle Scholar
23. Stephen, N. G., “The Second Spectrum of Timoshenko Beam Theory-Further Assesssment,” Journal of Sound and Vibration, 292, pp. 372–389 (2006).CrossRefGoogle Scholar
24. Bhaskar, A., “Elastic Waves in Timoshenko Beams: The ‘Lost and Found’ of an Eigenmode,” Proceedings of the Royal Society of London A, 465, pp. 239–255 (2009).Google Scholar
25. Manevich, A., “Dynamics of Timoshenko Beam on Linear and Nonlinear Foundation: Phase Relations, Significance of the Second Spectrum, Stability,” Journal of Sound and Vibration, 334, pp. 209–220 (2015).Google Scholar