DOI QR코드

DOI QR Code

A novel porosity-based homogenization scheme for propagation of waves in axially-excited FG nanobeams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Dabbagh, Ali (School of Mechanical Engineering, College of Engineering, University of Tehran)
  • Received : 2018.12.29
  • Accepted : 2019.09.26
  • Published : 2019.11.25

Abstract

Putting emphasis on the effect of existence of porosity in the functionally graded materials (FGMs) on the dynamic responses of waves scattered in FG nanobeams resulted in implementation of a novel porosity-based homogenization method for FGMs and show its applicability in a wave propagation problem in the presence of axial pre-load for the first time. In the employed porosity-dependent method, the coupling between density and Young's moduli is included to consider for the effective moduli of the FG nanobeam by the means of a more reliable homogenization technique. The beam-type element will be modeled via the classical theory of beams, namely Euler-Bernoulli beam theory. Also, the dynamic form of the principle of virtual work will be extended for such nanobeams to derive the motion equations. Applying the nonlocal constitutive equations of Eringen on the obtained motion equations will be resulted in derivation of the nanobeam's governing equations. Depicted results reveal that the dispersion responses of FG nanobeams will be decreased as the porosity volume fraction is increased which must be noticed by the designers of advanced nanosize devices who are interested in employment of wave dispersion approach in continuous systems for specific goals.

Keywords

References

  1. Akgoz, B. and Civalek, O . (2017a), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024
  2. Akgoz, B. and Civalek, O. (2017b), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.039
  3. Alshorbagy, A.E., Eltaher, M. and Mahmoud, F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  4. Alzahrani, E.O., Zenkour, A.M. and Sobhy, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. https://doi.org/10.1016/j.compstruct.2013.04.045
  5. Ansari, R., Arash, B. and Rouhi, H. (2011), "Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity", Compos. Struct., 93(9), 2419-2429. https://doi.org/10.1016/j.compstruct.2011.04.006
  6. Atmane, H.A., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  7. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., Int. J., 6(3), 257-278. https://doi.org/10.12989/anr.2018.6.3.257
  8. Barati, M.R. (2017), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11. https://doi.org/10.1016/j.ijengsci.2017.03.007
  9. Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2d and quasi-3d nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., Int. J., 7(4), 277-292. https://doi.org/10.12989/anr.2019.7.4.277
  10. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., Int. J., 6(3), 279-298. https://doi.org/10.12989/anr.2018.6.3.279
  11. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal hsdt for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
  12. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052
  13. Chen, D., Kitipornchai, S. and Yang, J. (2016a), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025
  14. Chen, D., Yang, J. and Kitipornchai, S. (2016b), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025
  15. Civalek, O. (2013), "Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches", Compos. Part B: Eng., 50, 171-179. https://doi.org/10.1016/j.compositesb.2013.01.027
  16. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098
  17. Ebrahimi, F. and Barati, M.R. (2016), "Hygrothermal buckling analysis of magnetically actuated embedded higher order functionally graded nanoscale beams considering the neutral surface position", J. Thermal Stress., 39(10), 1210-1229. https://doi.org/10.1080/01495739.2016.1215726
  18. Ebrahimi, F. and Dabbagh, A. (2017), "Wave propagation analysis of smart rotating porous heterogeneous piezo-electric nanobeams", Eur. Phys. J. Plus, 132(4), p. 153. https://doi.org/10.1140/epjp/i2017-11366-3
  19. Ebrahimi, F. and Dabbagh, A. (2018a), "Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets", Appl. Phys. A, 124(4), p. 301. https://doi.org/10.1007/s00339-018-1734-y
  20. Ebrahimi, F. and Dabbagh, A. (2018b), "Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates", Eur. Phys. J. Plus, 133(3), p. 97. https://doi.org/10.1140/epjp/i2018-11910-7
  21. Ebrahimi, F. and Rastgoo, A. (2008), "An analytical study on the free vibration of smart circular thin fgm plate based on classical plate theory", Thin-Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008
  22. Ebrahimi, F. and Salari, E. (2015a), "Thermal buckling and free vibration analysis of size dependent timoshenko fg nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  23. Ebrahimi, F. and Salari, E. (2015b), "Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory", J. Mech. Sci. Technol., 29(9), 3797-3803. https://doi.org/10.1007/s12206-015-0826-2
  24. Ebrahimi, F., Dabbagh, A. and Barati, M.R. (2016), "Wave propagation analysis of a size-dependent magneto-electro-elastic heterogeneous nanoplate", Eur. Phys. J. Plus, 131(12), p. 433. https://doi.org/10.1140/epjp/i2016-16433-7
  25. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, p. 1077546317711537. https://doi.org/10.1177/1077546317711537
  26. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2018), "Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects", Waves Random Complex Media, 28(2), 215-235. https://doi.org/10.1080/17455030.2017.1337281
  27. Ebrahimi, F., Hosseini, S.H.S. and Bayrami, S.S. (2019), "Nonlinear forced vibration of pre-stressed graphene sheets subjected to a mechanical shock: An analytical study", Thin-Wall. Struct., 141, 293-307. https://doi.org/10.1016/j.tws.2019.04.038
  28. Eltaher, M., Emam, S.A. and Mahmoud, F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  29. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013), "Vibration analysis of euler-bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  30. Eltaher, M., Fouda, N., El-midany, T. and Sadoun, A. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(3), p. 141. https://doi.org/10.1007/s40430-018-1065-0
  31. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  32. Farajpour, M., Shahidi, A., Hadi, A. and Farajpour, A. (2018), "Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magnetoelectro-elastic nanofilms", Mech. Adv. Mater. Struct., 26(17), 1469-1481. https://doi.org/10.1080/15376494.2018.1432820
  33. Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids, 41(12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N
  34. Gharibi, M., Zamani Nejad, M. and Hadi, A. (2017), "Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of frobenius", J. Computat. Appl. Mech., 48(1), 89-98. https://doi.org/10.22059/JCAMECH.2017.233633.143
  35. Ghiasian, S., Kiani, Y., Sadighi, M. and Eslami, M. (2014), "Thermal buckling of shear deformable temperature dependent circular/annular fgm plates", Int. J. Mech. Sci., 81, 137-148. https://doi.org/10.1016/j.ijmecsci.2014.02.007
  36. Ghiasian, S., Kiani, Y. and Eslami, M. (2015), "Nonlinear thermal dynamic buckling of FGM beams", Eur. J. Mech.-A/Solids, 54, 232-242. https://doi.org/10.1016/j.euromechsol.2015.07.004
  37. Ghorbanpour Arani, A., Jamali, M., Ghorbanpour-Arani, A., Kolahchi, R. and Mosayyebi, M. (2017), "Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(2), 387-403. https://doi.org/10.1177/0954406215627830
  38. Gupta, A. and Talha, M. (2018), "Static and stability characteristics of geometrically imperfect fgm plates resting on pasternak elastic foundation with microstructural defect", Arab. J. Sci. Eng., 43(9), 4931-4947. https://doi.org/10.1007/s13369-018-3240-0
  39. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. Anal., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  40. Hosseini, M., Hadi, A., Malekshahi, A. and Shishesaz, M. (2018), "A review of size-dependent elasticity for nanostructures", J. Computat. Appl. Mech., 49(1), 197-211. https://doi.org/10.22059/JCAMECH.2018.259334.289
  41. Henderson, J.P., Plummer, A. and Johnston, N. (2018), "An electro-hydrostatic actuator for hybrid active-passive vibration isolation", Int. J. Hydromechatron., 1(1), 47-71. https://doi.org/10.1504/IJHM.2018.090305
  42. Huang, Y. and Li, X.-F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform crosssection", J. Sound Vib., 329(11), 2291-2303. https://doi.org/10.1016/j.jsv.2009.12.029
  43. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Thermal Stress., 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768
  44. Jafarinezhad, M. and Eslami, M. (2017), "Coupled thermoelasticity of fgm annular plate under lateral thermal shock", Compos. Struct., 168, 758-771. https://doi.org/10.1016/j.compstruct.2017.02.071
  45. Kumar, B.R. (2018), "Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube van der waals forces", Adv. Nano Res., Int. J., 6(2), 133-145. https://doi.org/10.12989/anr.2018.6.2.135
  46. Mahmoud, F., Eltaher, M., Alshorbagy, A. and Meletis, E. (2012), "Static analysis of nanobeams including surface effects by nonlocal finite element", J. Mech. Sci. Technol., 26(11), 3555-3563. https://doi.org/10.1007/s12206-012-0871-z
  47. Mojahedin, A., Farzaneh Joubaneh, E. and Jabbari, M. (2014), "Thermal and mechanical stability of a circular porous plate with piezoelectric actuators", Acta Mechanica, 225(12), 3437-3452. https://doi.org/10.1007/s00707-014-1153-x
  48. Mojahedin, A., Jabbari, M., Khorshidvand, A. and Eslami, M. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-Wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008
  49. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Computat. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
  50. Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006
  51. Pradhan, S. and Murmu, T. (2010), "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E: Low-dimens. Syst. Nanostruct., 42(5), 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053
  52. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal timoshenko beam theory", International Journal of Engineering Science, 77, pp. 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  53. Rezaei, A. and Saidi, A. (2016), "Application of carrera unified formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", Compos. Part B: Eng., 91, 361-370. https://doi.org/10.1016/j.compositesb.2015.12.050
  54. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082
  55. Salari, E., Ashoori, A. and Sadough Vanini, S.A. (2019), "Porosity-dependent asymmetric thermal buckling of inhomogeneous annular nanoplates resting on elastic substrate", Adv. Nano Res., Int. J., 7(1), 25-38. https://doi.org/10.12989/anr.2019.7.1.025
  56. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016), "On sizedependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007
  57. Shen, H.-S. (2009), "A comparison of buckling and postbuckling behavior of fgm plates with piezoelectric fiber reinforced composite actuators", Compos. Struct., 91(3), 375-384. https://doi.org/10.1016/j.compstruct.2009.06.005
  58. Simsek, M. (2015), "Bi-directional functionally graded materials (bdfgms) for free and forced vibration of timoshenko beams with various boundary conditions", Compos. Struct., 133, 968-978. https://doi.org/10.1016/j.compstruct.2015.08.021
  59. Simsek, M., Kocaturk, T. and Akbas, S. (2012), "Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load", Compos. Struct., 94(8), 2358-2364. https://doi.org/10.1016/j.compstruct.2012.03.020
  60. Srividhya, S., Raghu, P., Rajagopal, A. and Reddy, J. (2018), "Nonlocal nonlinear analysis of functionally graded plates using third-order shear deformation theory", Int. J. Eng. Sci., 125, 1-22. https://doi.org/10.1016/j.ijengsci.2017.12.006
  61. Tanaka, Y. (2018), "Active vibration compensator on moving vessel by hydraulic parallel mechanism", Int. J. Hydromechatron., 1(3), 350-359. https://doi.org/10.1504/IJHM.2018.094887
  62. Tang, Y. and Yang, T. (2018), "Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material", Compos. Struct., 185, 393-400. https://doi.org/10.1016/j.compstruct.2017.11.032
  63. Thai, H.-T. and Choi, D.-H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos. Part B: Eng., 43(5), 2335-2347. https://doi.org/10.1016/j.compositesb.2011.11.062
  64. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003
  65. Wang, Z., Xie, Z. and Huang, W. (2018), "A pin-moment model of flexoelectric actuators", Int. J. Hydromechatron., 1(1), 72-90. https://doi.org/10.1504/IJHM.2018.090306
  66. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends fgm beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  67. Zamani Nejad, M., Hadi, A. and Rastgoo, A. (2016), "Buckling analysis of arbitrary two-directional functionally graded euler-bernoulli nano-beams based on nonlocal elasticity theory", Int. J. Eng. Sci., 103, 1-10. https://doi.org/10.1016/j.ijengsci.2016.03.001
  68. Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E: Low-dimens. Syst. Nanostruct., 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003
  69. Zenkour, A.M. (2018), "A quasi-3d refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147
  70. Zok, F.W. and Levi, C.G. (2001), "Mechanical properties of porous-matrix ceramic composites", Adv. Eng. Mater., 3(1-2), 15-23. https://doi.org/10.1002/1527-2648(200101)3:1/2<15::AID-ADEM15>3.0.CO;2-A