Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Dabbagh, Ali (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Rabczuk, Timon (Institute of Structural Mechanics (ISM), Bauhaus-University Weimar) ;
  • Tornabene, Francesco (Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna)
  • Received : 2018.08.30
  • Accepted : 2019.04.10
  • Published : 2019.03.25
⟨ Previous Next ⟩

Abstract

The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

Keywords

References

  1. Alshorbagy, M., Eltaher, M.A. and Mahmoud, F.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
  2. 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
  3. 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
  4. 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
  5. 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
  6. Castrucci, P. (2014), "Carbon nanotube/silicon hybrid heterojunctions for photovoltaic devices", Adv. Nano Res., Int. J., 2(1), 23-56. https://doi.org/10.12989/anr.2014.2.1.023
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. Ebrahimi, F. and Barati, M.R. (2018a), "Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory", Microsyst. Technol., 24(3), 1643-1658. https://doi.org/10.1007/s00542-017-3529-z
  13. Ebrahimi, F. and Barati, M.R. (2018b), "Effect of three-parameter viscoelastic medium on vibration behavior of temperaturedependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment", Mech. Adv. Mater. Struct., 25(5), 361-374. https://doi.org/10.1080/15376494.2016.1255831
  14. 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
  15. Ebrahimi, F. and Dabbagh, A. (2018a), "Effect of humid-thermal environment on wave dispersion characteristics of singlelayered graphene sheets", Appl Phys. A, 124(4), p. 301. https://doi.org/10.1007/s00339-018-1734-y
  16. 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
  17. Ebrahimi, F. and Dabbagh, A. (2019a), "On thermo-mechanical vibration analysis of multi-scale hybrid composite beams", J. Vib. Control, 25(4), 933-945. https://doi.org/10.1177/1077546318806800
  18. Ebrahimi, F. and Dabbagh, A. (2019b), "Thermo-mechanical wave dispersion analysis of nonlocal strain gradient single-layered graphene sheet rested on elastic medium", Microsyst. Technol., 25(2), 587-597. https://doi.org/10.1007/s00542-018-3972-5
  19. Ebrahimi, F. and Haghi, P. (2018), "Wave dispersion analysis of rotating heterogeneous nanobeams in thermal environment", Adv. Nano Res., Int. J., 6(1), 21-37. https://doi.org/10.21474/IJAR01/7640
  20. Ebrahimi, F. and Heidari, E. (2017), "Surface effects on nonlinear vibration of embedded functionally graded nanoplates via higher order shear deformation plate theory", Mech. Adv. Mater. Struct., pp. 1-29.
  21. Ebrahimi, F. and Karimiasl, M. (2018), "Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams", Mech. Adv. Mater. Struct., 25(11), 943-952. https://doi.org/10.1080/15376494.2017.1329468
  22. 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
  23. 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
  24. 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
  25. Ebrahimi, F. and Shafiei, N. (2017), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on reddy's higherorder shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772. https://doi.org/10.1080/15376494.2016.1196781
  26. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016a), "Wave dispersion characteristics of axially loaded magneto-electroelastic nanobeams", Appl. Phys. A, 122(11), p. 949. https://doi.org/10.1007/s00339-016-0465-1
  27. Ebrahimi, F., Dabbagh, A. and Barati, M.R. (2016b), "Wave propagation analysis of a size-dependent magneto-electroelastic heterogeneous nanoplate", Eur. Phys. J. Plus, 131(12), p. 433. https://doi.org/10.1140/epjp/i2016-16433-7
  28. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017a), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, p. 1077546317711537.
  29. Ebrahimi, F., Jafari, A. and Barati, M.R. (2017b), "Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations", Thin-Wall. Struct., 119, 33-46. https://doi.org/10.1016/j.tws.2017.04.002
  30. 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
  31. Eltaher, M.A., Emam, S.A. and Mahmoud, F.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
  32. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.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
  33. 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
  34. Farajpour, M.R., Shahidi, A.R., 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., 1-13.
  35. Gharibi, M., Nejad, M.Z. 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.
  36. Ghiasian, S.E., Kiani, Y., Sadighi, M. and Eslami, M.R. (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
  37. Ghiasian, S.E., Kiani, Y. and Eslami, M.R. (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
  38. Ghorbanpour Arani, A., Jamali, M., Ghorbanpour-Arani, A.H., 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
  39. 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., 1-17.
  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.
  41. 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
  42. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Thermal Stresses, 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768
  43. Jafarinezhad, M.R. and Eslami, M.R. (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
  44. Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E. and Meletis, E.I. (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
  45. Marani, R. and Perri, A.G. (2017), "An approach to model the temperature effects on IV characteristics of CNTFETs", Adv. Nano Res., Int. J., 5(1), 61-67. https://doi.org/10.12989/anr.2017.5.1.061
  46. Mojahedin, A., Joubaneh, E.F. 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
  47. Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (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
  48. 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
  49. 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
  50. Nejad, M.Z., 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
  51. Pradhan, S.C. 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-dimensional 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", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  53. Rezaei, A.S. and Saidi, A.R. (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. 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
  55. 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
  56. Simsek, M., Kocaturk, T. and Akbas, S.D. (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
  57. Srividhya, S., Raghu, P., Rajagopal, A. and Reddy, J.N. (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
  58. Stelson, K.A. (2018), "Academic fluid power research in the USA", Int. J. Hydromechatronics, 1(1), 126-152.
  59. 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
  60. 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
  61. Tian, T., Nakano, M. and Li, W. (2018), "Applications of shear thickening fluids: a review", Int. J. Hydromechatronics, 1(2), 238-257. https://doi.org/10.1504/IJHM.2018.092733
  62. 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
  63. 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
  64. Youcef, D.O., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., Int. J., 3(4), 177-191. https://doi.org/10.12989/anr.2015.3.4.177
  65. Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E: Low-dimensional Syst. Nanostruct., 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003
  66. 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

Cited by

  1. Flow of casson nanofluid along permeable exponentially stretching cylinder: Variation of mass concentration profile vol.38, pp.1, 2019, https://doi.org/10.12989/scs.2021.38.1.033
  2. Monitoring and control of multiple fraction laws with ring based composite structure vol.10, pp.2, 2021, https://doi.org/10.12989/anr.2021.10.2.129
  3. Flow of MHD Powell-Eyring nanofluid: Heat absorption and Cattaneo-Christov heat flux model vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.221
  4. Effect of suction on flow of dusty fluid along exponentially stretching cylinder vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.263
  5. The effects of ring and fraction laws: Vibration of rotating isotropic cylindrical shell vol.11, pp.1, 2021, https://doi.org/10.12989/anr.2021.11.1.019
  6. Propagation of waves with nonlocal effects for vibration response of armchair double-walled CNTs vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.183
  7. An investigation of mechanical properties of kidney tissues by using mechanical bidomain model vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.193