DOI QR코드

DOI QR Code

Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Shaghaghi, Gholam Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2015.05.17
  • 심사 : 2016.04.30
  • 발행 : 2016.12.25

초록

In this manuscript, the small scale and thermal effects on vibration behavior of preloaded nanobeams with non-ideal boundary conditions are investigated. The boundary conditions are assumed to allow small deflections and moments and the concept of non-ideal boundary conditions is applied to the nonlocal beam problem. Governing equations are derived through Hamilton's principle and then are solved applying Lindstedt-Poincare technique to derive fundamental natural frequencies. The good agreement between the results of this research and those available in literature validated the presented approach. The influence of various parameters including nonlocal parameter, thermal effect, perturbation parameter, aspect ratio and pre-stress load on free vibration behavior of the nanobeams are discussed in details.

키워드

참고문헌

  1. Ansari, R. and Sahmani, S. (2012), "Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models", Commun. Nonlinear Sci. Numer. Simul., 17(4), 1965-1979. https://doi.org/10.1016/j.cnsns.2011.08.043
  2. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimensional Systems and Nanostructures, 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  3. Aydogdu, M. and Ece, M.C. (2006), "Buckling and vibration of non-ideal simply supported rectangular isotropic plates", Mech. Res. Commun., 33(4), 532-540. https://doi.org/10.1016/j.mechrescom.2005.08.002
  4. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S. and Beg, O.A. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Composites Part B: Engineering, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  5. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  6. Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41(22), 225404. https://doi.org/10.1088/0022-3727/41/22/225404
  7. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 029. https://doi.org/10.12989/anr.2015.3.1.029
  8. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  9. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  10. Chang, T.P. (2012), "Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Appl. Math. Model., 36(5), 1964-1973. https://doi.org/10.1016/j.apm.2011.08.020
  11. Civalek, O. and Demir, C. (2011a), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math.Model., 35(5), 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004
  12. Civalek, O. and Demir, C. (2011b), "Buckling and bending analyses of cantilever carbon nanotubes using the euler-bernoulli beam theory based on non-local continuum model", Asian J. Civil Eng. (Building and Housing), 12(5), 651-661.
  13. Civalek, O., Demir, C. and AkgOz, B. (2010), "Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model", Math. Comput. Appl., 15(2), 289-298.
  14. Demir, C. and Civalek, O. (2013), "Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models", Appl. Math. Model., 37(22), 9355-9367. https://doi.org/10.1016/j.apm.2013.04.050
  15. Ebrahimi, F. and Salari E. (2015a), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Computer Modeling in Engineering & Sciences 105.2, 151-181.
  16. Ebrahimi, F. and Salari E. (2015b), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Composites Part B: Engineering, 79,156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  17. Eigoli, A.K. and Ahmadian, M. (2011), "Nonlinear vibration of beams under nonideal boundary conditions", Acta Mechanica, 218(3-4), 259-267. https://doi.org/10.1007/s00707-010-0423-5
  18. Ekici, H.O. and Boyaci, H. (2007), "Effects of non-ideal boundary conditions on vibrations of microbeams", J. Vib.Control, 13(9-10), 1369-1378. https://doi.org/10.1177/1077546307077453
  19. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  20. Eringen, A.C. (2002), Nonlocal continuum field theories: Springer Science & Business Media.
  21. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  22. Hamidi, A., Houari, M.S.A., Mahmoud, S. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  23. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. - ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  24. Mahmoud, S., Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A. and Beg, O.A. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425. https://doi.org/10.12989/scs.2015.18.2.425
  25. Malekzadeh, K., Khalili, S. and Abbaspour, P. (2010), "Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses", Compos. Struct., 92(6), 1478-1484. https://doi.org/10.1016/j.compstruct.2009.09.059
  26. Murmu, T. and Pradhan, S. (2009), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46(4), 854-859. https://doi.org/10.1016/j.commatsci.2009.04.019
  27. Pakdemirli, M. and Boyac, H. (2001), "Vibrations of a stretched beam with non-ideal boundary", Math. Comput. Appl., 6(3), 217-220.
  28. Pakdemirli, M. and Boyac, H. (2003), "Non-linear vibrations of a simple-simple beam with a non-ideal support in between", J. Sound Vib., 268(2), 331-341. https://doi.org/10.1016/S0022-460X(03)00363-8
  29. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  30. Pradhan, S. and Reddy, G. (2011), "Thermo mechanical buckling analysis of carbon nanotubes on winkler foundation using non-local elasticity theory and DTM", Sadhana, 36(6), 1009-1019. https://doi.org/10.1007/s12046-011-0052-2
  31. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", I Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  32. Sari, G. and Pakdemirli, M. (2012), "Effects of non-ideal boundary conditions on the vibrations of a slightly curved micro beam. Paper presented at the 9th international conference on mathematical problems in engineering, aerospace and sciences: ICNPAA 2012.
  33. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011
  34. Tounsi, A., Bourada, M., Kaci, A. and Houari, M.S.A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409. https://doi.org/10.12989/scs.2015.18.2.409
  35. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  36. Wang, L., Ni, Q., Li, M. and Qian, Q. (2008), "The thermal effect on vibration and instability of carbon nanotubes conveying fluid", Physica E: Low-dimensional Systems and Nanostructures, 40(10), 3179-3182. https://doi.org/10.1016/j.physe.2008.05.009
  37. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301. https://doi.org/10.1063/1.2141648
  38. Wang, Q., Zhou, G. and Lin, K. (2006), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solids Struct., 43(20), 6071-6084. https://doi.org/10.1016/j.ijsolstr.2005.11.005
  39. Wattanasakulpong, N. and Mao, Q. (2015), "Dynamic response of Timoshenko functionally graded beams with classical and non-classical boundary conditions using Chebyshev collocation method", Compos. Struct., 119, 346-354. https://doi.org/10.1016/j.compstruct.2014.09.004
  40. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143. https://doi.org/10.12989/sem.2015.53.6.1143
  41. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  42. Zhang, C.L. and Shen, H.S. (2007), "Buckling and postbuckling of single-walled carbon nanotubes under combined axial compression and torsion in thermal environments", Phys. Rev. B, 75(4), 045408. https://doi.org/10.1103/PhysRevB.75.045408
  43. Zhang, Y., Liu, G. and Wang, J. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys. Rev. B, 70(20), 205430. https://doi.org/10.1103/PhysRevB.70.205430
  44. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. On the electro-thermo-mechanical vibration characteristics of elastically restrained functionally graded nanobeams using differential transformation method vol.124, pp.12, 2018, https://doi.org/10.1007/s00339-018-2220-2
  2. Nonlinear vibration analysis of electro-hygro-thermally actuated embedded nanobeams with various boundary conditions pp.1432-1858, 2018, https://doi.org/10.1007/s00542-018-3924-0
  3. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
  4. Surface effects on vibration and buckling behavior of embedded nanoarches vol.64, pp.1, 2017, https://doi.org/10.12989/sem.2017.64.1.001
  5. Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment vol.64, pp.1, 2016, https://doi.org/10.12989/sem.2017.64.1.121
  6. Variability of thermal properties for a thermoelastic loaded nanobeam excited by harmonically varying heat vol.20, pp.4, 2016, https://doi.org/10.12989/sss.2017.20.4.451
  7. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  8. Analytical solution for scale-dependent static stability analysis of temperature-dependent nanobeams subjected to uniform temperature distributions vol.26, pp.4, 2018, https://doi.org/10.12989/was.2018.26.4.205
  9. Size-dependent vibration in two-directional functionally graded porous nanobeams under hygro-thermo-mechanical loading vol.134, pp.9, 2016, https://doi.org/10.1140/epjp/i2019-12795-6