Transient Dynamic Response of a Semi-infinite Elastic Permeable Solid with Cylindrical Hole Subject to Laser Pulse Heating Under Different Theories of Generalized Thermoelasticity
DOI:
https://doi.org/10.13052/ejcm1779-7179.29469Keywords:
Magneto-thermo-elasticity, thermo-elastic-diffusion, cylindrical cavity, non-gaussian laser pulse, three phase lagAbstract
Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole. The temporal scheme of laser beam is considered as non-Gaussian and is acted on the surface of the cylindrical hole. The problem is solved with the help of Laplace transform domain and finally illustrated graphically.
Note: This article will be very useful in material science specially, in powder metallurgy during sintering, hot pressing, wire and rods annealing are examined from a unified physical point of view, in different branches of engineering physics like plasma physics, nuclear physics, geophysics and related topics and also in oil industry (Lyashenko and Hryhorova (2014), Long and Heng-Wei (2018), Fryxell and Aitken (1969), Nowinski (1978), Legros et al. (1998), Galliero et al. (2019) etc.).
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References
Biot, M. (1956). Thermo-elasticity and irreversible thermo-dynamics. Journal of Applied Physics, 27(3), 240–253. doi:10.1063/1.1722351.
Lord, H., and Shulman, Y. (1967). A generalized dynamical theory of thermo-elasticity. Journal of Mechanics and Physics of Solids, 15(5), 299–309. doi:10.1016/0022-5096(67)90024-5.
Green, A. E., & Lindsay, K. A. (1972). Thermoelasticity. Journal of Elasticity, 2(1), 1–7. doi:10.1007/BF00045689.
Hetnarski, R. B., & Ignaczak, J. (1996). Soliton-like waves in a low temperature and nonlinear thermoelastic solid. International Journal of Engineering Science, 34(15), 1767–1787. doi:10.1016/S0020-7225(96)00046-8.
Green, A. E., & P. M. Naghdi. (1991). A re-examination of the basic postulates of thermomechanics. Proceedings of the Royal Society of London A, 432, 171–94. doi:10.1098/rspa.1991.0012.
Green, A. E., & P. M. Naghdi. (1992). On undamped heat waves in an elastic solid. Journal of Thermal Stresses, 15, 253–64. doi:10.1080/01495739208946136.
Green, A. E., & P. M. Naghdi. (1993). Thermoelasticity without energy dissipation, Journal of Elasticity, 31, 189–208. doi:10.1007/BF00044969.
Tzou, D. Y. (1995). A unified field approach for heat conduction from macro-to micro scales. Journal of Heat Transfer, 117, 8–16. doi:10.1115/1.2822329.
Chandrasekharaiah, D. S. (1998). Hyperbolic thermoelasticity: A review of recent literature. Applied Mechanics Reviews, 51(12), 705–29. doi:10.1115/1.3098984.
Choudhuri, S. K. R. (2007). On a thermoelastic three-phase-lag model. Journal of Thermal Stresses, 30, 231–38. doi:10.1080/01495730601130919.
Sherief, H., & Hamza, F. (1996). Generalized two-dimensional thermo-elastic problems in spherical regions under axisymmetric distributions. Journal of Thermal Stresses, 19(1), 55–76. doi:10.1080/0149573960089 46160.
Sherief, H., & Hamza, F. (1994). Generalized thermo-elastic problem of a thick plate under axisymmetric temperature distribution. Journal of Thermal Stresses, 17(3), 435–452. doi:10.1080/01495739408946271.
Chandrasekharaiah, D. S., & Keshavan, H. R. (1992). Axisymmetric Thermo-elastic Interactions in an Unbounded Body with Cylindrical Cavity. Acta Mechanica, 92(1–4), 61–76. doi:10.1007/BF01174167.
Youssef, H. M. (2006). Problem of Generalized Thermo-elastic Infinite Cylindrical Cavity Subjected to a Ramp-Type Heating and Loading. Archive of Applied Mechanics, 75(8–9), 553–565. doi:10.1007/s00419-005-0440-3.
Mukhopadhyay, S., & Kumar, R. (2008). A Problem on Thermo-elastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermo-elasticity III. Journal of Thermal Stresses, 31(5), 455–475. doi:10.1080/01495730801912561.
Nowinski, J. L. (1978). Theory of thermo-elasticity with applications. Sijthoff & Noordhoff Int., Alphen Aan, Den Rijn.
Nayfeh, A., & Nemat-Nasser, S. (1972). Electro-magneto-thermo-elastic plane waves in solids with thermal relaxation. Journal of Applied Mechanics, 39(1), 108-113. doi:10.1115/1.3422596.
Roy Choudhuri, S. K. (1984). Electro magneto-thermo-elastic plane waves in rotating media with thermal relaxation. International Journal of Engineering Science, 22(5), 519–530.doi:10.1016/0020-7225(84)90054-5.
Sherief, H. H. (1994). Problem in electro-magneto thermo-elasticity for an infinitely long solid conducting circular cylinder with thermal relaxation. International Journal of Engineering Science, 32(7), 1137–1149. doi:10.1016/0020-7225(94)90077-9.
Sherief, H. H., & Youssef, H. M. (2004). Short time solution for a problem in magneto-thermo-elasticity with thermal relaxation. Journal of Thermal Stresses, 27(6), 537–559. doi:10.1080/01495730490451468.
He, T., & Cao, L. (2009). A problem of generalized magneto-thermo-elastic thin slim strip subjected to a moving heat source. Mathematics and Computer Modelling, 49(7–8), 1710–1720. doi:10.1016/j.mcm.2008.12.004.
Baksi, A., Bera, R. K., & Debnath, L. A. (2005). A study of magneto-thermo-elastic problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium. International Journal of Engineering Science, 43(19–20), 1419–1434. doi:10.1016/j.ijengsci.2005.08.002.
McDonald, F. A. (1990). On the precursor in Laser-generated ultrasound waveforms in metals. Applied Physics Letters, 56(3), 230–232. doi:10.1063/1.102839.
Khader, S. E., & Khedr, M. El. M. (2016). A problem in different theories of magneto-thermo-elasticity in cylindrical region with laser pulse, Proceeding of the world congress on engineering, I, WCE 2016, London, U.K.
Abbas, I. A., & Abd Elmaboud, Y. (2015). Analytical solutions of thermoelastic interactions in a hollow cylinder with one relaxation time. Mathematics and Mechanics of Solids, 22(2), 210–223. doi:10.1177/1081286515579308.
Othman, M. I. A., & Eraki, E. E. M. (2016). Generalized magneto-thermoelastic half space with diffusion under initial tress using three phase lag model. Mechanics Based Design of Structures and Machines, doi:10.1080/15397734.2016.1152193
Sherief, H., El-Marhraby, N. M., & Abbas, M. F. (2020). Two dimensional axisymmetric thermoelastic problem for an infinite space with a cylindrical heat source of a different material under Green-Lindsy theory. Mechanics Based Design of Structures and Machines, doi:10.1080/15397734.2020.1807361
Nowacki, W. (1974a). Dynamical problems of thermodiffusion in solids I. Bulletin of the Polish Academy of Sciences: Technical Sciences, 22, 55–64.
Nowacki, W. (1974b). Dynamical problems of thermodiffusion in solids II. Bulletin of the Polish Academy of Sciences: Technical Sciences, 22, 129–135.
Nowacki, W. (1974c). Dynamic problems of thermo-elastic diffusion in solids III. Bulletin of the Polish Academy of Sciences: Technical Sciences, 22, 266–275.
Nowacki, W. (1976). Dynamic problems of diffusion in solids. Engineering Fracture Mechanics, 8(1), 261–266. doi:10.1016/0013-7944(76)90 091-6.
Sherief, H. H., F. Hamza, & H. A. Saleh. (2004). The theory of generalized thermoelastic diffusion. International Journal of Engineering Science, 42(5–6), 591–608. doi:10.1016/j.ijengsci.2003.05.001.
Sherief, H. H., & H. Saleh. (2005). A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15), 4484–93. doi:10.1016/j.ijsolstr.2005.01.001.
Aouadi, M. (2006). Variable electrical and thermal conductivity in the theory of generalized thermo-elastic diffusion. Zeitschrift fr Angewandte Mathematik und Physik (ZAMP), 57(2), 350–366. doi:10.1007/s00033-005-0034-5.
Aouadi, M. (2006). A generalized thermo-elastic diffusion problem for an infinitely long solid cylinder. International Journal of Mathematics and Mathematical Science, 2006, 1–15. doi:10.1155/IJMMS/2006/25976.
Elhagary, M. (2011). Generalized thermo-elastic diffusion problem for an infinitely long hollow cylinder for short times. Acta Mechanica, 218(3–4), 205–215. doi:10.1007/s00707-010-0415-5.
Paul, K., & Mukhopadhyay, B. (2019). Two dimensional generalized magneto-thermo-elastic diffusion problem for a thick plate under laser pulse heating with three phase lag effect. Journal of Engineering Physics and Thermophysics, 92(2), 516–527. doi:10.1007/s10891-019-01959-x.
Paul, K., & Mukhopadhyay, B. (2020). Electromagnetic, thermal and diffusive wave analysis on a two-temperature generalized thermoelastic problem in a semi-infinite solid with cylindrical cavity subject to thermal loads. Journal of Electromagnetic Waves and Applications, 34(17), 2266–2288. doi:10.1080/09205071.2020.1769505.
Tang, D., & Araki, N. (1999). Weavy, wave-like and diffusive thermal responses of finite rigid slab to high speed heating of laser-pulses. International Journal of Heat and Mass Transfer, 42(5), 855–860. doi:10.1016/S0017-9310(98)00244-0.
Wang, X., & Xu, X. (2001). Thermo-elastic Wave Induced by Pulsed Laser Heating. Applied Physics Archives, 73, 107–114. doi:10.1007/s003390 000593.
Wang, X., & Xu, X. (2002). Thermo-elastic Wave in Metal Induced by Ultrafast Laser Pulses. Journal of Thermal Stresses, 25(5), 457–473. doi:10.1080/01495730252890186.
Sun, Y., Fang, D., Saka, M., & Soh, A. (2008). Laser-Induced Vibrations of Micro-Beams under Different Boundary Conditions. International Journal of Solids and Structures, 45(7–8), 1993–2013. doi:10.1016/j.ijsolstr.2007.11.006.
Elhagary, M. A. (2014). A 2-Dimensional thermo-elastic diffusion problem for a thick plate subjected to thermal loading due to laser-pulse. Journal of Thermal Stresses, 37(12), 1416–1432. doi:10.1080/01495739.2014.937256.
Li, Y., & He, T. (2020). The transient response of a functionally graded half-space heated by a laser pulse based on the generalized thermoelasticity with memory dependent derivatives, Mechanics of Advanced Material and Structures, doi:10.1080/15376494.2020.1731888.
Sur, A., & Kanoria, M. (2015). Three phase lag elasto-thermo-diffusive response in an elastic solid under hydrostatic pressure. International Journal of advances in Applied Mathematics and Mechanics, 3(2):121–137.
He, T., & Li, C. (2014). Normal Mode Analysis to a Two-Dimensional Generalized electro-magneto-thermo-elastic problem with diffusion. Journal of Thermal Stresses, 37(10), 1244-1263. doi:10.1080/01495739.2014. 936213.
Honig, G., & Hirdes, U. (1984). A method for the numerical inversion of the Laplace Transform. Journal of Computation and Applied Mathematics, 10(1), 113–132. doi:10.1016/0377-0427(84)90075-X.
Amin, M. M., Alla-Nasr, A. M. A., El-Bary, A. A., & Abo-Dahab, S. M. (2020). Propagation of surface waves in generalized thermoelastic media under influence of magnetic field and rotation and its application in engineering and geophysics. Mechanics Based Design and Structures and Machines, doi:10.1080/15397734.2020.1804934.
Sur, A., Mondal, S., & Kanoria, M. (2019). Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field. Mechanics Based Design and Structures and Machines, doi:10.1080/15397734.2019.1672558.
Shaw, S., & Mukhopadhyay, B. (2015). Analysis of Rayleigh surface wave propagation in isotropic micropolar solid under three phase lag model of thermoelasticity. European Journal of Computational Mechanics, doi:10.1080/17797179.2015.1074012
Said, S. M., & Othman, M. I. A. (2015). Influence of the mechanical force and the magnetic field on fiber-reinforced medium for three phase lag model. European Journal of Computational Mechanics, doi:10.1080/17797179.2015.1137751.
Lyashenko, V., & Hryhorova, T. (2014). Generalized mathematical model of thermal diffusion in powder metallurgy. Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc. 1629, 85–93, doi:10.1063/1.4902262.
Long, Z., & Heng-Wei, Z. (2018). Sintering driving force of Al2O3
powder at the initial stage of pulse electric current sintering under thermoelastic diffusion. International Journal of Mechanics and Mathematical Engineering, doi:10.1186/s40712-018-0095-9.
Fryxel, R. A., & Aitken E. A. (1969). High temperature studies of Uranium in a thermal gradient. Journal of Nuclear Materials, doi:10.1016/0022-3115(69)90167-6.
Legros, J. C., D’arcy, H., & Francosis, M. (1998). Measurement of soret coefficients of crude oil in microgravity. Space technology and application international forum-1998, AIP Conference Proceedings, doi:10.1063/1.54944.
Galliero, G., Bataller, H., Bazile, J. P., & Diaz, J. (2019). SCCO: Thermaldiffusion for the oil and gas industry. In book, Physical Science under microgravity: Experiments on Board the SJ-10 Recordable Stellite, doi:n10.1007/978-981.
Nowinski, J. (1978). The theory of thermoelasticity with applications. Mechanics of Surface Structure. Alphen den Rijn: Sijtho and Noordhoff International Publishers. ISBN: 978-94-009-9931-2.
