Thermoelastic Interactions in a Rotating Infinite Orthotropic Elastic Body with a Cylindrical Hole and Variable Thermal Conductivity

• Autorzy: Mashat D. S. , Zenkour A. M. , Abouelregal A. E.

Identyfikatory

DOI

10.1515/meceng-2017-0028

• Języki publikacji: EN

Abstrakty

EN

In the present article, we introduced a new model of the equations of generalized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.

Słowa kluczowe

EN

thermoelasticity; phase lags; rotation; orthotropic body; cylindrical hole; variable thermal conductivity

PL

termoelastyczność; opóźnienia fazowe; obrót; ciało ortotropowe; otwór cylindryczny; zmienna przewodność cieplna

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. LXIV, nr 4
• Strony: 481--498
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Mashat D. S.

• Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

autor

Zenkour A. M.

• Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
• Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

autor

Abouelregal A. E.

• Department of Mathematics, College of Science and Arts, Aljouf University, Al-Qurayat, Saudi Arabia
• Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Bibliografia

• [1] R. Berman. The thermal conductivity of dielectric solids at low temperatures. Advances in Physics, 2(5):103–140, 1953. doi: 10.1080/00018735300101192.
• [2] M.A. Biot. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3):240–253, 1956. doi: 10.1063/1.1722351.
• [3] H.W. Lord and Y. Shulman. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5):299–309, 1967. doi: 10.1016/0022-5096(67)90024-5.
• [4] A.E. Green and K.A. Lindsay. Thermoelasticity. Journal of Elasticity, 2(1):1–7, 1972. doi: 10.1007/BF00045689.
• [5] A.M. Zenkour. Three-dimensional thermal shock plate problem within the framework of different thermoelasticity theories. Composite Structures, 132:1029–1042, 2015. doi: 10.1016/j.compstruct.2015.07.013.
• [6] A.M. Zenkour. Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions. Microsystem Technologies, 23(1):55–65, 2017. doi: 10.1007/s00542-015-2703-4.
• [7] A.M. Zenkour. Thermoelastic response of a microbeam embedded in visco-Pasternak’s medium based on GN-III model. Journal of Thermal Stresses, 40(2):198–210, 2017. doi: 10.1080/01495739.2016.1249039.
• [8] A.M. Zenkour. Vibration analysis of generalized thermoelastic microbeams resting on visco-Pasternak’s foundations. Advances in Aircraft and Spacecraft Science, 4(3):269–280, 2017. doi: 10.12989/aas.2017.4.3.269.
• [9] D.Y. Tzou. A unified field approach for heat conduction from macro-to micro-scales. Journal of Heat Transfer, 117(1):8–16, 1995. doi: 10.1115/1.2822329.
• [10] A.M. Zenkour. Two-dimensional coupled solution for thermoelastic beams via generalized dual-phase-lags model. Mathematical Modelling and Analysis, 21(3):319–335, 2016. doi: 10.3846/13926292.2016.1157835.
• [11] A.E. Abouelregal. Fractional order generalized thermo-piezoelectric semi-infinite medium with temperature-dependent properties subjected to a ramp-type heating. Journal of Thermal Stresses, 34(11):1139–1155, 2011. doi: 10.1080/01495739.2011.606018.
• [12] A.M. Zenkour and A.E. Abouelregal. Nonlocal thermoelastic vibrations for variable thermal conductivity nanobeams due to harmonically varying heat. Journal of Vibroengineering, 16(8):3665–3678, 2014.
• [13] A.M. Zenkour, A.E. Abouelregal, K.A. Alnefaie, X. Zhang, and E.C. Aifantis. Nonlocal thermoelasticity theory for thermal-shock nanobeams with temperature-dependent thermal conductivity. Journal of Thermal Stresses, 38(9):1049–1067, 2015. doi: 10.1080/01495739.2015.1038490.
• [14] M.A. Ezzat and A.A. El-Bary. Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder. International Journal of Thermal Sciences, 108:62–69, 2016. doi: 10.1016/j.ijthermalsci.2016.04.020.
• [15] A.E. Abouelregal and S.M. Abo-Dahab. Dual phase lag model on magneto-thermoelasticity infinite non-homogeneous solid having a spherical cavity. Journal of Thermal Stresses, 35(9):820–841, 2012. doi: 10.1080/01495739.2012.697838.
• [16] A.E. Abouelregal and S.M. Abo-Dahab. Dual-phase-lag diffusion model for Thomson’s phenomenon on electromagneto-thermoelastic an infinitely long solid cylinder. Journal of Computational and Theoretical Nanoscience, 11(4):1031–1039, 2014. doi: 10.1166/jctn.2014.3459.
• [17] A.E. Abouelregal and A.M. Zenkour. The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium. Chinese Physics B, 22(10):108102, 2013.
• [18] R. Singh and V. Kumar. Eigen value approach to two dimensional problem in generalized magneto micropolar thermoelastic medium with rotation effect. International Journal of Applied Mechanics and Engineering, 21(1):205–219, 2016. doi: 10.1515/ijame-2016-0013.
• [19] C. Xiong and Y. Guo. Effect of variable properties and moving heat source on magnetothermoelastic problem under fractional order thermoelasticity. Advances in Materials Science and Engineering, 2016:5341569, 2016. doi: 10.1155/2016/5341569.
• [20] R. Kumar, K. Singh, and D. Pathania. Interactions due to hall current and rotation in a magneto-micropolar fractional order thermoelastic half-space subjected to ramp-type heating. Multidiscipline Modeling in Materials and Structures, 12(1):133–150, 2016. doi: 10.1108/MMMS-03-2015-0016.
• [21] H.H. Sherief and F.A. Hamza. Modeling of variable thermal conductivity in a generalized thermoelastic infinitely long hollow cylinder. Meccanica, 51(3):551–558, 2016. doi: 10.1007/s11012-015-0219-8.
• [22] A.M. Zenkour and A.E. Abouelregal. Effects of phase-lags in a thermoviscoelastic orthotropic continuum with a cylindrical hole and variable thermal conductivity. Archives of Mechanics, 67(6):457–475, 2015.
• [23] A.M. Zenkour and A.E. Abouelregal. Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat. Earthquakes and Structures, 10(3):681–697, 2016. doi: 10.12989/eas.2016.10.3.681.
• [24] A.M. Zenkour. Effect of temperature-dependent physical properties on nanobeam structures induced by ramp-type heating. KSCE Journal of Civil Engineering, 21(5):1820–1828, 2017. doi: 10.1007/s12205-016-1004-5.
• [25] J.N. Sharma and V. Walia. Effect of rotation on Rayleigh waves in piezothermoelastic half space. International Journal of Solids and Structures, 44(3):1060–1072, 2007. doi: 10.1016/j.ijsolstr.2006.06.005.
• [26] S.G. Lekhnitskij. Theory of the Elasticity of Anisotropic Bodies. Mir Publishers, Mocow, 1981.
• [27] B.A. Boley and J.H.Weiner. Theory of Thermal Stresses. John Wiley & Sons, New York, 1960.
• [28] F. Szuecs, M. Werner, R.S. Sussmann, C.S.J. Pickles, and H.J. Fecht. Temperature dependence of Young’s modulus and degradation of chemical vapor deposited diamond. Journal of Applied Physics, 86(11):6010–6017, 1999. doi: 10.1063/1.371648.
• [29] O.R. Budaev, M.N. Ivanova, and B.B. Damdinov. Temperature dependence of shear elasticity of some liquids. Advances in Colloid and Interface Science, 104(1):307–310, 2003. doi: 10.1016/S0001-8686(03)00050-2.
• [30] V.V. Rishin, B.A. Lyashenko, K.G. Akinin, and G.N. Nadezhdin. Temperature dependence of adhesion strength and elasticity of some heat-resistant coatings. Strength of Materials, 5(1):123–126, 1973. doi: 10.1007/BF00762888.
• [31] S.S. Manson. Behavior of materials under conditions of thermal stress. NACA Technical Report 1170, 1954.
• [32] N. Noda. Thermal stresses in materials with temperature-dependent properties. In R.B. Hetnarski, editor, Thermal Stresses I, chapter 6. North-Holland, Amsterdam, 1986.
• [33] G. Honig and U. Hirdes. A method for the numerical inversion of Laplace transforms. Journal of Computational and Applied Mathematics, 10(1):113–132, 1984. doi: 10.1016/0377-0427(84)90075-X.
• [34] D.Y. Tzou. Macro-To Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, Washington DC, 1996.
• [35] J.C. Misra, N.C. Chattopadhyay, and S.C. Samanta. Study of the thermoelastic interactions in an elastic half space subjected to a ramp-type heating – A state-space approach. International Journal of Engineering Science, 34(5):579–596, 1996. doi: 10.1016/0020-7225(95)00128-X.

Uwagi

EN

1. This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. G-199-130-36.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).