Effect of Initial Stress on Wave Frequencies of Elastic Solid with Rotation

G. A. Yahya; S. H. Elhag; M. F. Sanaa; A. M. A. Amry; A. M. Abd-Alla

doi:10.4236/jmp.2014.518197

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JMP> Vol.5 No.18, December 2014

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Effect of Initial Stress on Wave Frequencies of Elastic Solid with Rotation ()

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DOI: 10.4236/jmp.2014.518197 3,051 Downloads 3,453 Views Citations

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G. A. Yahya^1,2*, S. H. Elhag³, M. F. Sanaa^1,2, A. M. A. Amry^1,4, A. M. Abd-Alla^3,5

Affiliation(s)

¹Physics Department, Faculty of Science, Taif University, Taif, KSA.
²Physics Department, Faculty of Science, Aswan University, Aswan, Egypt.
³Mathematics Department, Faculty of Science, Taif University, Taif, KSA.
⁴Physics Department, Faculty of Science, Assiut University, Assiut, Egypt.
⁵Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt.

ABSTRACT

In this paper, the effect of initial stress on the radial vibrations of elastic hollow cylinder with rotation is discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free; fixed and mixed boundary condition is examined numerically. The determination is concerned with the eigenvalues of the natural frequency of the radial vibrations in the case of harmonic vibrations. The effect of rotation and initial stress on the natural frequencies was examined. It was shown that the dispersion curves of guided waves were significantly influenced by the rotation and initial stress of the elastic cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation and initial stress are very pronounced.

KEYWORDS

Ealstodynamics, Radial Vibrations, Isotropic Material, Rotation, Elastic Hollow Cylinder, Initial Stress

Cite this paper

Yahya, G. , Elhag, S. , Sanaa, M. , Amry, A. and Abd-Alla, A. (2014) Effect of Initial Stress on Wave Frequencies of Elastic Solid with Rotation. Journal of Modern Physics, 5, 2012-2021. doi: 10.4236/jmp.2014.518197.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Hasheminejad, S.M. and Mirzaei, Y. (2011) Journal of Sound and Vibration, 330, 229-244. http://dx.doi.org/10.1016/j.jsv.2010.08.011

[2]	Ootao, Y. and Ishihara, M. (2012) Applied Mathematical Modeling, 36, 1431-1443. http://dx.doi.org/10.1016/j.apm.2011.08.043

[3]	Bayóna, A., Gascónb, F., Medinaa, R., Nievesb, F.J. and Salazara, F. (2011) European Journal of Mechanics— A/Solids, 30, 423-431. http://dx.doi.org/10.1016/j.euromechsol.2010.12.006

[4]	Buchanan, G.R. and Liu, Y.J. (2005) International Journal of Mechanical Sciences, 47, 277-292. http://dx.doi.org/10.1016/j.ijmecsci.2004.12.004

[5]	Yu, J.Q., Ma, Q.J. and Su, S. (2008) Journal of Ultrasonics, 48, 664-677. http://dx.doi.org/10.1016/j.ultras.2008.03.005

[6]	Abd-Alla, A.M., Nofal, T.A. and Farhan, A.M. (2008) Physics Letters A, 372, 4861-4864. http://dx.doi.org/10.1016/j.physleta.2008.01.088

[7]	Abd-Alla, A.M. and Abo-Dahab, S.M. (2009) Applied Mathematical Modelling, 33, 2388-2402. http://dx.doi.org/10.1016/j.apm.2008.07.008

[8]	El-Naggar, A.M., Abd-Alla, A.M., Fahmy, M.A. and Ahmed, S.M. (2002) Journal of Heat and Mass Transfer, 39, 41-46. http://dx.doi.org/10.1007/s00231-001-0285-4

[9]	El-Naggar, A.M., Abd-Alla, A.M. and Ahmed, S.M. (1994) Bulletin of the Calcutta Mathematical Society, 86, 205-212.

[10]	El-Naggar, A.M., Abd-Alla, A.M. and Ahmed, S.M. (1995) Journal of Applied Mathematics and Computation, 69, 147-157. http://dx.doi.org/10.1016/0096-3003(94)00074-E

[11]	Abd-Alla, A.M., Mahmoud, S.R. and Al-Shehri, N.A. (2011) Applied Mathematics and Computation, 217, 8914-8922. http://dx.doi.org/10.1016/j.amc.2011.03.077

[12]	Abd-Alla, A.M., Mahmoud, S.R., Abo-Dahab, S.M. and Helmy, M.I. (2011) Applied Mathematics and Computation, 217, 4321-4332. http://dx.doi.org/10.1016/j.amc.2010.10.029

[13]	Gupta, S.K. and Shukla, R.K. (1994) Indian Journal of Pure and Applied Mathematics, 25, 1089-1097.

[14]	Chatzigeorgiou, G., Charalambakis, N. and Murat, F. (2008) International Journal of Solids and Structures, 45, 5165-5180. http://dx.doi.org/10.1016/j.ijsolstr.2008.05.015

[15]	Abd-Alla, A.M., Abd-Alla, A.N. and Zeidan, N.A. (2001) Journal of Applied Mathematics and Computation, 121, 93-122. http://dx.doi.org/10.1016/S0096-3003(99)00265-9

[16]	Ahmed, F. and Rahman, A. (2000) International Journal of Engineering Science, 38, 325-335. http://dx.doi.org/10.1016/S0020-7225(99)00031-2

[17]	Buchanan, G.R. and Yii, C.B. (2002) Applied Acoustics, 63, 547-566. http://dx.doi.org/10.1016/S0003-682X(01)00048-2

[18]	Ding, H., Wang, H. and Chen, W. (2002) Acta Mechanica Sinica, 18, 621-628. http://dx.doi.org/10.1007/BF02487964

[19]	Ding, H.J., Wang, H.M. and Chen, W.Q. (2003) Journal of Sound and Vibration, 263, 815-829. http://dx.doi.org/10.1016/S0022-460X(02)01075-1

[20]	Wang, X. and Shen, Y.P. (2003) International Journal of Engineering Science, 41, 85-102. http://dx.doi.org/10.1016/S0020-7225(02)00110-6

[21]	Ding, H.J., Wang, H.M. and Hou, P.F. (2003) International Journal of Solids and Structures, 40, 105-123. http://dx.doi.org/10.1016/S0020-7683(02)00525-5

[22]	Hearmon, R.F.S. (1946) Reviews of Modern Physics, 18, 409-440.

[23]	Hou, P.F. and Leung, A.Y.T. (2004) Smart Material Structure, 13, 762-776. http://dx.doi.org/10.1088/0964-1726/13/4/014