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Wave Propagation Analysis in Beams Using Shear Deformable Beam Theories Considering Second Spectrum

  • U. Gul (a1) and M. Aydogdu (a1)

Abstract

In this study, wave propagation in beams is studied using different beam theories like Euler-Bernoulli, Timoshenko and Reddy beam theories. Dispersion curves obtained for these beam theories are compared with the exact plane elasticity solutions. It is obtained that, there are two branches for Reddy beam theory similar to the Timoshenko beam theory. However, one branch is obtained for Euler-Bernoulli beam theory. The effects of in-plane load on Timoshenko and Reddy beam theories are examined and dispersion curves of the Timoshenko and Reddy beams are compared with exact plane elasticity solution. In Timoshenko beam theory, qualitative difference between the two spectrums has been lost with in-plane loads for some wave numbers.

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*Corresponding author (ufukgul@trakya.edu.tr)

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1. Traill-Nash, R. W. and Collar, A. R., “The Effect of Shear Flexibility and Rotary Inertia on the Bending Vibrations of Beams,” Quarterly Journal of Mechanics and Applied Mathematics, 6, pp. 186222 (1953).
2. Stephen, N. G., “The Second Frequency Spectrum of Timoshenko Beams,” Journal of Sound and Vibration, 80, pp. 578582 (1982).
3. Stephen, N. G., “The Second Spectrum of Timoshenko Beam Theory-Further Assessment,” Journal of Sound and Vibration, 292, pp. 372389 (2006).
4. Renton, J. D., “A Check on the Accuracy of Timoshenko's Beam Theory,” Journal of Sound and Vibration, 245, pp. 559561 (2001).
5. Bhaskar, A., “Elastic Waves in Timoshenko Beams: the ‘Lost and Found’ of an Eigenmode,” Proceedings of the Royal Society A, 465, pp. 239255 (2009).
6. Elishakoff, I. and Lubliner, E., Random Vibration of a Structure Via Classical and Nonclassical Theories, in Probabilistic Methods in Mechanics and Structures, S. Eggwertz, ed., Springer Verlag, Berlin, pp. 455468 (1985).
7. Elishakoff, I. and Livshits, D., “Some Closed form Solutions in Random Vibrations of Timoshenko Beams,” Journal of Probabilistic Engineering Mechanics, 4, pp. 4954 (1989).
8. Elishakoff, I., An Equation Both More Consistent and Simpler than Bresse-Timoshenko Equation, in Advances in Mathematical Modeling and Experimental Methods for Materials and Structures, R. Gilat and L. Sills-Banks, eds., Springer Verlag, Berlin, pp. 249254 (2009).
9. Bhashyam, G. R. and Prathap, G., “The Second Frequency Spectrum of Timoshenko Beams,” Journal of Sound and Vibration, 76, pp. 407420 (1981).
10. Abbas, B. A. H. and Thomas, J., “The Second Frequency Spectrum of Timoshenko Beams,” Journal of Sound and Vibration, 51, pp. 123137 (1977).
11. Manevich, A. I., “Dynamics of Timoshenko Beam on Linear and Nonlinear Foundation: Phase Relations, Significance of the Second Spectrum, Stability,” Journal of Sound and Vibration, 344, pp. 209220 (2015).
12. Elishakoff, I., Kaplunov, J. and Nolde, E., “Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia,” Applied Mechanics Reviews, 67, 060802 (2015).
13. Elishakoff, I. and Soret, C., “A Consistent Set of Nonlocal Bresse-Timoshenko Equations for Nonlocal Nano-Beams with Surface Effects,” Journal of Applied Mechanics, 80, 061001 (2013).
14. Elishakoff, I., Ghyselinck, G. and Bucas, S., “Virus Sensor Based on Single-Walled Carbon Nanotube treated as Bresse-Timoshenko beam,” Journal of Applied Mechanics, 79, 064502 (2012).
15. Elishakoff, I. and Pentaras, D., “Natural Frequencies of Carbon Nanotubes Based on Simplified Bresse-Timoshenko Theory,” Journal of Computational and Theoretical Nanoscience, 6, pp. 15271531 (2009).
16. Reddy, J. N., “A Simple Higher-Order Theory for Laminated Composite Plates,” Journal of Applied Mechanics, 51, pp. 745752 (1984).
17. Aydogdu, M., “A General Nonlocal Beam Theory: Its Application to Nanobeam Bending, Buckling and Vibration,” Physica E, 41, pp. 16511655 (2009).
18. Aydogdu, M., “Vibration of Multi-Walled Carbon Nanotubes by Generalized Shear Deformation Theory,” International Journal of Mechanical Sciences, 50, pp. 837844 (2008).
19. Soldatos, K. P. and Sophocleous, C., “On Shear Deformable Beam Theories: The Frequency and Normal Mode Equations of the Homogeneous Orthotropic Bickford Beam,” Journal of Sound and Vibration, 242, pp. 215245 (2001).
20. 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. 34883497 (2011).
21. Cowper, G. R., “On the Accuracy of Timoshenko's Beam Theory,” Proceedings ASCE Journal of the Engineering Mechanics Division, 94, pp. 14471453 (1968).
22. Cowper, G. R., “The Shear Coefficient in Timoshenko Beam Theory,” Journal of Applied Mechanics, 33, pp. 335340 (1966).
23. Hutchinson, J. R., “Shear Coefficients for Timoshenko Beam Theory,” Journal of Applied Mechanics, 68, pp. 8792 (2001).
24. Kaneko, T., “On Timoshenko's Correction for Shear in Vibrating Beams,” Journal of Physics D: Applied Physics, 8, pp. 19271936 (1975).
25. Corradi Dell'Acqua, L., Meccanica delle Strutture, McGraw-Hill Inc., New York, 1, pp. 346350 (1992).
26. Franco-Villafañe, J. A. and Méndez-Sánchez, R. A., “On the Accuracy of the Timoshenko Beam Theory Above the Critical Frequency: Best Shear Coefficient,” Journal of Mechanics, 32, pp. 515518 (2016).

Keywords

Wave Propagation Analysis in Beams Using Shear Deformable Beam Theories Considering Second Spectrum

  • U. Gul (a1) and M. Aydogdu (a1)

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