The study of vibrations in the context of porous micropolar media thermoelasticity and the absence of energy dissipation
Document Type : Research Paper
Authors
1 Department of Mathematics and Computer Science, Transilvania University of Braşov, B-dul Eroilor nr.29, 500036 Braşov, Romania.
2 Academy of Romanian Scientists, Str. Oltet, nr. 3, 050045 Bucharest, Romania.
3 Romanian Academy Technical Sciences, 030167 Bucharest, Romania.
Abstract
In the present article, the theory of linear thermoelasticity without energy dissipation is addressed from the perspective of the analysis of the spatial evolution of harmonic vibrations in time, in the context of a porous micropolar media. Some preliminary identities are determined that will lead to estimates of the harmonic vibration amplitude, some of these estimates being consequences of the distance influence from the disturbed base, provided that a certain critical value for the vibration frequency is considered.
Keywords
Main Subjects
[1] M. Ciarletta, A. Scalia, Some results in linear theory of thermomicrostretch elastic solids, Meccanica, Vol. 39, pp. 191-206, 2004.
[2] L. F. Codarcea-Munteanu, A. N. Chirilă, M. I. Marin, Modeling fractional order strain in dipolar thermoelasticity, IFAC-PapersOnLine, Vol. 51, No. 2, pp. 601-606, 2018.
[3] L. Codarcea-Munteanu, M. Marin, Influence of Geometric Equations in Mixed Problem of Porous Micromorphic Bodies with Microtemperature, Mathematics, Vol. 8, No. 8, pp. 1386, 2020.
[4] M. Marin, R. Agarwal, L. Codarcea, A mathematical model for three-phase-lag dipolar thermoelastic bodies, Journal of Inequalities and Applications, Vol. 2017, pp. 1-16, 2017.
[5] I. Abbas, A. Hobiny, M. Marin, Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity, Journal of Taibah University for Science, Vol. 14, No. 1, pp. 1369-1376, 2020.
[6] S. M. Abo-Dahab, A. E. Abouelregal, M. Marin, Generalized thermoelastic functionally graded on a thin slim strip non-Gaussian laser beam, Symmetry, Vol. 12, No. 7, pp. 1094, 2020.
[7] D. Chandrasekharaiah, A uniqueness theorem in the theory of elastic materials with voids, Journal of elasticity, Vol. 18, No. 2, pp. 173-179, 1987.
[8] S. Chiriţă, On some exponential decay estimates for porous elastic cylinders, Archives of Mechanics, Vol. 56, No. 3, pp. 233-246, 2004.
[9] L. Codarcea-Munteanu, M. Marin, A study on the thermoelasticity of three-phase-lag dipolar materials with voids, Boundary Value Problems, Vol. 2019, pp. 1-24, 2019.
[10] R. Kumar, S. Mukhopadhyay, Effects of three phase lags on generalized thermoelasticity for an infinite medium with a cylindrical cavity, Journal of Thermal Stresses, Vol. 32, No. 11, pp. 1149-1165, 2009.
[11] R. Kumar, A. K. Vashisth, S. Ghangas, Waves in anisotropic thermoelastic medium with phase lag, two-temperature and void, Mater. Phys. Mech, Vol. 35, No. 1, pp. 126-138, 2018.
[12] M. Marin, Contributions on uniqueness in thermoelastodynamics on bodies with voids, Cienc. Mat.(Havana), Vol. 16, No. 2, pp. 101-109, 1998.
[13] M. Marin, M. I. Othman, S. Vlase, L. Codarcea-Munteanu, Thermoelasticity of initially stressed bodies with voids: a domain of influence, Symmetry, Vol. 11, No. 4, pp. 573, 2019.
[14] M. Alizadeh, M. Choulaei, M. Roshanfar, J. Dargahi, Vibrational characteristic of heart stent using finite element model, International journal of health sciences, Vol. 6, No. S4, pp. 4095-4106, 06/15, 2022.
[15] L. Codarcea-Munteanu, M. Marin, Micropolar thermoelasticity with voids using fractional order strain, Models and Theories in Social Systems, pp. 133-147, 2019.
[16] R. Kumar, P. Kaushal, R. Sharma, Axisymmetric vibration for micropolar porous thermoelastic circular plate, 2017.
[17] M. Marin, Generalized solutions in elasticity of micropolar bodies with voids, Revista de la Academia Canaria de Ciencias:= Folia Canariensis Academiae Scientiarum, Vol. 8, No. 1, pp. 101-106, 1996.
[18] M. Goodman, S. Cowin, A continuum theory for granular materials, Archive for Rational Mechanics and Analysis, Vol. 44, No. 4, pp. 249-266, 1972.
[19] S. C. Cowin, J. W. Nunziato, Linear elastic materials with voids, Journal of elasticity, Vol. 13, pp. 125-147, 1983.
[20] J. W. Nunziato, S. C. Cowin, A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis, Vol. 72, No. 2, pp. 175-201, 1979/06/01, 1979.
[21] D. Ieşan, Mecanica generalizată a solidelor, Univ.„Al. I. Cuza"“Iași, 1980.
[22] D. Ieşan, A theory of thermoelastic materials with voids, Acta Mechanica, Vol. 60, pp. 67-89, 1986.
[23] A. E. Green, P. Naghdi, A re-examination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, Vol. 432, No. 1885, pp. 171-194, 1991.
[24] A. Green, P. Naghdi, Thermoelasticity without energy dissipation, Journal of elasticity, Vol. 31, No. 3, pp. 189-208, 1993.
[25] A. E. Green, P. Naghdi, On thermodynamics and the nature of the second law, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 357, No. 1690, pp. 253-270, 1977.
[26] D. Chandrasekharaiah, A uniqueness theorem in the theory of thermoelasticity without energy dissipation, Journal of Thermal Stresses, Vol. 19, No. 3, pp. 267-272, 1996.
[27] M. Choulaei, A.-H. Bouzid, Stress analysis of bolted flange joints with different shell connections, in Proceeding of, American Society of Mechanical Engineers, pp. V012T12A029.
[28] M. Ciarletta, A theory of micropolar thermoelasticity without energy dissipation, Journal of Thermal Stresses, Vol. 22, No. 6, pp. 581-594, 1999.
[29] L. Nappa, Spatial decay estimates for the evolution equations of linear thermoelasticity without energy dissipation, Journal of thermal stresses, Vol. 21, No. 5, pp. 581-592, 1998.
[30] F. Passarella, V. Zampoli, On the theory of micropolar thermoelasticity without energy dissipation, Journal of Thermal Stresses, Vol. 33, No. 4, pp. 305-317, 2010.
[31] S. Chiriţă, M. Ciarletta, Reciprocal and variational principles in linear thermoelasticity without energy dissipation, Mechanics Research Communications, Vol. 37, No. 3, pp. 271-275, 2010.
[32] M. Marin, A. Seadawy, S. Vlase, A. Chirila, On mixed problem in thermoelasticity of type III for Cosserat media, Journal of Taibah University for Science, Vol. 16, No. 1, pp. 1264-1274, 2022.
[33] D. Chandrasekharaiah, Hyperbolic thermoelasticity: a review of recent literature, 1998.
[34] R. Quintanilla, Existence in thermoelasticity without energy dissipation, Journal of thermal stresses, Vol. 25, No. 2, pp. 195-202, 2002.
[35] M. Marin, A. Chirilă, L. Codarcea, S. Vlase, On vibrations in Green-Naghdi thermoelasticity of dipolar bodies, Analele ştiinţifice ale Universităţii" Ovidius" Constanţa. Seria Matematică, Vol. 27, No. 1, pp. 125-140, 2019.
[36] I. A. Abbas, Generalized magneto-thermoelastic interaction in a fiber-reinforced anisotropic hollow cylinder, International Journal of Thermophysics, Vol. 33, pp. 567-579, 2012.
[37] E. M. Abo-Eldahab, R. Adel, H. M. Mobarak, M. Abdelhakem, The effects of magnetic field on boundary layer nano-fluid flow over stretching sheet, Appl Math Inf Sci, Vol. 15, No. 6, pp. 731-741, 2021.
[38] M. I. Othman, M. Fekry, M. Marin, Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating, Struct. Eng. Mech, Vol. 73, No. 6, pp. 621-629, 2020.
[39] A. M. Zenkour, I. A. Abbas, Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method, Journal of Vibration and Control, Vol. 20, No. 12, pp. 1907-1919, 2014.
[40] S. Chirită, Spatial decay estimates for solutions describing harmonic vibrations in a thermoelastic cylinder, Journal of thermal stresses, Vol. 18, No. 4, pp. 421-436, 1995.
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Volume 54, Issue 3
September 2023Pages 437-454
- Receive Date: 20 September 2023
- Accept Date: 20 September 2023