Abstract
Purpose:
The objective of the present work is to study the disturbances in a rotating microelongated thermoelastic solid half-space with two temperature and temperature dependent properties. The problem has been modeled by employing Lord-Shulman and Green-Lindsay theories to carry out the investigation.
Methods:
To explore the impact of inclined mechanical load on microelongated thermoelastic half space, normal mode technique has been applied and the analytical expressions for the displacement components, stresses, temperature fields and microelongation are obtained.
Results:
In order to illustrate the analytical results, the numerical solution is carried out for aluminum epoxy like material. Influences of rotation, two temperatures, temperature dependent properties and time on the physical quantities are analyzed for Green-Lindsay theory.
Conclusions:
Theoretical and numerical results show the significant dependence of physical fields under consideration on rotation, elongation parameter, temperature dependent properties, two temperature parameter and inclination angle. Also the results of the present study have been compared with the previously published results for validation.
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References
Lord HW, Shulman YA (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309. https://doi.org/10.1016/0022-5096(67)90024-5
Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7. https://doi.org/10.1007/BF00045689
Kumar A, Shivay ON, Mukhopadhyay S (2019) Infinite speed behavior of two-temperature Green-Lindsay thermoelasticity theory under temperature-dependent thermal conductivity. Z Angew Math Phys 70:1–16. https://doi.org/10.1007/s00033-018-1064-0
Sheoran SS, Chaudhary S, Deswal S (2021) Thermo-mechanical interactions in a nonlocal transversely isotropic material with rotation under Lord-Shulman model. Waves Random Complex Media 16:1–25. https://doi.org/10.1080/17455030.2021.1986648
Sadeghi M, Kiani Y (2022) Generalized magneto-thermoelasticity of a layer based on the Lord-Shulman and Green-Lindsay theories. J Therm Stresses 45:319–340. https://doi.org/10.1080/01495739.2022.2038745
Eringen AC, Suhubi E (1964) Nonlinear theory of simple micro-elastic solids-I. Int J Eng Sci 2:189–203. https://doi.org/10.1016/0020-7225(64)90004-7
Eringen AC (1999) Theory Of Micropolar Elasticity. Springer, New York, In Microcontinuum Field Theories. https://doi.org/10.1007/978-1-4612-0555-5_5
Eringen AC (1971) Micropolar elastic solids with stretch. Ari Kitabevi Matbassi 24:1–18
Eringen AC (1990) Theory of thermomicrostretch elastic solids. Int J Eng Sci 28:1291–1301. https://doi.org/10.1016/0020-7225(90)90076-U
Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15:909–923
Eringen AC (1966) Theory of micropolar fluids. J Math Mech 15:1–18. https://www.jstor.org/stable/24901466
Kiris A, Inan E (2005) Eshelby tensors for a spherical inclusion in microelongated elastic fields. Int J Eng Sci 43:49–58. https://doi.org/10.1016/j.ijengsci.2004.06.002
Shaw S, Mukhopadhyay B (2012) Periodically varying heat source response in a functionally graded microelongated medium. Appl Math Comput 218:6304–6313. https://doi.org/10.1016/j.amc.2011.11.109
Shaw S, Mukhopadhyay B (2013) Moving heat source response in a thermoelastic microelongated solid. J Eng Phys Thermophys 86:716–722. https://doi.org/10.1007/s10891-013-0887-y
Sachdeva SK, Ailawalia P (2015) Plane strain deformation in thermoelastic microelongated solid. Civil Environ Res 7:92–98. https://doi.org/10.1515/ijame-2015-0047
Othman MIA, Atwa SY, Eraki EEM, Ismail MF (2021) The initial stress effect on a micro-elongated solid under the dual-phase-lag model. Appl Phys A 127:1–8. https://doi.org/10.1007/s00339-021-04809-x
Hilal MIM (2021) Thermodynamic modeling of a laser pulse heating in a rotating microelongated nonlocal thermoelastic solid due to GN theory. J Appl Math Mech 102:e202100285. https://doi.org/10.1002/zamm.202100285
Sharma A, Ailawalia P (2022) Two-dimensional analysis of functionally graded thermoelastic microelongated solid. Int J Appl Mech Eng 27:155–169. https://doi.org/10.2478/ijame-2022-0056
Othman MIA, Atwa SY, Eraki EEM, Ismail MF (2023) The effect of rotation on thermoelastic microelongated medium under DPL model. Appl Math Comput 7:1–14. https://doi.org/10.26855/jamc.2023.03.001
Chen PJ, Gurtin ME (1968) On a theory of heat conduction involving two temperatures. Z Angew Math Phys 19:614–627. https://doi.org/10.1007/BF01594969
Chen PJ, Gurtin ME, Williams WO (1968) A note on non-simple heat conduction. Z Angew Math Phys 19:969–970. https://doi.org/10.1007/BF01602278
Chen PJ, Gurtin ME, Williams WO (1969) On the thermodynamics of non-simple elastic materials with two temperatures. Z Angew Math Phys 20:107–112. https://doi.org/10.1007/BF01591120
Warren WE, Chen PJ (1973) Wave propagation in the two temperature theory of thermoelasticity. Acta Mech 16:21–33. https://doi.org/10.1007/BF01177123
Youssef HM (2006) Theory of two-temperature-generalized thermoelasticity. IMA J Appl Math 71:383–390. https://doi.org/10.1093/imamat/hxh101
Abouelregal AE, Moaaz O, Khalil KM, Abouhawwash M, Nasr ME (2023) A phase delay thermoelastic model with higher derivatives and two temperatures for the Hall current effect on a micropolar rotating material. J Vibrat Eng Tech 1–19. https://doi.org/10.1007/s42417-023-00922-8
Lomakin VA (1976) Theory Elasticity Inhomogeneous Bodies. Moscow University, Moscow
Ezzat MA, Othman MIA, El-Karamany AS (2001) The dependence of modulus of elasticity on the reference temperature in generalized thermoelasticity. J Therm Stresses 24:1159–1176. https://doi.org/10.1080/014957301753251737
Othman MIA (2003) State-space approach to generalized thermoelasticity plane waves with two relaxation times under dependence of the modulus of elasticity on reference temperature. Can J Phys 81:1403–1418. https://doi.org/10.1139/p03-100
Aouadi M (2006) Temperature dependence of an elastic modulus in generalized linear micropolar thermoelasticity. Z Angew Math Phys 57:1057–1074. https://doi.org/10.1007/s00033-005-0055-0
Othman MIA, Elmaklizi YD, Said SM (2013) Generalized thermoelastic medium with temperature-dependent properties for different theories under the effect of gravity field. Int J Thermophys 34:521–537. https://doi.org/10.1007/s10765-013-1425-z
Othman MIA, Sarkar N, Atwa SY (2013) Effect of fractional parameter on plane waves of generalized magneto-thermoelastic diffusion with reference temperature-dependent elastic medium. Comput Math Appl 65:1103–1118. https://doi.org/10.1016/j.camwa.2013.01.047
Othman MIA, Said SM (2014) 2D problem of magneto-thermoelasticity fiber-reinforced medium under temperature dependent properties with three-phase-lag model. Meccanica 49:1225–1241. https://doi.org/10.1007/s11012-014-9879-z
Mamen B, Bouhadra A, Bourada F, Bourada M, Tounsi A, Mahmoud SR, Hussain M (2022) Combined effect of thickness stretching and temperature-dependent material properties on dynamic behavior of imperfect FG beams using three variable quasi-3D model. J Vibrat Eng Tech. https://doi.org/10.1007/s42417-022-00704-8
Khader SE, Marrouf AA, Khedr M (2023) Influence of electromagnetic generalized thermoelasticity interactions with nonlocal effects under temperature dependent properties in a solid cylinder. Mech Adv Compos Struct 10:157–166. https://doi.org/10.22075/macs.2022.28137.1429
Schoenberg M, Censor D (1973) Elastic waves in a rotating media. Q Appl Math 31:115–125. https://doi.org/10.1090/qam/99708
Othman MIA (2005) Effect of rotation and relaxation time on a thermal shock problem for a half-space in generalized thermo-viscoelasticity. Acta Mech 174:129–143. https://doi.org/10.1007/s00707-004-0190-2
Bijarnia R, Singh B (2016) Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids. Int J Appl Mech Eng 21:285–301. https://doi.org/10.1515/ijame-2016-0018
Abo-Dahab SM, Abd-Alla AM, Alqarni AJ (2017) A two-dimensional problem with rotation and magnetic field in the context of four thermoelastic theories. Results Phys 7:2742–2751. https://doi.org/10.1016/j.rinp.2017.07.017
Bayones FS, Abd-Alla AM (2018) Eigenvalue approach to coupled thermoelasticity in a rotating isotropic medium. Results Phys 8:7–15. https://doi.org/10.1016/j.rinp.2017.09.021
Deswal S, Punia BS, Kalkal KK (2019) Propagation of waves at an interface between a transversely isotropic rotating thermoelastic solid half space and a fiber-reinforced magneto-thermoelastic rotating solid half space. Acta Mech 230:2669–2686. https://doi.org/10.1007/s00707-019-02418-7
Othman MIA, Zidan MEM, Hilal MIM (2014) Effect of gravitational field and temperature dependent properties on two-temperature thermoelastic medium with voids under GN theory. Comput, Materials Continua 40:179–201. https://doi.org/10.3970/cmc.2014.040.179
Othman MIA, Atwa SY, Eraki EEM, Ismail MF (2022) Dual-phase-lag model on microelongated thermoelastic rotating medium. J Eng Therm Sci 2:13–26. https://doi.org/10.21595/jets.2022.22597
Funding
One of the authors, Ms. Pooja Kadian has received financial support from University Grant Commission, New Delhi, India, Vide Letter No. F.16-6(DEC. 2018)/2019(NET/CSIR)-Ref. 997/(CSIR-UGC NET DEC. 2018).
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Kadian, P., Kumar, S. & Sangwan, M. Effect of Inclined Mechanical Load on a Rotating Microelongated Two Temperature Thermoelastic Half Space with Temperature Dependent Properties. J. Vib. Eng. Technol. 12, 4053–4074 (2024). https://doi.org/10.1007/s42417-023-01105-1
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DOI: https://doi.org/10.1007/s42417-023-01105-1