Rayleigh waves in generalized magneto-thermo-viscoelastic granular medium under the influence of rotation, gravity field, and initial stress. (English) Zbl 1237.74105
Summary: The surface waves propagation in generalized magneto-thermo-viscoelastic granular medium subjected to continuous boundary conditions has been investigated. In addition, it is also subjected to thermal boundary conditions. The solution of the more general equations are obtained for thermoelastic coupling. The frequency equation of Rayleigh waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular media which determines Rayleigh waves velocity as a real part and the attenuation coefficient as an imaginary part, and the effects of rotation, magnetic field, initial stress, viscosity, and gravity field on Rayleigh waves velocity and attenuation coefficient of surface waves have been studied in detail. Dispersion curves are computed numerically for a specific model and presented graphically. Some special cases have also been deduced. The results indicate that the effect of rotation, magnetic field, initial stress, and gravity field is very pronounced.
MSC:
| 74J99 | Waves in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74E30 | Composite and mixture properties |
References:
| [1] | N. Oshima, “A symmetrical stress tensor and its application to a granular medium,” in Proceedings of the 3 rd Japan National congress for Applied Mechanics, vol. 77, pp. 77-83, 1955. |
| [2] | A. M. El-Naggar, “On the dynamical problem of a generalized thermoelastic granular infinite cylinder under initial stress,” Astrophysics and Space Science, vol. 190, no. 2, pp. 177-190, 1992. · Zbl 0755.73039 · doi:10.1007/BF00644845 |
| [3] | N. C. Dawan and S. K. Chakraporty, “On Rayleigh waves in Green-Lindsay model of generalized thermoelastic media,” Indian Journal Pure and Applied Mathematics, vol. 20, pp. 276-283, 1998. |
| [4] | A. M. Abd-Alla, H. A. H. Hammad, and S. M. Abo-Dahab, “Rayleigh waves in a magnetoelastic half-space of orthotropic material under influences of initial stress and gravity field,” Applied Mathematics and Computation, vol. 154, no. 2, pp. 583-597, 2004. · Zbl 1078.74018 · doi:10.1016/S0096-3003(03)00767-7 |
| [5] | A. M. El-Naggar, A. M. Abd-Alla, and S. M. Ahmed, “Rayleigh waves in a magnetoelastic initially stressed conducting medium with the gravity field,” Bulletin of the Calcutta Mathematical Society, vol. 86, no. 3, pp. 243-248, 1994. · Zbl 0813.73016 |
| [6] | S. M. Ahmed, “Rayleigh waves in a thermoelastic granular medium under initial stress,” International Journal of Mathematics and Mathematical Sciences, vol. 23, no. 9, pp. 627-637, 2000. · Zbl 0963.74031 · doi:10.1155/S0161171200002155 |
| [7] | A. M. Abd-Alla and S. M. Ahmed, “Rayleigh waves in an orthotropic thermoelastic medium under gravity and initial stress,” Earth, Moon and Planets, vol. 75, pp. 185-197, 1998. · Zbl 0882.73021 · doi:10.1007/BF02592996 |
| [8] | A. M. Abd-Alla and S. R. Mahmoud, “Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model,” Meccanica, vol. 45, no. 4, pp. 451-462, 2010. · Zbl 1258.74055 · doi:10.1007/s11012-009-9261-8 |
| [9] | M. Venkatesan and P. Ponnusamy, “Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section immersed in a fluid,” International Journal of Mechanical Sciences, vol. 49, no. 6, pp. 741-751, 2007. · doi:10.1016/j.ijmecsci.2006.10.003 |
| [10] | S. K. Roychoudhuri and N. Bandyopadhyay, “Thermoelastic wave propagation in a rotating elastic medium without energy dissipation,” International Journal of Mathematics and Mathematical Sciences, no. 1, pp. 99-107, 2005. · Zbl 1127.74327 · doi:10.1155/IJMMS.2005.99 |
| [11] | J. N. Sharma and D. Grover, “Body wave propagation in rotating thermoelastic media,” Mechanics Research Communications, vol. 36, no. 6, pp. 715-721, 2009. · Zbl 1258.74118 · doi:10.1016/j.mechrescom.2009.03.005 |
| [12] | A. M. El-Naggar, A. M. Abd-Alla, M. A. Fahmy, and S. M. Ahmed, “Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder,” Heat and Mass Transfer, vol. 39, no. 1, pp. 41-46, 2002. · doi:10.1007/s00231-001-0285-4 |
| [13] | M. R. Abd-El-Salam, A. M. Abd-Alla, and H. A. Hosham, “A numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite-difference method,” Applied Mathematical Modelling, vol. 31, no. 8, pp. 1662-1670, 2007. · Zbl 1136.78004 · doi:10.1016/j.apm.2006.05.009 |
| [14] | S. Mukhopadhyay, “Effects of thermal relaxations on thermoviscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary,” Journal of Thermal Stresses, vol. 23, no. 7, pp. 675-684, 2000. |
| [15] | A. M. Abd-Alla, “Propagation of Rayleigh waves in an elastic half-space of orthotropic material,” Applied Mathematics and Computation, vol. 99, no. 1, pp. 61-69, 1999. · Zbl 0926.74050 · doi:10.1016/S0096-3003(97)10170-9 |
| [16] | Masa. Tanaka, T. Matsumoto, and M. Moradi, “Application of boundary element method to 3-D problems of coupled thermoelasticity,” Engineering Analysis with Boundary Elements, vol. 16, no. 4, pp. 297-303, 1995. |
| [17] | W. Nowacki, Thermoelasticity, Addison-Wesley, London, UK, 1962. · Zbl 0227.73009 |
| [18] | M. A. Biot, Mechanics of Incremental Deformations. Theory of Elasticity and Viscoelasticity of Initially Stressed Solids and Fluids, Including Thermodynamic Foundations and Applications to Finite Strain, John Wiley & Sons, New York, NY, USA, 1965. |
| [19] | P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, NY, USA, 1953. · Zbl 0051.40603 |
| [20] | A. M. Abd-Alla, S. M. Abo-Dahab, H. A. Hammad, and S. R. Mahmoud, “On generalized magneto-thermoelastic rayleigh waves in a granular medium under the influence of a gravity field and initial stress,” Journal of Vibration and Control, vol. 17, no. 1, pp. 115-128, 2011. · Zbl 1271.74239 · doi:10.1177/1077546309341145 |
| [21] | J. N. Sharma and M. Pal, “Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate,” International Journal of Engineering Science, vol. 42, no. 2, pp. 137-155, 2004. · Zbl 1211.74136 · doi:10.1016/S0020-7225(03)00282-9 |
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