Steel and Composite Structures

  • 제35권3호
  • /
  • Pages.449-462
  • /
  • 2020
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free axial vibration of cracked axially functionally graded nanoscale rods incorporating surface effect

  • 투고 : 2019.09.18
  • 심사 : 2020.04.03
  • 발행 : 2020.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

키워드

참고문헌

  1. Aal, A.A., El-Sheikh, S. and Ahmed, Y. (2009), "Electrodeposited composite coating of Ni-W-P with nano-sized rod-and spherical-shaped SiC particles", Mater. Res. Bull., 44(1), 151-159. https://doi.org/10.1016/j.materresbull.2008.03.008.
  2. Akgoz, B. and Civalek, O. (2013), "Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)", Compos. Part B: Eng., 55, 263-268. https://doi.org/10.1016/j.compositesb.2013.06.035.
  3. Akgoz, B. and Civalek, O. (2014), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Vib. Control, 20(4), 606-616. https://doi.org/10.1177/1077546312463752.
  4. Arefi, M. and Zenkour, A.M. (2017), "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., 28(17), 2403-2413. https://doi.org/10.1177/1045389X17689930.
  5. Ashok, C. and Rao, K.V. (2014), "ZnO/TiO2 nanocomposite rods synthesized by microwave-assisted method for humidity sensor application", Superlattices and Microstruct., 76, 46-54. https://doi.org/10.1016/j.spmi.2014.09.029.
  6. Aydogdu, M. (2012), "Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity", Mech. Res. Commun., 43, 34-40. https://doi.org/10.1016/j.mechrescom.2012.02.001.
  7. Aydogdu, M. (2014), "Longitudinal wave propagation in multiwalled carbon nanotubes", Compos. Struct., 107, 578-584. https://doi.org/10.1016/j.compstruct.2013.08.031.
  8. Aydogdu, M. (2015), "A nonlocal rod model for axial vibration of double-walled carbon nanotubes including axial van der Waals force effects", J. Vib. Control, 21(16), 3132-3154. https://doi.org/10.1177/1077546313518954.
  9. Chang, T.P. (2013), "Axial vibration of non-uniform and nonhomogeneous nanorods based on nonlocal elasticity theory", Appl. Math. Comput., 219(10), 4933-4941. https://doi.org/10.1016/j.amc.2012.11.059.
  10. Civalek, O. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005.
  11. Danesh, M., Farajpour, A. and Mohammadi, M. (2012), "Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method", Mech. Res., 39(1), 23-27. https://doi.org/10.1016/j.mechrescom.2011.09.004.
  12. Gul, U., Aydogdu, M. and Gaygusuzoglu, G. (2017), "Axial dynamics of a nanorod embedded in an elastic medium using doublet mechanics", Compos. Struct., 160, 1268-1278. https://doi.org/10.1016/j.compstruct.2016.11.023.
  13. Guo, SQ. and Yang, S.P. (2012), "Axial vibration analysis of nanocones based on nonlocal elasticity theory", Acta Mechanica Sinica, 28(3), 801-807. https://doi.org/10.1007/s10409-012-0109-4.
  14. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Archive for Rational Mechanics and Analysis, 57(4), 291-323. https://doi.org/10.1007/BF00261375.
  15. Hosseini-Hashemi, S., Fakher, M. and Nazemnezhad, R. (2017), "Longitudinal vibrations of aluminum nanobeams by applying elastic moduli of bulk and surface: molecular dynamics simulation and continuum model", Mater. Res. Express, 4(8), 085036. https://doi.org/10.1088/2053-1591/aa8152
  16. Jandaghian, A.A. and Rahmani, O. (2017), "Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions", Steel Compos. Struct., 25(1), 67-78. https://doi.org/10.12989/scs.2017.25.1.067.
  17. Karlicic, D., Cajic, M., Murmu, T. and Adhikari, S. (2015), "Nonlocal longitudinal vibration of viscoelastic coupled doublenanorod systems", Eur. J. Mech.-A/Solids, 49, 183-196. https://doi.org/10.1016/j.euromechsol.2014.07.005.
  18. Kiani, K. (2010), "Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique", Physica E: Low-Dimensional Syst. Nanostruct., 43(1), 387-397. https://doi.org/10.1016/j.physe.2010.08.022.
  19. Li, L., Hu, Y. and Li, X. (2016), "Longitudinal vibration of sizedependent rods via nonlocal strain gradient theory", Int. J. Mech. Sci., 115-116, 135-144. https://doi.org/10.1016/j.ijmecsci.2016.06.011.
  20. Li, X.F., Tang, G.J., Shen, Z.B. and Lee, K.Y. (2017), "Sizedependent resonance frequencies of longitudinal vibration of a nonlocal Love nanobar with a tip nanoparticle", Math. Mech. Solids, 22(6), 1529-1542. https://doi.org/10.1177/1081286516640597.
  21. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  22. Murmu, T. and Adhikari, S. (2010), "Nonlocal effects in the longitudinal vibration of double-nanorod systems", Physica E: Low-Dimensional Syst. Nanostruct., 43(1), 415-422. https://doi.org/10.1016/j.physe.2010.08.023.
  23. Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Free vibration analysis of multi-layer graphene nanoribbons incorporating interlayer shear effect via molecular dynamics simulations and nonlocal elasticity", Physics Lett. A, 378(44), 3225-3232. https://doi.org/10.1016/j.physleta.2014.09.037.
  24. Nazemnezhad, R. and Kamali, K. (2018a), "An analytical study on the size dependent longitudinal vibration analysis of thick nanorods", Mater. Res. Express, 5(7), 075016. https://doi.org/10.1088/2053-1591/aacf6e
  25. Nazemnezhad, R. and Kamali, K. (2018b), "Free axial vibration analysis of axially functionally graded thick nanorods using nonlocal Bishop's theory", Steel Compos. Struct., 28(6), 749-758. https://doi.org/10.12989/scs.2018.28.6.749.
  26. Nazemnezhad, R. and Shokrollahi, H. (2019), "Free axial vibration analysis of functionally graded nanorods using surface elasticity theory", Modares Mech. Eng., 18(9), 131-141.
  27. Nazemnezhad, R., Shokrollahi, H. and Hosseini-Hashemi, S. (2014), "Sandwich beam model for free vibration analysis of bilayer graphene nanoribbons with interlayer shear effect", J. Appl. Phys., 115(17), 174303. ttps://doi.org/10.1063/1.4874221.
  28. Oveissi, S., Eftekhari, S.A. and Toghraie, D. (2016), "Longitudinal vibration and instabilities of carbon nanotubes conveying fluid considering size effects of nanoflow and nanostructure", Physica E: Low-Dimensional Syst. Nanostruct., 83, 164-173. https://doi.org/10.1016/j.physe.2016.05.010.
  29. Patil, A.V., Beker, A.F., Wiertz, F.G., Heering, H.A., Coslovich, G., Vlijm, R. and Oosterkamp, T.H. (2010), "Fabrication and characterization of polymer insulated carbon nanotube modified electrochemical nanoprobes", Nanoscale, 2(5), 734-738. https://doi.org/10.1039/b9nr00281b
  30. Rahmani, O., Hosseini, S., Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., 26(5), 607-620. https://doi.org/10.12989/scs.2018.26.5.607.
  31. Rao, S.S. (2007). Vibration of Continuous Systems: John Wiley & Sons.
  32. Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials", Appl. Math. Model., 36(7), 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073.
  33. Simsek, M. (2012), "Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods", Comput. Mater. Sci., 61, 257-265. https://doi.org/10.1016/j.commatsci.2012.04.001.
  34. Tagrara, S., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  35. Watanabe, Y., Inaguma, Y., Sato, H. and Miura-Fujiwara, E. (2009), "A novel fabrication method for functionally graded materials under centrifugal force: The centrifugal mixed-powder method", Materials, 2(4), 2510-2525. https://doi.org/10.3390/ma2042510.
  36. Zhang, T., Kumari, L., Du, G., Li, W., Wang, Q., Balani, K. and Agarwal, A. (2009), "Mechanical properties of carbon nanotube-alumina nanocomposites synthesized by chemical vapor deposition and spark plasma sintering", Compos. Part A: Appl. Sci. Manufact., 40(1), 86-93. https://doi.org/10.1016/j.compositesa.2008.10.003.
  37. Zheng, Y., Wang, S., You, M., Tan, H. and Xiong, W. (2005), "Fabrication of nanocomposite Ti (C, N)-based cermet by spark plasma sintering", Mater. Chem. Phys., 92(1), 64-70. https://doi.org/10.1016/j.matchemphys.2004.12.031.

피인용 문헌

  1. An investigation of mechanical properties of kidney tissues by using mechanical bidomain model vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.193