[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/scs.2015.18.4.909

Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux

Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
Abouelregal, Ahmed E. (Department of Mathematics, Faculty of Science, Mansoura University)

Publication Information

Steel and Composite Structures / v.18, no.4, 2015 , pp. 909-924 More about this Journal

Abstract

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

Keywords

thermoelasticity; DPL model; FG nanobeam; nonlocal Euler-Bernoulli theory; heat flux;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Abbas, I.A. and Zenkour, A.M. (2013), "LS model on electro-magneto-thermo-elastic response of an infinite functionally graded cylinder", Compos. Struct., 96, 89-96. DOI ScienceOn
2	Al-Huniti, N.S., Al-Nimr, M.A. and Naij, M. (2001), "Dynamic response of a rod due to a moving heat source under the hyperbolic heat conduction model", J. Sound Vib., 242(4), 629-640. DOI ScienceOn
3	Biot, M. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27, 240-253. DOI
4	Ching, H.K. and Yen, S.C. (2006), "Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply", Compos. Struct., 73(4), 381-393. DOI
5	Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. DOI
6	Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. DOI
7	Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. DOI
8	Fang, D.N., Sun, Y.X. and Soh, A.K. (2006), "Analysis of frequency spectrum of laser-induced vibration of microbeam resonators", Chinese Phys. Lett., 23, 1554-1557. DOI
9	Green, A. and Laws, N. (1972) "On the entropy production inequality", Arch. Rat. Anal., 45(1), 47-53.
10	Green, A.E. and Lindsay, K.A. (1972) "Thermoelasticity", J. Elast., 2(1), 1-7. DOI
11	Green, A.E. and Naghdi, P.M. (1993) "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-209. DOI
12	Kidawa-Kukla, J. (2003), "Application of the Green functions to the problem of the thermally induced vibration of a beam", J. Sound Vib., 262(4), 865-876. DOI ScienceOn
13	Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. DOI
14	Malekzadeh, P. and Shojaee, A. (2014), "Dynamic response of functionally graded beams under moving heat source", J. Vib. Control, 20(6), 803-814. DOI
15	Mareishi, S., Mohammadi, M. and Rafiee, M. (2013), "An analytical study on thermally induced vibration analysis of FG beams using different HSDTs", Appl. Mech. Mater., 249-250, 784-791.
16	Mukhopadhyay, S., Prasad, R. and Kumar, R. (2011), "On the theory of two-temperature thermoelasticity with two phase-lags", J. Therm. Stresses, 34(4), 352-365. DOI
17	Muller, I. (1971), "The coldness, a universal function in thermo-elastic solids", Arch. Rat. Mech. Anal., 41(5), 319-332. DOI
18	Prasad, R., Kumar, R. and Mukhopadhyay, S. (2010), "Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags", Int. J. Eng. Sci., 48(12), 2028-2043. DOI
19	Prasad, R., Kumar, R. and Mukhopadhyay, S. (2011), "Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source", Acta Mech., 217(3-4), 243-256. DOI
20	Tzou, D.Y. (1995a), "A unified field approach for heat conduction from macro- to micro-scales", J. Heat Transfer, 117(1), 8-16. DOI
21	Tzou, D.Y. (1995b), "Experimental support for the Lagging behavior in heat propagation", J. Thermophys. Heat Transfer, 9(4), 686-693. DOI
22	Zenkour, A.M. (2014), "On the magneto-thermo-elastic responses of FG annular sandwich disks", Int. J. Eng. Sci., 75, 54-66. DOI ScienceOn
23	Tzou, D.Y. (1996), Macro-to-Microscale Heat Transfer: The Lagging Behavior, Taylor & Francis, Washington, D.C., USA.
24	Wang, Q. and Wang, C.M. (2007), "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes", Nanotech., 18(7), 075702. DOI
25	Zenkour, A.M. (2006), "Steady-state thermoelastic analysis of a functionally graded rotating annular disk", Int. J. Struct. Stab. Dynam., 6(4), 1-16. DOI
26	Zenkour, A.M. and Abouelregal, A.E. (2014a), "The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating", Struct. Eng. Mech., Int. J., 51(2), 199-214. DOI
27	Zenkour, A.M. and Abouelregal, A.E. (2014b), "Effect of harmonically varying heat on FG nanobeams in the context of a nonlocal two-temperature thermoelasticity theory", Eur. J. Comput. Mech., 23(1-2), 1-14.
28	Zenkour, A.M. and Abouelregal, A.E. (2014c), "Vibration of FG nanobeams induced by sinusoidal pulse heating via a nonlocal thermoelastic model", Acta Mech., 225(12), 3409-3421. DOI

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