Rayleigh Wave Propagation With Rotation, Two Temperature With Diffusion in Context to Dual Phase Lag Thermoelasticity
DOI:
https://doi.org/10.26713/cma.v14i3.2398Keywords:
Generalized thermoelasticity, Rayleigh Wave (RW), Rotation, 2-temperature, Diffusion, Wave speed, Dual-Phase Lag (DPL), Secular equationAbstract
In the present paper, the theory of generalized thermoelasticity projected by Lord and Shulman (LS) [29] is used to originate the frequency equation for Rayleigh Wave (RW) through rotating isotropic Dual Phase Lag (DPL) with 2-temperature thermo-elastic medium with diffusion. The methodology of surface wave solution is deployed to solve these equation, further these equations are summarized to isotropic case in xz-plane. The characteristic equation related to speed of Rayleigh Wave (RW) is also obtained in context to the suitable boundary conditions and is solved for half space using programming. Some significant results are also concluded in the present study in a half space. The effects of various parameters in the present problem such as 2-temperature, rotation, dual phase lag, frequency and diffusion on the wave speed of Rayleigh wave is depicted by graph.
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E. A. A. Ahmed, M. S. Abou-Dina and A. F. Ghaleb, Magnetic field effect on piezo-thermoelastic wave propagation in a half-space within dual-phase-lag, Indian Journal of Physics 95 (2021), 1101 – 1111, DOI: 10.1007/s12648-020-01779-3.
E. A. A. Ahmed, M. S. Abou-Dina and A. R. El Dhaba, Effect of gravity on piezo-thermoelasticity within the dual-phase-lag model, Microsystem Technologies 25 (2019), 1 – 10, DOI: 10.1007/s00542-018-3959-2.
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range, The Journal of the Acoustical Society of America 28 (1956), 168 – 178, DOI: 10.1121/1.1908239.
M. A Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range, The Journal of the Acoustical Society of America 28 (1956), 179 – 191, DOI: 10.1121/1.1908241.
M. A. Biot, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27 (1956), 240 – 253, DOI: 10.1063/1.1722351.
P. Chadwick, Thermoelasticity, the dynamical theory, in: Progress in Solid Mechanics, 2nd edition, I. N. Sneddon and R. Hill (editors), Vol. 1, North-Holland Publishing Co., Amsterdam, pp. 263 – 328 (1960).
P. Chadwick and D. W. Windle, Propagation of Rayleigh waves along isothermal and insulated boundaries, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 280 (1964), 47 – 71, DOI: 10.1098/rspa.1964.0130.
D. S. Chandrasekharaiah, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews 51 (1998), 705 – 729, DOI: 10.1115/1.3098984.
P. J. Chen and M. E. Gurtin, On a theory of heat conduction involving two temperatures, Zeitschrift für angewandte Mathematik und Physik ZAMP 19 (1968), 614 – 627, DOI: 10.1007/BF01594969.
P. J. Chen and W. O. Williams, A note on non-simple heat conduction, Zeitschrift für angewandte Mathematik und Physik ZAMP 19 (1968), 969 – 970, DOI: 10.1007/BF01602278.
P. J. Chen, M. E. Gurtin and W. O. Williams, On the thermodynamics of non-simple elastic materials with two temperatures, Zeitschrift für angewandte Mathematik und Physik ZAMP 20 (1969), 107 – 112, DOI: 10.1007/BF01591120.
H. Deresiewicz, A note on thermoelastic rayleigh waves, Journal of the Mechanics and Physics of Solids 9(3) (1961), 191 – 195, DOI: 10.1016/0022-5096(61)90017-5.
A. S. El-Karamany and M. A. Ezzat, On the dual-phase-lag thermoelasticity theory, Meccanica 49 (2014), 79 – 89, DOI: 10.1007/s11012-013-9774-z.
M. A. Ezzat, A. S. El-Karamany and A. A. El-Bary, On dual-phase-lag thermoelasticity theory with memory-dependent derivative, Mechanics of Advanced Materials and Structures 24(11) (2017), 908 – 916, DOI: 10.1080/15376494.2016.1196793.
M. A. Ezzat, A. S. El-Karamany and S. M. Ezzat, Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer, Nuclear Engineering and Design 252 (2012), 267 – 277, DOI: 10.1016/j.nucengdes.2012.06.012.
M. Fabrizio and B. Lazzari, Stability and Second Law of Thermodynamics in dual-phase-lag heat conduction, International Journal of Heat and Mass Transfer 74 (2014), 484 – 489, DOI: 10.1016/j.ijheatmasstransfer.2014.02.027.
A. E. Green, A note on linear thermoelasticity, Mathematika 19(1) (1972), 69 – 75, DOI: 10.1112/S0025579300004952.
A. E. Green and K. A. Lindsay, Thermoelasticity, Journal of Elasticity 2 (1972), 1 – 7, DOI: 10.1007/BF00045689.
A. E. Green and P. M. Naghdi, Thermoelasticity without energy dissipation, Journal of Elasticity 31 (1993), 189 – 208, DOI: 10.1007/BF00044969.
M. E. Gurtin and W. O. Williams, An axiomatic foundation for continuum thermodynamics, Archive for Rational Mechanics and Analysis 26 (1967), 83 – 117, DOI: 10.1007/BF00285676.
M. E. Gurtin and W. O. Williams, On the Clausius-Duhem inequality, Zeitschrift für angewandte Mathematik und Physik ZAMP 17 (1966), 626 – 633, DOI: 10.1007/BF01597243.
A. Hobiny and I. Abbas, Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model, International Journal of Numerical Methods for Heat & Fluid Flow 30(11) (2020), 4865 – 4881, DOI: 10.1108/HFF-12-2019-0917.
D. Ie¸san, On the linear coupled thermoelasticity with two temperatures, Zeitschrift für angewandte Mathematik und Physik ZAMP 21 (1970), 583 – 591, DOI: 10.1007/BF01587687.
J. Ignaczak, Uniqueness in generalized thermoelasticity, Journal of Thermal Stresses 2 (1979), 171 – 175, DOI: 10.1080/01495737908962399.
A. D. Kovalenko, Fundamentals of thermoelasticity, Strength of Materials 3 (1971), 1134 – 1135, DOI: 10.1007/BF01527541.
S. Kumari, Bharti and B. Singh, Effects of two-temperature on rayleigh wave in generalized magneto-thermoelastic media with hydrostatic initial stress, ASME Journal of Heat and Mass Transfer 141(7) (2019), 072002, DOI: 10.1115/1.4043677.
Z. Liu and R. Quintanilla, Time decay in dual-phase-lag thermoelasticity: Critical case, Communications on Pure and Applied Analysis 17(1) (2018), 177 – 190, DOI: 10.3934/cpaa.2018011.
F .J. Lockett, Effect of thermal properties of a solid on the velocity of Rayleigh waves, Journal of the Mechanics and Physics of Solids 7(1) (1958), 71 – 75, DOI: 10.1016/0022-5096(58)90040-1.
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15 (1967), 299 – 309, DOI: 10.1016/0022-5096(67)90024-5.
M. F. McCarthy, Wave propagation in generalized thermoelasticity, International Journal of Engineering Science 10(7) (1972), 593 – 602, DOI: 10.1016/0020-7225(72)90085-7.
S. Mondal, N. Sarkar and N. Sarkar, Waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity, Journal of Thermal Stresses 42 (2019), 1035 – 1050, DOI: 10.1080/01495739.2019.1591249.
R. Quintanilla, On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures, Acta Mechanica 168 (2004), 61 – 73, DOI: 10.1007/s00707-004-0073-6.
R. Quintanilla and R. Racke, A note on stability in dual-phase-lag heat conduction, International Journal of Heat and Mass Transfer 49(7-8) (2006), 1209 – 1213, DOI: 10.1016/j.ijheatmasstransfer.2005.10.016.
R. Quintanilla and R. Racke, Qualitative aspects in dual-phase-lag thermoelasticity, SIAM Journal on Applied Mathematics 66(3) (2006), 977 – 1001, DOI: 10.1137/05062860X.
H. H. Sherief, F. A. Hamza and H. A. Saleh, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42(5-6) (2004), 591 – 608, DOI: 10.1016/j.ijengsci.2003.05.001.
B. Singh, Wave propagation in dual-phase-lag anisotropic thermoelasticity, Continuum Mechanics and Thermodynamics 25 (2013), 675 – 683, DOI: 10.1007/s00161-012-0261-x.
B. Singh, S. Kumari and J. Singh, Propagation of the rayleigh wave in an initially stressed transversely isotropic dual-phase-lag magnetothermoelastic half-space, Journal of Engineering Physics and Thermophysics 87 (2014), 1539 – 1547, DOI: 10.1007/s10891-014-1160-8.
D. Y. Tzou, A unified field approach for heat conduction from macro- to micro-scales, ASME Journal of Heat and Mass Transfer 117(1) (1995), 8 – 16, DOI: 10.1115/1.2822329.
D. Y. Tzou, Macro- to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons, Ltd., (2014), DOI: 10.1002/9781118818275.
W. E. Warren and P. J. Chen, Wave propagation in the two temperature theory of thermoelasticity, Acta Mechanica 16 (1973), 21 – 33, DOI: 10.1007/BF01177123.
H. M. Youssef, Theory of two-temperature thermoelasticity without energy dissipation, Journal of Thermal Stresses 34(2) (2011), 138 – 146, DOI: 10.1080/01495739.2010.511941.
H. M. Youssef, Theory of two-temperature-generalized thermoelasticity, IMA Journal of Applied Mathematics 71(3) (2006), 383 – 390, DOI: 10.1093/imamat/hxh101.
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