Analysis of Reflection Phenomena in a Fiber Reinforced Piezo-Thermoelastic Half Space with Diffusion and Two-Temperature
Subject Areas : EngineeringK Jain 1 , S Kumar 2 , S Deswal 3
1 - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, Haryana, India
2 - Department of Basic and Applied Sciences, BPS Mahila Vishwavidyalaya, Khanpur Kalan, Sonepat-131305, Haryana, India
3 - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, Haryana, India
Keywords:
Abstract :
[1] Biot M.A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[3] Ignaczak J., Ostoja-Starzewski M., 2010, Thermoelasticity with Finite Wave Speeds, Mathematical Monographs, Oxford University Press, Oxford.
[4] Lata P., 2018, Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermo-elastic medium , Structural Engineering and Mechanics 66: 113-124.
[5] Lata P., 2018, Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium, Steel and Composite Structures 27: 439-451.
[6] Lata P., Kaur I., 2019, Plane wave propagation in transversely isotropic magneto-thermoelastic rotating medium with fractional order generalized heat transfer, Structural Monitoring and Maintenance-An International Journal 6: 191-218.
[7] Lata P., Kaur I., 2019, Thermomechanical interactions due to time harmonic sources in a transversely isotropic magneto thermoelastic solids with rotation, International Journal of Microstructure and Materials Properties 14: 549-577.
[8] Mindlin R.D., 1961, On the Equations of Motion of Piezoelectric Crystals, Problems of Continuum Mechanics, N.I. Muskelishvili’s Birthday 70, SIAM, Philadelphia 1961: 282-290.
[9] Nowacki W., 1978, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses 1: 171-182.
[10] Nowacki W., 1979, Foundations of Linear Piezoelectricity, Parkus H., (Ed.), Electromagnetic Interactions in Elastic Solids, Springer, Wien, Chapter 1.
[11] Nowacki W., 1983, Mathematical Models of Phenomenological Piezoelectricity, New problems in Mechanics of Continua, University of Waterloo Press, Ontario 1983: 29-49.
[12] Chandrasekharaiah D.S., 1984, A temperature rate dependent theory of piezoelectricity, Journal of Thermal Stresses 7: 293-306.
[13] Chandrasekharaiah D.S., 1988, A generalized linear thermoelasticity theory of piezoelectric media, Acta Mechanica 71: 39-49.
[14] Sharma J.N., Walia V., Gupta S.K., 2008, Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space, International Journal of Engineering Science 46: 131-146.
[15] Kuang Z.B., Yuan X.G., 2011, Reflection and transmission of waves in pyroelectric and piezoelectric materials, Journal of Sound and Vibration 330: 1111-1120.
[16] Yuan X., Jiang Q., 2016, Reflection of plane waves from rotating pyroelectric half-space under initial stresses, Zeitschrift für Angewandte Mathematik und Mechanik 97: 365-374.
[17] Vashishth A.K., Sukhija H., 2015, Reflection and transmission of plane waves from fluid- piezothermo- elastic solid interface, Applied Mathematics and Mechanics 36: 11-36.
[18] Othman M.I.A., Ahmed E.A.A., 2019, Exact analytical solution of a homogeneous anisotropic piezo- thermoelasic half-space of a hexagonal type under different fields with three theories, Microsystem Technologies 25: 1423-1435.
[19] Pipkin A.C., 1973, Finite Deformations of Ideal Fiber-Reinforced Composites, Sendeckyj G.P., (Ed.), Composites Materials, Academic Press, New York 2: 251-308.
[20] Rogers T.G., 1975, Anisotropic Elastic and Plastic Materials, Thoft Christensen P., (Ed.), Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics, Reidel, Dordrecht 1975: 177-200.
[21] Belfield A.J., Rogers T.G., Spencer A.J.M., 1983, Stress in elastic plates reinforced by fiber lying in concentric circles, Journal of the Mechanics and Physics of Solids 31: 25-54.
[22] Singh S.S., Tomar S.K., 2007, Shear waves at a corrugated interface between two dissimilar fiber reinforced elastic half spaces, Journal of Mechanics of Materials and Structures 2: 167-188.
[23] Abbas I.A., Abd-Alla A.N., Othman M.I.A., 2011, Generalized magnetothermoelasticity in a fiber-reinforced anisotropic half-space, International Journal of Thermophysics 32: 1071-1085.
[24] Said S.M., Othman M.I.A., 2016, Effects of gravitational and hydrostatic initial stress on a two-temperature fiber-reinforced thermoelastic medium for three-phase-lag, Journal of Solid Mechanics 8: 806-822.
[25] Deswal S., Sheokand S.K., Kalkal K.K., 2019, Reflection at the free surface of fiber-reinforced thermoelastic rotating medium with two-temperature and phase-lag, Applied Mathematical Modelling 65: 106-119.
[26] Lata P., Kaur I., 2020, Thermomechanical interactions in transversely isotropic magneto-thermoelastic medium with fractional order generalized heat transfer and hall current, Arab Journal of Basic and Applied science 27: 13-26.
[27] Chen P.J., Gurtin M.E., 1968, On a theory of heat conduction involving two temperatures, Zeitschrift für Angewandte Mathematik und Physik 19: 614-627.
[28] Chen P.J., Gurtin M.E., Williams W.O., 1968, A note on non-simple heat conduction, Zeitschrift für Angewandte Mathematik und Physik 19: 969-970.
[29] Chen P.J., Gurtin M.E., Williams W.O., 1969, On the thermodynamics of non-simple elastic material with two temperatures, Zeitschrift fur angewandte Mathematik und Physik 20: 107-112.
[30] Youssef H.M., 2006, Theory of two-temperature generalized thermoelasticity, IMA Journal of Applied Mathematics 71: 383-390.
[31] Youssef H.M., Bassiouny E., 2008, Two-temperature generalized thermopiezoelasticity for one dimensional problems—State space approach, Computational Methods in Science and Technology 14: 55-64.
[32] Islam M., Kanoria M., 2014, One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity, Mathematics and Mechanics of Solids 19: 672-693.
[33] Kaur I., Lata P., 2019, Effect of hall current on propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer, SN Applied Sciences 1: 900.
[34] Lata P., Kaur I., 2019, Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation, Steel & Composite Structures 32: 779-793.
[35] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-I, Bulletin of the Polish Academy of Sciences, Technical Sciences 22: 55-64.
[36] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-II, Bulletin of the Polish Academy of Sciences, Technical Sciences 22: 129-135.
[37] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-III, Bulletin of the Polish Academy of Sciences, Technical Sciences 22: 257-266.
[38] Sherief H.H., Hamza F.A., Saleh H.A., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591-608.
[39] Kuang Z.B., 2010, Variational principles for generalized thermodiffusion theory in pyroelectricity, Acta Mechanica 214: 275-289.
[40] Kumar R., Chawla V., 2012, General steady-state solution and Green’s function in orthotropic piezothermoelastic diffusion medium, Archives of Mechanics 64: 555-579.
[41] Kumar R., Sharma P., 2016, Analysis of plane waves in anisotropic piezothermoelastic diffusive medium, Multidiscipline Modeling in Materials and Structures 12: 93-109.
[42] Kaur I., Lata P., 2019, Rayleigh wave popagation in transversely isotropic magneto thermoelastic
medium with three-phase=lag heat transfer and diffusion, International Journal of Mechanical and Materials Engineering 14: 12.
[43] Kansal T., 2019, Fundamental solution in the theory of thermoelastic diffusion materials with double porosity, Journal of Solid Mechanics 11: 281-296.
[44] Bijarnia R., Singh B., 2004, Propagation of plane waves in an isotropic two-temperature thermoelastic solid half-space with diffusion, Annals of Solid and Structural Mechanics 6: 37-45.