DOI QR코드

DOI QR Code

Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress

  • Arani, Ali Ghorbanpour (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Pourjamshidian, Mahmoud (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arefi, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arani, M.R. Ghorbanpour (Electrical Engineering Faculty, Amirkabir University of Technology)
  • 투고 : 2018.06.20
  • 심사 : 2019.01.15
  • 발행 : 2019.02.25

초록

This research deals with wave propagation of the functionally graded (FG) nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano-beam is resting in Winkler-Pasternak foundation. It is assumed that the material properties of the nano-beam changes continuously along the thickness direction according to simple power-law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non-classical nano-beam model containg flexoelectric effect is used. Also, the effects of surface elasticity, dielectricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano-beam as well as cut-off frequency. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Winkler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on the wave propagation characteristics of FG nano-beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned parameters on the occurrence cut-off frequency point are very small.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  3. Ansari, R., Shojaei, M.F., Mohammadi, V., Gholami, R. and Darabi, M.A. (2014), "Nonlinear vibrations of functionally graded mindlin microplates based on the modified couple stress theory", Compos Struct., 114, 124-134. https://doi.org/10.1016/j.compstruct.2014.04.013
  4. Arani, A.G., Fereidoon, A. and Kolahchi, R. (2014), "Nonlinear surface and nonlocal piezoelasticity theories for vibration of embedded single-layer boron nitride sheet using harmonic differential quadrature and differential cubature methods", J. Intel. Mat. Syst. Str., 26(10), 1150-1163. https://doi.org/10.1177/1045389X14538331
  5. Arani, A.G., Jalilvand, A. and Kolahchi, R. (2014), "Wave propagation of magnetic nanofluid-conveying double-walled carbon nanotubes in the presence of longitudinal magnetic field", Proc IMechE Part N: J Nanoengineering and Nanosystems, 228(2), 82-92. https://doi.org/10.1177/1350650113499742
  6. Arani, A.G., Jamali, M., Ghorbanpour Arani, A.H., Kolahchi, R. and Mosayyebi, M. (2016), "Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects", Proc IMechE Part C: J Mechanical Engineering Science, 1-17.
  7. Arani, A.G., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2015), "Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electro-magnetic field", Proc IMechE Part N: J Nanoengineering and Nanosystems, 1-17.
  8. Arani, A.G., Kolahchi, R. and Mortazavi, S.A. (2014), "Nonlocal piezoelasticity based wave propagation of bonded doublepiezoelectric nanobeam-systems", Int. J. Mech. Mater. Des., 10, 179-191. https://doi.org/10.1007/s10999-014-9239-0
  9. Arani, A.G., Kolahchi, R., Mosallaie Barzoki, A.A., Mozdianfard, M.R. and Noudeh Farahani, M. (2012), "Elastic foundation effect on nonlinear thermo-vibration of embedded doublelayered orthotropic graphene sheets using differential quadrature method", Proc IMechE Part C: J Mechanical Engineering Science, 1-18.
  10. Arefi, M., Karroubi, R. and Irani-Rahaghi, M. (2016), "Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer", Appl. Math. Mech., 37(7), 821-834. https://doi.org/10.1007/s10483-016-2098-9
  11. Arefi, M., Pourjamshidian, M. and Arani, A.G. (2017), "Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electrothermal environment", Appl. Phys. A, 123(5), 1-18.
  12. Arefi, M. and Zenkour, M.A. (2017a), "Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model", J. Intel. Mat. Syst. Str., https://doi.org/10.1177/1045389X17689930.
  13. Arefi, M. and Zenkour, A.M. (2017b), "Effect of thermo-magnetoelectro-mechanical fields on the bending behaviors of a threelayered nanoplate based on sinusoidal shear-deformation plate theory", J. Sandw. Struct. Mater., Doi: 1099636217697497.
  14. Arefi, M. and Zenkour, A.M. (2017c), "Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezomagnetic curved nanobeam", Acta. Mech., 228 (10) 3657-3674. https://doi.org/10.1007/s00707-017-1892-6
  15. Arefi, M. and Zenkour, A.M. (2017d), "Influence of magnetoelectric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory", J. Sandw. Struct. Mater., In Press.
  16. Arefi, M. Zamani, M.H. and Kiani, M. (2017), "Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak's foundation", J. Intel. Mater. Syst. Struct., 29(5), 774-786 https://doi.org/10.1177/1045389X17721039
  17. Arvin, H., Sadighi, M. and Ohadi, A.R. (2010), "A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core", Compos. Struct., 92, 996-1008. https://doi.org/10.1016/j.compstruct.2009.09.047
  18. Asghari, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2010), "A nonlinear Timoshenko beam formulation based on the modified couple stress theory", Int. J. Eng. Sci., 48, 1749-1761. https://doi.org/10.1016/j.ijengsci.2010.09.025
  19. Asgharifard Sharabiani, P. and Haeri Yazdi, M.R. (2013), "Nonlinear free vibrations of functionally graded nanobeams with surface effects", Compos. Part B, 45, 581-586. https://doi.org/10.1016/j.compositesb.2012.04.064
  20. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  21. 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), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  22. Bouafia, K., Kaci, A., Houari, M.S., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  23. 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
  24. Chen, H., Li, X.P., Chen, Y.Y. and Huang, G.L. (2017), "Wave propagation and absorption of sandwich beams containing interior dissipative multi-resonators", Ultrasonics, 76, 99-108. https://doi.org/10.1016/j.ultras.2016.12.014
  25. Ding, L., Zhu, H.P. and Wu, L. (2016), "Effects of axial load and structural damping on wave propagation in periodic Timoshenko beams on elastic foundations under moving loads", Phys. Lett. A, 380(31-32), 2335-2341. https://doi.org/10.1016/j.physleta.2016.05.023
  26. Ebrahimi, F. and Barati, M.R. (2017), "Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams", J. Intel. Mat. Syst. Str., In press.
  27. Ebrahimi, F. and Barati, M.R. (2017), "Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory", Eur. Phys. J. Plus., 132(19), 1-13. https://doi.org/10.1140/epjp/i2017-11280-8
  28. Ebrahimy. F and Hosseini, S.H. (2016), "Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates", Appl. Phys. A, in press.
  29. 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. https://doi.org/10.1063/1.332803
  30. Fantuzzi, N. and Tornabene, F. (2017), "Strong Formulation Isogeometric Analysis (SFIGA) for laminated composite arbitrarily shaped plates", Appl. Sci., 7(131), 1-39 .
  31. Faraji Oskouie, M. and Ansari, R. (2017), "Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects", Appl. Math. Model., 43 337-350. https://doi.org/10.1016/j.apm.2016.11.036
  32. Gholami, R., Darvizeh, A., Ansari, R. and Hosseinzadeh, M. (2014), "Sizedependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory", Meccanica, 49(7), 1679-1695. https://doi.org/10.1007/s11012-014-9944-7
  33. Hosseini-Hashemi, S. and Nazemnezhad, R. (2013), "An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects", Compos. Part B, 52, 199-206. https://doi.org/10.1016/j.compositesb.2013.04.023
  34. Joglekar, D.M. and Mitra, M. (2016), "Analysis of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method", Mech. Syst. Signal Pr., 76-77, 576-591. https://doi.org/10.1016/j.ymssp.2016.02.010
  35. Kanani, A.S., Niknam, H., Ohadi, A.R. and Aghdam, M.M. (2014), "Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam", Compos. Struct., 115, 60-68. https://doi.org/10.1016/j.compstruct.2014.04.003
  36. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92, 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024
  37. Kiani, K. (2016), "Surface and shear energy effects on vibrations of magnetically affected beam-like nanostructures carrying direct currents", Int. J. Mech.Sci., 113, 221-238. https://doi.org/10.1016/j.ijmecsci.2016.05.002
  38. Komijani, M., Esfahani, S.E., Reddy, J.N., Liu, Y.P. and Eslami, M.R. (2014), "Nonlinear thermal stability and vibration of pre/post-buckled temperature-and microstructure-dependent functionally graded beams resting on elastic foundation", Compos. Struct., 112, 292-307. https://doi.org/10.1016/j.compstruct.2014.01.041
  39. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  40. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  41. Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Systems and Nanostructures, 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028
  42. Liang, X., Hu, S. and Shen, S. (2014), "Effects of surface and flexoelectricity on a piezoelectric nanobeam", Smart Mater. Struct., 23, 035020
  43. Liang, X., Hu, S. and Shen, S. (2014), "Effects of surface and flexoelectricity on a piezoelectric nanobeam", Smart Mater. Struct., 23, 035020
  44. Liew, K.M., Hu, Y.G. and He, X.Q. (2008), "Flexural wave propagation in single-walled carbon nanotubes", J. Comput Theor. Nanosci., 5(4), 581-586. https://doi.org/10.1166/jctn.2008.019
  45. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  46. Lim, C.W., Zhanga, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  47. Ma, L.H., Kea, L.L., Wang, Y.Z. and Wang, Y.S. (2017), "Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models", Physica E: Low-dimensional Systems and Nanostructures, 86, 253-261. https://doi.org/10.1016/j.physe.2016.10.036
  48. Marin, L. (2005), "Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional Functionally Graded Materials", Int. J. Solids Struct., 42 4338-4351. https://doi.org/10.1016/j.ijsolstr.2005.01.005
  49. Nateghi, A. and Salamat-talab, M. (2013), "Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory", Compos. Struct., 96, 97-110. https://doi.org/10.1016/j.compstruct.2012.08.048
  50. Nazemnezhad, R., Salimi, M., Hosseini Hashemi, S. and Asgharifard Sharabiani, P. (2012), "An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects", Compos. Part B, 43, 2893-2897. https://doi.org/10.1016/j.compositesb.2012.07.029
  51. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M. and Greil, P. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng. A, 362, 40-60. https://doi.org/10.1016/S0921-5093(03)00580-X
  52. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005
  53. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119(3), 1019-1032. https://doi.org/10.1007/s00339-015-9061-z
  54. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  55. Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59, 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008
  56. Reddy, J.N. and El-Borgi, S. (2014), "Eringen's nonlocal theories of beams accounting for moderate rotations", Int. J. Eng. Sci., 82, 159-177. https://doi.org/10.1016/j.ijengsci.2014.05.006
  57. Sari, M.S. (2016), "Superharmonic resonance analysis of nonlocal nano beam subjected to axial thermal and magnetic forces and resting on a nonlinear elastic foundation", Microsyst. Technol., 1-12.
  58. Shafiei, N., Kazemi. M and Ghadiri, M. (2016), "Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen's nonlocal elasticity and DQM", Appl. Phys. A, in press.
  59. Shakeri, M., Akhlaghi, M. and Hoseini, S.M. (2006), "Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", Compos.Struct., 76(1), 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022
  60. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Method. Appl. M., 198 2911-2935 . https://doi.org/10.1016/j.cma.2009.04.011
  61. Tornabene, F., Brischetto, S., Fantuzzi, N. and Bacciocchi, M. (2016), "Boundary conditions in 2D numerical and 3D exact models for cylindrical bending analysis of functionally graded structures", J. Shock Vib., 2373862, 1-17 .
  62. Tornabene, F. and Viola, E. (2009), "Free vibrations of fourparameter functionally graded parabolic panels and shells of revolution", Eur. J. Mech.-A/Solids, 28 991-1013. https://doi.org/10.1016/j.euromechsol.2009.04.005
  63. Tornabene, F. and Viola, E. (2013), "Static analysis of functionally graded doubly-curved shells and panels of revolution", Meccanica, 48 901-930 . https://doi.org/10.1007/s11012-012-9643-1
  64. Waksmanski, N. and Pan, E. (2016), "An analytical threedimensional solution for free vibration of a magneto-electroelastic plate considering the nonlocal effect", J. Intel. Mat. Syst. Str., In press.
  65. Watari, F., Yokoyama, A., Omori, M., Hirai, T., Kondo, H. and Uo, M. (2004), "Biocompatibility of materials and development to functionally graded implant for bio-medical application", Compos. Sci. Technol., 64, 893-908. https://doi.org/10.1016/j.compscitech.2003.09.005
  66. Yan, Z. and Jiang, L. (2013), "Size-dependent bending and vibration behaviour of piezoelectric nanobeams due to flexoelectricity", J. Phys. D: Appl. Phys., 46(35), 355502 https://doi.org/10.1088/0022-3727/46/35/355502
  67. Yang, F., Chong, A., Lam, D. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solid. Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  68. Yao, R.X. and Shi, Z.F. (2011), "Steady-state forced vibration of functionally graded piezoelectric beams", J. Intel. Mat. Syst. Str., 22(8), 769-779. https://doi.org/10.1177/1045389X11409604
  69. 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
  70. Zhang, R., Liang, X. and Shen, S. (2016), "A Timoshenko dielectric beam model with flexoelectric effect", Meccanica, 51(5), 1181-1188. https://doi.org/10.1007/s11012-015-0290-1
  71. Zhang, Z. and Jiang, L. (2014), "Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity", J. Appl. Phys., 116, 134308 https://doi.org/10.1063/1.4897367
  72. Zhang, Z., Yan, Z. and Jiang, L. (2014), "Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate", J. Appl. Phys., 116, 014307.
  73. Zhang, Z.J. and Paulino, G.H. (2007), "Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements", Int. J. Solids Struct., 44(11), 3601-3626. https://doi.org/10.1016/j.ijsolstr.2005.05.061
  74. Zhong, Z. and Yu, T. (2007), "Electroelastic analysis of functionally graded piezoelectric material beams", J. Intel. Mat. Syst. Str., 19(6), 707-713. https://doi.org/10.1177/1045389X07079453

피인용 문헌

  1. Frequency and thermal buckling information of laminated composite doubly curved open nanoshell vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.001
  2. Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.281