Impact of Memory-dependent Response of a Thermoelastic Thick Solid Cylinder

Document Type : Research Paper

Author

Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, 441210, India

Abstract

An internal heat source is assumed to act on a cylindrical body with radiation-like boundary conditions to explore the memory-dependent thermoelastic response of a solid object. The top and bottom surfaces of the solid cylinder are subjected to additional heating conditions. To obtain the thermal behaviour of the considered medium, the integral transform method is used, while the inversion solution of the heat transfer equation, the thermoelastic displacement and stress functions are presented in the Laplace domain due to the complexity of the calculation. To understand the numerical calculations, the material properties of aluminium metal are taken into account, and all the obtained results are presented graphically.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Oldham, K.B., Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.
[2] Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Amsterdam, 1993.
[3] Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley–Blackwell, New York, 1993.
[4] Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
[5] Diethelm, K., The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
[6] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
[7] Povstenko, Y.Z., Fractional heat conduction equation and associated thermal stresses, Journal of Thermal Stresses, 28(1), 2005, 83–102.
[8] Povstenko, Y.Z., Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation, International Journal of Solids and Structures, 44(7–8), 2007, 2324–2348.
[9] Povstenko, Y.Z., Thermoelasticity which uses fractional heat conduction equation, Mathematical Methods and Physicomechanical Fields, 51(2), 2008, 239–246.
[10] Povstenko, Y.Z., Fractional radial diffusion in a cylinder, Journal of Molecular Liquids, 137(1–3), 2008, 46–50.
[11] Povstenko, Y.Z., Thermoelasticity which uses fractional heat conduction equation, Journal of Mathematical Sciences, 162, 2009, 296–305.
[12] Povstenko, Y.Z., Theory of thermoelasticity based on the space-time-fractional heat conduction equation, Physica Scripta, 136, 2009, 014017-1-6.
[13] Lamba, N.K., Thermosensitive response of a functionally graded cylinder with fractional order derivative, International Journal of Applied Mechanics and Engineering, 27(1), 2022, 107-124.
[14] Lamba, N.K., Deshmukh, K.C., Hygrothermoelastic response of a finite solid circular cylinder, Multidiscipline Modeling in Materials and Structures, 16(1), 2020, 37-52.
[15] Lamba, N.K., Deshmukh, K.C., Hygrothermoelastic response of a finite hollow circular cylinder, Waves in Random and Complex Media, 2022, doi: 10.1080/17455030.2022.2030501.
[16] Thakare, S., Warbhe, M.S., Lamba, N.K., Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses, International Journal of Thermodynamics, 23(4), 2020, 281-302.
[17] Wang J.L., Li, H.F., Surpassing the fractional derivative: Concept of the memory-dependent derivative, Computers and Mathematics with Applications, 62, 2011, 1562–1567.
[18] Ahmed, S.K., Ezzat, M.A., Modified Fourier's Law with Time-Delay and Kernel Function: Application in Thermoelasticity, Journal of Thermal Stresses, 38(7), 2015, 811-834.
[19] Sun, W.W., Wang, J.L., Reconstruct the Heat Conduction Model with Memory Dependent Derivative, Applied Mathematics, 9, 2018, 1072-1080.
[20] Xue, Z.N., Chen, Z.T., Tian, X.G., Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model, Theoretical and Applied Fracture Mechanics, 96, 2018, 123–133.
[21] Ma, Y., Gao, Y., Dynamic response of a hollow cylinder subjected to thermal shock considering scale effect and memory dependent effect, Mechanics of Advanced Materials and Structures, 29(25), 2022, 4468-4477.
[22] Marchi, E., Fasulo, A., Heat conduction in sector of hollow cylinder with radiation, Atti della Reale Accademia delle scienze di Torino, 1, 1967, 373-382.
[23] Ozisik, M.N., Boundary Value Problems of Heat Conductions, International text book Company, Scranton, Pennsylvania, 1986.
[24] Noda, N., Hetnarski, R.B., Tanigawa, Y., Thermal stresses, Second ed., Taylor and Francis, New York, 2003.
[25] Kumar, R., Lamba N.K., Varghese, V., Analysis of thermoelastic disc with radiation conditions on the curved surfaces, Materials Physics and Mechanics, 16, 2013, 175-186.
[26] Marin M., Contributions on uniqueness in thermoelastodynamics on bodies with voids, Ciencias Matematicas (Havana), 16(2), 1998, 101-109.
[27] Marin M., A temporally evolutionary equation in elasticity of micropolar bodies with voids, UPB Scientific Bulletin, Series A: Applied Mathematics Physics, 60(3-4), 1998, 3-12.
[28] Kamdi, D., Lamba, N.K., Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field, Journal of Applied and Computational Mechanics, 2(2), 2016, 118-127.
[29] Manthena, V.R., Lamba, N.K., Kedar, G.D., Springbackward Phenomenon of a Transversely Isotropic Functionally Graded Composite Cylindrical Shell, Journal of Applied and Computational Mechanics, 2(3), 2016, 134-143.
[30] Varghese, V., An Analysis of Thermal-Bending Stresses in a Simply Supported Thin Elliptical Plate, Journal of Applied and Computational Mechanics, 4(4), 2018, 299-309.
[31] Abouelregal, A.E., Moustapha, M.V., Nofal, T.A., Rashid, S., Ahmad, H., Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay, Results in Physics, 20, 2021, 103705.
[32] Abouelregal, A.E., Sedighi, H.M., Faghidian, S.A., Shirazi, A.H., Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load, Facta Universitatis, Series: Mechanical Engineering, 19(4), 2021, 633-656.
[33] Abouelregal, A.E., Atta, D., Sedighi, H.M., Vibrational behavior of thermoelastic rotating nanobeams with variable thermal properties based on memory-dependent derivative of heat conduction model, Archive of Applied Mechanics, 93, 2023, 197–220.
[34] Abouelregal, A.E., Askar, S.S., Marin, M., Badahiould M., The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod, Scientific Reports, 13, 2023, 9052.
[35] Atta, D., Thermal Diffusion Responses in an Infinite Medium with a ‎Spherical Cavity using the Atangana-Baleanu Fractional ‎Operator, Journal of Applied and Computational Mechanics, 8(4), 2022, 1358-1369.