Browse > Article
http://dx.doi.org/10.12989/sem.2020.74.3.341

Time harmonic interactions in non local thermoelastic solid with two temperatures  

Lata, Parveen (Department of Basic and applied Sciences, Punjabi University Patiala)
Singh, Sukhveer (Punjabi University APS Neighbourhood Campus)
Publication Information
Structural Engineering and Mechanics / v.74, no.3, 2020 , pp. 341-350 More about this Journal
Abstract
The present investigation is concerned with two dimensional deformation in a non local thermoelastic solid with two temperatures due to time harmonic sources. The nonlocal thermoelastic solid is homogeneous with the effect of two temperature parameters. Fourier transforms are used to solve the problem. The bounding surface is subjected to concentrated and distributed sources. The analytical expressions of displacement, stress components and conductive temperature are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of nonlocal parameter and frequency on the components of displacements, stresses and conductive temperature. Some special cases are also deduced from the present investigation.
Keywords
thermoelasticity; nonlocality; nonlocal theory of thermoelasticity; Eringen model of nonlocal theories; two temperature; time harmonic sources;
Citations & Related Records
Times Cited By KSCI : 43  (Citation Analysis)
연도 인용수 순위
1 Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysus of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.   DOI
2 Kroner, E. (1967), "Elasticity theory of materials with long range cohesive forces", J. Solids Struct., 3, 731-742. https://doi.org/10.1016/0020-7683(67)90049-2.   DOI
3 Kumar, R., Sharma, N. and Lata, P. (2016a), "Thermomechanical interactions in the transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Modelling, 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.   DOI
4 Kumar, R., Sharma, N. and Lata, P. (2016b), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091.   DOI
5 Lata, P and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33(1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.   DOI
6 Lata, P. (2018a), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113.   DOI
7 Lata, P. (2018b), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(2), 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
8 Marin, M. (1997), "An uniqueness result for body with voids in linear thermoelasticity", Rendiconti di Matematica, Roma, 17(7), 103-113.
9 Marin, M. (2010), "Lagrange identity method for microstretch thermoelastic materials", J. Math. Anal. Appl., 363(1), 275-286. https://doi.org/10.1016/j.jmaa.2009.08.045.   DOI
10 Marin, M. and Craciun, E.M. (2017), "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials", Compos Part B Eng., 126, 27-37. https://doi.org/10.1016/j.compositesb.2017.05.063.   DOI
11 Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by the Lagrange's identity", Boundary Value Problems, 135, 1-14. https://doi.org/10.1186/1687-2770-2013-135.
12 Marin, M., Baleanu, D. and Vlase, S. (2017), "Effect of microtemperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61(3), 381-387. https://doi.org/10.12989/sem.2017.61.3.381.   DOI
13 Marin, M., Ellahi, R. and Chirila, A. (2017b), "On solutions of saint-venant's problem for elastic dipolar bodies with voids", Carpathian J. Math., 33(2), 219-232. www.jstor.org/stable/90017791.   DOI
14 Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.   DOI
15 Artan, R. (1996), "Nonlocal elastic half plane loaded by a concentrated force", J. Eng. Sci., 34(8), 943-950. https://doi.org/10.1016/0020-7225(95)00132-8.   DOI
16 Mokhtar, Y., Heireche, H., Bousahla, A. A., Houari, M.S.A, Tounsi, A. and Mahmoud S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.   DOI
17 Othman, M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a non-homogeneous isotropic hollow cylinder with energy dissipation", J. Thermophys., 33, 913-923. https://doi.org/10.1007/s10765-012-1202-4.   DOI
18 Othman, M.I.A. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory", Results Phys., 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.012.   DOI
19 Abbas, I.A. and Zenkour, A.M. (2014), "Two temperature generalized thermoelastic interaction in an infinite fibre- reinforced anisotropic plate containing a circular cavity with two relaxation times", J. Comput. Theoretical Nanosci., 11(1), 1-7. https://doi.org/10.1166/jctn.2014.3309.   DOI
20 Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.   DOI
21 Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized thermo-microstretch elastic solid", J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9.   DOI
22 Belkorissat, I., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new non-local refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.   DOI
23 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.   DOI
24 Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory" Adv. Aircraft Spacecraft Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.   DOI
25 Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fibre-reinforced magneto-thermoelastic medium with three-phase-lag-model", Struct. Eng. Mech., 57(2), 201-220. https://doi.org/10.12989/sem.2016.57.2.201.   DOI
26 Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan A. (2015), "The effect of rotation on plane waves in generalized thermo-microstretch elastic solid for a mode-I crack under green naghdi theory", J. Comput. Theoretical Nanosci. ,12(11), 4987-4997. https://doi.org/10.1166/jctn.2015.4022.   DOI
27 Polizzotto, C. (2001), "Nonlocal elasticity and related variational principles", J. Solids Struct., 38, 7359-7380. https://doi.org/10.1016/S0020-7683(01)00039-7.   DOI
28 Press W.H., Teukolshy S.A., Vellerling W.T. and Flannery B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge, United Kingdom.
29 Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.   DOI
30 Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.   DOI
31 Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.   DOI
32 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.   DOI
33 Boutaleb, S., Benrahou, K.A., Bakora, A., Bousahla, A.A, Tounsi, A., Tounsi, A. and Mahmoud, S.R.. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.189.
34 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.   DOI
35 Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys., 19, 614-627. https://doi.org/10.1007/BF01594969.
36 Soleimani, A., Dastani, K., Hadi, A. and Naei, M.H. (2019), "Effect of out of plane defects on the postbuckling behaviour of graphene sheets based on nonlocal elasticity theory", Steel Compos. Struct., 30(6), 517-534. https://doi.org/10.12989/scs.2019.30.6.517.   DOI
37 Sharma, N., Kumar, R. and Lata, P. (2015), "Thermomechanical response of transversely isotropic thermoelastic solids with two temperature and without energy dissipation due to time harmonic sources", Mater. Phys. Mech., 22, 107-117. www.ipme.ru/e-journals/MPM/no_22215/MPM222_02_kumar.html.
38 Sharma, N., Kumar, R. and Ram, P. (2008), "Dynamical behavior of generalized thermoelastic diffusion with two relaxation times in frequency domain", Struct. Eng. Mech., 28(1), 19-38. https://doi.org/10.12989/sem.2008.28.1.039.   DOI
39 Simsek, M. (2011), "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal timoshenko beam theory", Steel Compos. Struct., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059.   DOI
40 Ebrahimi, F and Shafiei, N. (2016), "Application of eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837.   DOI
41 Edelen, D.G.B, Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Rational Mech. Anal., 43, 36-44. https://doi.org/10.1007/BF00251543.   DOI
42 Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Rational Mech. Anal., 43, 24-35. https://doi.org/10.1007/BF00251543.   DOI
43 Eringen, A.C. (2002), Nonlocal Continum Field Theories, Springer, New York, USA.
44 Hassan, M., Marin, M., Ellahi, R. and Almari, S.Z. (2018), "Exploration of convective heat transfer and flow characteristics synthesis by Cu-Ag/water hybrid-nanofluids", Heat Transfer Res., 49(18), 1837-1848. https://doi.org/ 10.1615/HeatTransRes.2018025569.   DOI
45 Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.   DOI
46 Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.   DOI
47 Vasiliev, V.V. and Lurie, S.A. (2016), "On correct nonlocal generalized theories of elasticity", Physical Mesomechanics, 19(3), 47-59. https://doi.org/10.1134/S102995991603005X.
48 Wang, J. and Dhaliwal, R.S. (1993), "On some theorems in the nonlocal theory of micropolar elasticity", J. Solids Struct., 30(10), 1331-1338. https://doi.org/10.1016/0020-7683(93)90215-S.   DOI
49 Youssef, H.M. (2005), "Theory of two-temperature-generalized thermoelasticity", IMA J. Appl. Math., 71, 383-390. https://doi.org/10.1093/imamat/hxh101.   DOI
50 Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.   DOI
51 Karami, B., Janghorban, M. and Tounsi, A. (2019b),"Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
52 Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.   DOI
53 Youssef, H.M. and Al-Lehaibi, E.A. (2007), "State space approach of two-temperature generalized thermoelasticity of one-dimensional problem", J. Solids Struct., 44, 1550-1562. https://doi.org/10.1016/j.ijsolstr.2006.06.035.   DOI
54 Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.   DOI