Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University) ;
  • Abouelregal, Ahmed E. (Department of Mathematics, Faculty of Science, Mansoura University)
  • Received : 2013.09.22
  • Accepted : 2014.04.04
  • Published : 2014.07.25
⟨ Previous Next ⟩

Abstract

The present investigation is concerned with the effect of two temperatures on functionally graded (FG) nanobeams subjected to sinusoidal pulse heating sources. 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 FG nanobeam is fully ceramic whereas the lower surface is fully metal. The generalized two-temperature nonlocal theory of thermoelasticity in the context of Lord and Shulman's (LS) model is used to solve this problem. The governing equations are solved in the Laplace transformation domain. The inversion of the Laplace transformation is computed numerically using a method based on Fourier series expansion technique. Some comparisons have been shown to estimate the effects of the nonlocal parameter, the temperature discrepancy and the pulse width of the sinusoidal pulse. Additional results across the thickness of the nanobeam are presented graphically.

Keywords

References

  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. https://doi.org/10.1016/j.compstruct.2012.08.046
  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, 629-640. https://doi.org/10.1006/jsvi.2000.3383
  3. Biot, M. (1956), "Thermoelasticity and irreversible thermo-dynamics", J. Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351
  4. Boley, B.A. (1972), "Approximate analyses of thermally induced vibrations of beams and plates", J. Appl Mech., 39, 212-216. https://doi.org/10.1115/1.3422615
  5. Boley, M. (1956), "Thermoelastic and irreversible thermo dynamics", J. Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351
  6. Chen, P.J., Gurtin, M.E. and Willams, W.O. (1969), "On the thermodynamics of non-simple Elastic material with two temperatures", Z. Angew Math. Phys., 20, 107-112. https://doi.org/10.1007/BF01591120
  7. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", Z. Angew Math. Phys., 19, 614-627. https://doi.org/10.1007/BF01594969
  8. 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, 381-393. https://doi.org/10.1016/j.compstruct.2005.02.021
  9. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  10. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  11. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  12. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast. 2, 1-7. https://doi.org/10.1007/BF00045689
  13. Kidawa-Kukla, J. (2003), "Application of the Green functions to the problem of the thermally induced vibration of a beam", J. Sound Vib., 262, 865-876. https://doi.org/10.1016/S0022-460X(02)01133-1
  14. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  15. Malekzadeh, P., Golbahar Haghighi, M.R. and Heydarpour, Y. (2012), "Heat transfer analysis of functionally graded hollow cylinders subjected to an axisymmetric moving boundary heat flux", Numer. Heat Trans., Part A: Appl., 61(8), 614-632. https://doi.org/10.1080/10407782.2012.670587
  16. Malekzadeh, P. and Heydarpour, Y. (2012), "Response of functionally graded cylindrical shells under moving thermo-mechanical loads", Thin Wall. Struct., 58, 51-66. https://doi.org/10.1016/j.tws.2012.04.010
  17. Malekzadeh, P. and Shojaee, A. (2014), "Dynamic response of functionally graded beams under moving heat source", J. Vib. Control, 20(6), 803-814. https://doi.org/10.1177/1077546312464990
  18. Manolis, G.D. and Beskos, D.E. (1980), "Thermally induced vibrations of beam structures", Comput. Meth. Appl. Mech. Eng., 21, 337-355. https://doi.org/10.1016/0045-7825(80)90101-2
  19. 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.
  20. Quintanilla, R. (2004a), "Exponential stability and uniqueness in thermoelasticity with two temperatures", Ser. A Math. Anal., 11, 57-68.
  21. Quintanilla, R. (2004b), "On existence, structural stability, convergence and spatial behavior in thermoelastic with two temperature", Acta Mech., 168, 161-173.
  22. Tzou, D. (1996), Macro-to-Micro Heat Transfer, Taylor & Francis, Washington, D.C.
  23. Wang, Q. and Wang, C.M. (2007), "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes", Nanotech., 18, 075702. https://doi.org/10.1088/0957-4484/18/7/075702
  24. Warren, W.E. and Chen, P.J. (1973), "Wave propagation in the two temperature theory of thermoelasticity", Acta Mech., 16, 21-23. https://doi.org/10.1007/BF01177123
  25. Zenkour, A.M. and Abouelregal, A.E. (2014), "State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction", Zeitschr. Angew. Math. Phys. (ZAMP), 65(1), 149-164.
  26. Zenkour, A.M. (2006), "Steady-state thermoelastic analysis of a functionally graded rotating annular disk", Int. J. Struct. Stab. Dyn., 6, 1-16. https://doi.org/10.1142/S0219455406001800
  27. Zenkour, A.M. (2014) "On the magneto-thermo-elastic responses of FG annular sandwich disks", Int. J. Eng. Sci. 75, 54-66. https://doi.org/10.1016/j.ijengsci.2013.11.001

Cited by

  1. Laser Pulse Heating of a Semi-Infinite Solid Based on a Two-Temperature Theory with Temperature Dependence 2017, https://doi.org/10.1142/S2251237317500083
  2. Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat vol.10, pp.3, 2016, https://doi.org/10.12989/eas.2016.10.3.681
  3. Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux vol.18, pp.4, 2015, https://doi.org/10.12989/scs.2015.18.4.909
  4. Effect of temperature-dependent physical properties on nanobeam structures induced by ramp-type heating vol.21, pp.5, 2017, https://doi.org/10.1007/s12205-016-1004-5
  5. Effect of ramp-type heating on the vibration of functionally graded microbeams without energy dissipation vol.23, pp.5, 2016, https://doi.org/10.1080/15376494.2015.1007186
  6. Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions vol.23, pp.1, 2017, https://doi.org/10.1007/s00542-015-2703-4
  7. A hybrid inverse method for small scale parameter estimation of FG nanobeams vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.1119
  8. Vibrational Analysis for an Axially Moving Microbeam with Two Temperatures vol.38, pp.6, 2015, https://doi.org/10.1080/01495739.2015.1015837
  9. A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment vol.18, pp.5, 2016, https://doi.org/10.1177/1099636216652581
  10. Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating vol.27, pp.3, 2017, https://doi.org/10.1080/17455030.2016.1262974
  11. Thermoelastic Vibration of an Axially Moving Microbeam Subjected to Sinusoidal Pulse Heating vol.15, pp.06, 2015, https://doi.org/10.1142/S0219455414500813
  12. Response of thermoelastic microbeams to a periodic external transverse excitation based on MCS theory 2017, https://doi.org/10.1007/s00542-017-3589-0
  13. Vibration analysis of a single-layered graphene sheet embedded in visco-Pasternak’s medium using nonlocal elasticity theory vol.18, pp.4, 2016, https://doi.org/10.21595/jve.2016.16585
  14. Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis vol.229, pp.9, 2018, https://doi.org/10.1007/s00707-018-2172-9
  15. Fractional viscoelastic Voigt’s model for initially stressed microbeams induced by ultrashort laser heat source pp.1745-5049, 2019, https://doi.org/10.1080/17455030.2018.1554927
  16. Thermoviscoelastic orthotropic solid cylinder with variable thermal conductivity subjected to temperature pulse heating vol.13, pp.2, 2014, https://doi.org/10.12989/eas.2017.13.2.201
  17. Variability of thermal properties for a thermoelastic loaded nanobeam excited by harmonically varying heat vol.20, pp.4, 2014, https://doi.org/10.12989/sss.2017.20.4.451
  18. Two-temperature thermoelastic surface waves in micropolar thermoelastic media via dual-phase-lag model vol.4, pp.6, 2017, https://doi.org/10.12989/aas.2017.4.6.711
  19. Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory vol.64, pp.6, 2014, https://doi.org/10.12989/sem.2017.64.6.683
  20. Thermoviscoelastic response of an axially loaded beam under laser excitation and resting on Winkler’s foundation vol.15, pp.6, 2019, https://doi.org/10.1108/mmms-11-2018-0200
  21. On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory vol.142, pp.2, 2014, https://doi.org/10.1115/1.4045241
  22. Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects vol.7, pp.2, 2014, https://doi.org/10.12989/aas.2020.7.2.169
  23. A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams vol.9, pp.1, 2014, https://doi.org/10.12989/amr.2020.9.1.033
  24. Dynamic characteristics of initially stressed viscoelastic microbeams induced by ultra-intense lasers vol.94, pp.6, 2014, https://doi.org/10.1007/s12648-019-01530-7
  25. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201
  26. Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative vol.13, pp.18, 2014, https://doi.org/10.3390/ma13183953
  27. Vibration of multilayered functionally graded deep beams under thermal load vol.24, pp.6, 2014, https://doi.org/10.12989/gae.2021.24.6.545