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Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space. (English) Zbl 1451.74114

Summary: The paper deals with Rayleigh wave propagation in a nonlocal thermoelastic layer, and the layer is lying over a nonlocal thermoelastic half-space. The problem is treated in the context of Eringen’s nonlocal thermoelasticity and Green-Naghdi model type III of hyperbolic thermoelasticity. The frequency equation of Rayleigh waves is derived, and different cases are also discussed. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss, and penetration depth is presented graphically.

MSC:

74J15 Surface waves in solid mechanics
74F05 Thermal effects in solid mechanics
Full Text: DOI

References:

[1] Eringen, AC, Theory of nonlocal thermoelasticity, Int. J. Eng. Sci., 12, 1063-1077 (1974) · Zbl 0289.73061
[2] Eringen, AC, Memory dependent nonlocal elastic solids, Lett. Appl. Eng. Sci., 2, 3, 145-149 (1974)
[3] Eringen, AC, Edge dislocation on nonlocal elasticity, Int. J. Eng. Sci., 15, 177-183 (1977) · Zbl 0357.73079
[4] Eringen, AC, A mixture theory of electromagnetism and superconductivity, Int. J. Eng. Sci, 36, 5-6, 525-543 (1998) · Zbl 1210.78007
[5] Eringen, AC, Nonlocal Continuum Field Theories (2002), New York: Springer, New York · Zbl 1023.74003
[6] Altan, BS, Uniqueness in the linear theory of nonlocal elasticity, Bull. Tech. Univ. Istanb., 37, 373-385 (1984) · Zbl 0574.73007
[7] Eringen, AC; Edelen, DGB, On nonlocal elasticity, Int. J. Eng. Sci, 10, 233-248 (1972) · Zbl 0247.73005
[8] Eringen, AC, Nonlocal polar elastic continua, Int. J. Eng. Sci., 10, 1-16 (1972) · Zbl 0229.73006
[9] Eringen, AC, On Rayleigh surface waves with small wave lengths, Lett. Appl. Eng. Sci., 1, 11-17 (1973)
[10] Eringen, AC, Plane waves in nonlocal micropolar elasticity, Int. J. Eng. Sci., 22, 1113-1121 (1984) · Zbl 0564.73029
[11] Pramanik, AS; Biswas, S., Surface waves in nonlocal thermoelastic medium with state space approach, J. Therm. Stresses, 43, 6, 667-686 (2020)
[12] Biswas, S., Surface waves in porous nonlocal thermoelastic orthotropic medium, Acta Mech., 231, 2741-2760 (2020) · Zbl 1440.74172
[13] Khurana, A.; Tomar, SK, Wave propagation in nonlocal microstretch solid, Appl. Math. Model., 40, 5885-6875 (2016)
[14] Yu Jun, Y.; Tian, X-G; Liu, X-R, Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity, Eur. J. Mech. A/Sol., 60, 238-253 (2016) · Zbl 1406.74187
[15] Khurana, A.; Tomar, SK, Rayleigh-type waves in nonlocal micropolar solid half space, Ultrasonics, 73, 162-168 (2017)
[16] Biot, M., Thermoelasticity and irreversible Thermoelasticity, J. Appl. Phys., 27, 240-253 (1956) · Zbl 0071.41204
[17] Lord, H.; Shulman, Y., A generalized dynamic theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299-309 (1967) · Zbl 0156.22702
[18] Green, AE; Lindsay, KA, Thermoelasticity, J. Elast., 2, 1-7 (1972) · Zbl 0775.73063
[19] Green, AE; Naghdi, PM, A re-examination of the basic properties of thermomechanics, Proc. R. Soc. Lond. Ser. A, 432, 171-194 (1991) · Zbl 0726.73004
[20] Green, AE; Naghdi, PM, On damped heat waves in an elastic solid, J. Therm. Stress., 15, 252-264 (1992)
[21] Green, AE; Naghdi, PM, Thermoelasticity without energy dissipation, J. Elast., 31, 189-208 (1993) · Zbl 0784.73009
[22] Chandrasekharaih, DS, Hyperbolic thermoelasticity: a review of recent literature, Appl. Mech. Rev., 51, 12, 705-729 (1998)
[23] Ignaczak, J.; Ostoja-Starzewski, M., Thermoelasticity with Finite Wave Speeds (2010), Oxford: Oxford University Press, Oxford · Zbl 1183.80001
[24] Dwan, NC; Chakraborty, SK, On Rayleigh waves in Green-Lindsay’s model of generalized thermoelastic media, Indian J. Pure Appl. Math., 20, 3, 276-283 (1988) · Zbl 0657.73005
[25] Rossikin, YA; Shitikova, MV, Nonstationary Rayleigh waves on the thermally-insulated surfaces of some thermoelastic bodies of revolution, Acta Mech., 150, 1-2, 87-105 (2001) · Zbl 1026.74040
[26] Singh, B.; Kumari, S.; Singh, J., Propagation of the Rayleigh wave in an initially stressed transversely isotropic dual phase lag magnetothermoelastic half space, J. Eng. Phys. Thermophys., 87, 6, 1539-1547 (2014)
[27] 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)
[28] Biswas, S.; Abo-Dahab, SM, Effect of phase-lags on Rayleigh waves in initially stressed magneto-thermoelastic orthotropic medium, Appl. Math. Model., 59, 713-727 (2018) · Zbl 1480.74162
[29] Abd-Alla, AN; Al-Dawy, AAS, Thermal relaxation times effect on Rayleigh waves in generalized thermoelastic media, J. Therm. Stress., 24, 4, 367-382 (2001)
[30] Wojnar, R.: Rayleigh waves in thermoelasticity with relaxation times. In: International Conference on Surface Waves in Plasma and Solids, Ohrid, Yugoslavia, Sept. 5-11, 1985, World Scientific, Singapore, (1986) · Zbl 0605.73009
[31] Biswas, S., Stroh analysis of Rayleigh waves in anisotropic thermoelastic medium, J. Therm. Stress., 41, 5, 627-644 (2018)
[32] Biswas, S.; Mukhopadhyay, B., Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase-lags, Waves Random Complex Media, 29, 4, 722-742 (2019) · Zbl 1505.74104
[33] Singhal, A.; Sahu, SA, Transference of Rayleigh waves in corrugated orthotropic layer over a pre-stressed orthotropic half space with self-weight, Proc. Eng., 173, 972-979 (2017)
[34] Puri, P.; Cowin, SC, Plane waves in linear elastic materials with voids, J. Elast., 15, 167-183 (1985) · Zbl 0564.73027
[35] Kolsky, H., Stress Waves in Solids (1963), New York: Dover Press, New York · Zbl 0109.43303
[36] Nowinski, JL, Theory of Thermoelasticity with Applications (1978), Mechanics of Surface Structures: Sijthoff and Noordhoff International Publishing, Alphen aan den Rijn, Netherlands, Mechanics of Surface Structures · Zbl 0379.73004
[37] Nayfeh, A.; Nemat-Nasser, S., Thermoelastic waves in solids with thermal relaxation, Acta Mech., 12, 53-69 (1971) · Zbl 0241.73026
[38] Agarwal, VK, On surface waves in generalized thermoelasticity, J. Elast., 8, 171-177 (1978) · Zbl 0372.73017
[39] Biswas, S., Fundamental solution of steady oscillations equations in nonlocal thermoelastic medium with voids, J. Therm. Stress., 43, 3, 284-304 (2020)
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