Effect of phase-lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium. (English) Zbl 1480.74162
Summary: The present article deals with Rayleigh surface wave propagation in homogeneous magneto-thermoelastic orthotropic medium. Effect of initial stress and magnetic field on Rayleigh waves is studied in the context of three-phase-lag model of generalized thermoelasticity. The normal mode analysis is used to obtain the exact expressions for the displacement components, stresses and temperature distribution. Various frequency equations are derived and compared with the existing literature. The path of surface particles is elliptical during Rayleigh wave propagation. Effect of phase-lags on Rayleigh wave velocity, attenuation coefficient and specific loss are presented graphically. It is observed from graphical presentation that the effect of magnetic field and initial stress on different wave characteristics is pronounced.
MSC:
| 74J15 | Surface waves in solid mechanics |
Keywords:
Rayleigh waves; magnetic field; initial stress; orthotropic medium; three-phase-lag model; path of surface particlesReferences:
| [1] | Rayleigh, W. S., On waves propagating along the plane surface of an elastic solid, Proc. Land. Math. Soc., 17, 4-11 (1887) · JFM 17.0962.01 |
| [2] | Victorov, I. A., Rayleigh and Lamb waves: Physical Theory and Applications (1967), Plenum Press: Plenum Press New York |
| [3] | Reinhardt, H. W.; Dally, J. W., Some characteristics of Rayleigh wave interaction with surface flaws, Mater. Eval., 28, 200-213 (1970) |
| [4] | Richard, M. W., Surface elastic waves, Proc. IEEE, 58, 1278-1281 (1990) |
| [5] | Hetnarski, R. B.; Ignaczak, J., Nonclassical dynamical thermoelasticity, Int. J. Solids Struct., 37, 215-224 (2000) · Zbl 1075.74033 |
| [6] | Cattaneo, C., A form of heat equation which eliminates the paradox of instantaneous propagation, Camptes Rendus de l’ Academie des Sciences serie IIa: Sciences de la Terre et des planets, 247, 431-433 (1958) · Zbl 1339.35135 |
| [7] | Lord, H. W.; Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solid, 15, 299-309 (1967) · Zbl 0156.22702 |
| [8] | Green, A. E.; Lindsay, K. A., Thermoelasticity, J. Elast., 2, 1-7 (1972) · Zbl 0775.73063 |
| [9] | Hetnarski, R. B.; Ignaczak, J., Generalized thermoelasticity: closed form solutions, J. Therm. Stress., 16, 473-498 (1993) |
| [10] | Hetnarski, R. B.; Ignaczak, J., Soliton like waves in a low temperature non-linear thermoelastic solid, Int. J. Eng. Sci., 34, 1767-1787 (1996) · Zbl 0914.73016 |
| [11] | Green, A. E.; Naghdi, P. M., Thermoelasticity without energy dissipation, J. Elast., 31, 189-208 (1993) · Zbl 0784.73009 |
| [12] | Tzou, D. Y., A unique field approach for heat conduction from macro to micro scales, ASME J. Heat Transf., 117, 8-16 (1995) |
| [13] | Roychoudhuri, S. K., On a thermoelastic three phase lag model, J. Therm. Stress., 30, 231-238 (2007) |
| [14] | Abd-Alla, A. M.; Ahmed, S. M., Rayleigh waves in an orthotropic thermoelastic medium under gravity and initial stress, Earth Moon Planets, 75, 185-197 (1996) · Zbl 0882.73021 |
| [15] | Abd-Alla, A. M.; Abo-Dahab, S. M.; Hammad, H. A.H., Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field, Appl. Math. Model., 35, 2981-3000 (2011) · Zbl 1219.74022 |
| [16] | Sharma, J. N.; Kaur, D., Rayleigh waves in rotating thermoelastic solids with voids, Int. J. Appl. Math Mech., 6, 3, 43-61 (2010) |
| [17] | Sharma, J. N.; Kumar, S.; Sharma, Y. D., Effect of micropolarity, microstretch and relaxation times on Rayleigh surface waves in thermoelastic solids, Int. J. of Appl. Math Mech., 5, 2, 17-38 (2009) |
| [18] | Kumar, R.; Chawla, V.; Abbas, I. A., Effect of viscocity in anisotropic thermoelastic medium with three phase lag model, Theor. Appl. Mech., 39, 4, 313-341 (2012) · Zbl 1299.74125 |
| [19] | Kumar, R.; Chawla, V., A study of plane wave propagation in anisotropic three phase lag and two phase lag model, Int. Commun. Heat Mass Transf., 38, 1262-1268 (2011) |
| [20] | Sharma, J. N.; Singh, H., Thermoelastic surface waves in a transversely isotropic half space with thermal relaxations, Indian J. Pure Appl. Math., 16, 10, 1202-1212 (1985) · Zbl 0577.73031 |
| [21] | Singh, B.; Kumari, S.; Singh, J., Propagation of the Rayleigh wave in an initially stressed transversely isotropic dual phase lag magneto-thermoelastic half space, J. Eng. Phys. Thermophys., 87, 6, 1539-1547 (2014) |
| [22] | Singh, B.; Renu, Surface wave propagation in an initially stressed transversely isotropic thermoelastic solid, Adv. Stud. Theor. Phys., 6, 6, 263-271 (2012) · Zbl 1250.74017 |
| [23] | Abo-Dahab, S. M.; Biswas, S., Effect of rotation on Rayleigh waves in magneto-thermoelastic transversely isotropic medium with thermal relaxation times, J. Electromagn. Waves Appl., 31, 1485-1507 (2017) |
| [24] | Biswas, S.; Mukhopadhyay, B.; Shaw, S., Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model, J. Therm. Stress., 40, 4, 403-419 (2017) |
| [25] | Chirita, S., On the Rayleigh waves on an anisotropic homogeneous thermoelastic half space, Acta Mechanica, 224, 657-674 (2013) · Zbl 1401.74149 |
| [26] | Chirita, S.; Ciarletta, M.; Tibullo, V., On the wave propagation in the time differential dual-phase-lag thermoelastic model, Proc. R. Soc. A, 471, Article 20150400 pp. (2015) · Zbl 1371.80014 |
| [27] | Nowinski, J. L., Theory of thermoelasticity with applications, Mech. Surf. Struct. (1978) · Zbl 0379.73004 |
| [28] | Puri, P.; Cowin, S. C., Plane waves in linear elastic materials with voids, J. Elast., 15, 167-183 (1985) · Zbl 0564.73027 |
| [29] | Kolsky, H., Stress Waves in Solids (1963), Dover Press: Dover Press New York · Zbl 0109.43303 |
| [30] | Biswas, S.; Mukhopadhyay, B., Eigenfunction expansion method to analyze thermal shock behavior in magneto-thermoelastic orthotropic medium under three theories, J. Therm. Stress., 41, 3, 366-382 (2018) |
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