Advances in nano research

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Effect of three-dimensional thermal stresses on torsional vibration of cracked nanorods surrounded by an elastic medium

  • Abdullah, Sardar S. (School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Hashemi, Shahrokh H. (School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Hussein, Nazhad A. (Mechanical Department, College of Engineering, Salahaddin University-Erbil) ;
  • Nazemnezhad, Reza (School of Engineering, Damghan University)
  • Received : 2020.09.30
  • Accepted : 2021.06.29
  • Published : 2021.09.25
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Abstract

The effect of thermal stresses on the torsional vibration of non, single, and double-cracked nanorods surrounded by an elastic medium is investigated. The differential constitutive relation of the nonlocal theory is applied to the motion equation. Three-dimensional linear thermal strains raised from the thermal stresses are derived using nonlinear Green's strains. The surrounding elastic medium acts as infinite torsional springs. The crack is modeled as a rotational spring. Using Hamilton's principle, the motion equation is obtained. Effect of the crack position and severity, number of cracks, high and low temperatures, nonlocal coefficient, elastic medium stiffness, and nanorod length are examined. The temperature effect on the frequencies depends on the values of the crack parameters, crack numbers, elastic medium stiffness, and nanorod length, and it is independent of the nonlocal scale coefficient. The crack leads to a decrease in the frequencies at any temperature. The elastic medium causes an increase in the frequencies at any temperature.The effect of thermal stresses on the torsional vibration of non, single, and double-cracked nanorods surrounded by an elastic medium is investigated. The differential constitutive relation of the nonlocal theory is applied to the motion equation. Three-dimensional linear thermal strains raised from the thermal stresses are derived using nonlinear Green's strains. The surrounding elastic medium acts as infinite torsional springs. The crack is modeled as a rotational spring. Using Hamilton's principle, the motion equation is obtained. Effect of the crack position and severity, number of cracks, high and low temperatures, nonlocal coefficient, elastic medium stiffness, and nanorod length are examined. The temperature effect on the frequencies depends on the values of the crack parameters, crack numbers, elastic medium stiffness, and nanorod length, and it is independent of the nonlocal scale coefficient. The crack leads to a decrease in the frequencies at any temperature. The elastic medium causes an increase in the frequencies at any temperature.

Keywords

Acknowledgement

The authors are grateful to the Iran University of Science and Technology and the University of Salahaddin-Erbil for supporting this work.

References

  1. Abdullah, S.S., Hosseini-Hashemi, S., Hussein, N.A. and Nazemnezhad, R. (2020a), "Effect of temperature on vibration of cracked single-walled carbon nanotubes embedded in an elastic medium under different boundary conditions", Mech. Based Des. Struct., 1-26. https://doi.org/10.1080/15397734.2020.1759431.
  2. Abdullah, S.S., Hosseini-Hashemi, S., Hussein, N.A. and Nazemnezhad, R. (2020b), "Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium", J. Therm. Stress., 43(10), 1316-1332. https://doi.org/10.1080/01495739.2020.1780175.
  3. Abdullah, S.S., Hosseini-Hashemi, S., Hussein, N.A. and Nazemnezhad, R. (2020c), "Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh-Ritz method", J. Brazil. Soc. Mech. Sci. Eng., 42(11), 1-20. https://doi.org/10.1007/s40430-020-02664-0.
  4. Akbas, S.D. (2017), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X.
  5. Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039.
  6. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  7. Apuzzo, A., Barretta, R., Luciano, R., de Sciarra, F.M. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model", Compos. Part B Eng., 123, 105-111. https://doi.org/10.1016/j.compositesb.2017.03.057.
  8. Azrar, A., Azrar, L. and Aljinaidi, A.A. (2016), "Analytical and numerical modeling of higher order free vibration characteristics of single-walled carbon nanotubes", Mech. Adv. Mater. Struct., 23(11), 1245-1262. https://doi.org/10.1080/15376494.2015.1068405.
  9. Barretta, R., Faghidian, S.A. and Luciano, R. (2019), "Longitudinal vibrations of nano-rods by stress-driven integral elasticity", Mech. Adv. Mater. Struct., 26(15), 1307-1315. https://doi.org/10.1080/15376494.2018.1432806.
  10. Berghouti, H., Adda Bedia, E., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  11. Berrabah, H., Tounsi, A., Semmah, A. and Adda Bedia, E. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351.
  12. Demir, C. and Civalek, O. (2017), "A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix", Compos. Struct., 168, 872-884. https://doi.org/10.1016/j.compstruct.2017.02.091.
  13. Dona, M., Palmeri, A. and Lombardo, M. (2015), "Dynamic analysis of multi-cracked Euler-Bernoulli beams with gradient elasticity", Comput. Struct., 161, 64-76. https://doi.org/10.1016/j.compstruc.2015.08.013.
  14. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. A Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004.
  15. Ebrahimi, F. and Mahmoodi, F. (2018), "Vibration analysis of carbon nanotubes with multiple cracks in thermal environment", Adv. Nano Res., 6(1), 57-80. https://doi.org/10.12989/anr.2018.6.1.057.
  16. Ebrahimi, F., Daman, M. and Mahesh, V. (2019), "Thermo-mechanical vibration analysis of curved imperfect nano-beams based on nonlocal strain gradient theory", Adv. Nano Res., 7(4), 249-263. https://doi.org/10.12989/anr.2019.7.4.249.
  17. 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.
  18. Fazelzadeh, S. and Pouresmaeeli, S. (2013), "Thermo-mechanical vibration of double-orthotropic nanoplates surrounded by elastic medium", J. Therm. Stress., 36(3), 225-238. https://doi.org/10.1080/01495739.2013.765170.
  19. Hosseini-Hashemi, S., Nazemnezhad, R. and Rokni, H. (2015), "Nonlocal nonlinear free vibration of nanobeams with surface effects", Eur. J. Mech. A Solid, 52, 44-53. https://doi.org/10.1016/j.euromechsol.2014.12.012.
  20. Hussein, N.A., Rasul, H.A. and Abdullah, S.S. (2020), "The free vibration analysis of multi-cracked nanobeam using nonlocal elasticity theory", Zanco J. Pure Appl. Sci., 32(2), 39-54. https://doi.org/10.21271/ZJPAS.32.2.5.
  21. Khorshidi, M.A. and Shariati, M. (2016), "Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory", , J. Brazil. Soc. Mech. Sci. Eng., 38(8), 2607-2619. https://doi.org/10.1007/s40430-015-0388-3.
  22. Loya, J., Aranda-Ruiz, J.A. and Fernandez-Saez, J. (2014), "Torsion of cracked nanorods using a nonlocal elasticity model", J. Phys. D Appl. Phys., 47(11), 115304. https://doi.org/10.1088/0022-3727/47/11/115304.
  23. Loya, J., Lopez-Puente, J., Zaera, R. and Fernandez-Saez, J. (2009), "Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model", J. Appl. Phys., 105(4), 044309. https://doi.org/10.1063/1.3068370.
  24. Lu, J.P. (1997), "Elastic properties of single and multilayered nanotubes", J. Phys. Chem. Solid, 58(11), 1649-1652. https://doi.org/10.1016/S0022-3697(97)00045-0.
  25. Ma'en, S.S. (2017), "Superharmonic resonance analysis of nonlocal nano beam subjected to axial thermal and magnetic forces and resting on a nonlinear elastic foundation", Microsyst. Technol., 23(8), 3319-3330. https://doi.org/10.1007/s00542-016-3161-3.
  26. Mehta, V. and Kumar, S. (1994), "Temperature dependent torsional properties of high performance fibres and their relevance to compressive strength", J. Mater. Sci., 29(14), 3658-3664. https://doi.org/10.1007/BF00357332.
  27. Nazemnezhad, R. and Fahimi, P. (2017), "Free torsional vibration of cracked nanobeams incorporating surface energy effects", Appl. Math. Mech., 38(2), 217-230. https://doi.org/10.1007/s10483-017-2167-9.
  28. Nazemnezhad, R., Mahoori, R. and Samadzadeh, A. (2019), "Surface energy effect on nonlinear free axial vibration and internal resonances of nanoscale rods", Eur. J. Mech. A Solids, 77, 103784. https://doi.org/10.1016/j.euromechsol.2019.05.001.
  29. Numanoglu, H.M. and Civalek, O. (2019), "On the torsional vibration of nanorods surrounded by elastic matrix via nonlocal FEM", Int. J. Mech. Sci., 161, 105076. https://doi.org/10.1016/j.ijmecsci.2019.105076.
  30. Polizzotto, C. (2014), "Stress gradient versus strain gradient constitutive models within elasticity", Int. J. Solid Struct., 51(9), 1809-1818. https://doi.org/10.1016/j.ijsolstr.2014.01.021.
  31. Polizzotto, C. (2015), "A unifying variational framework for stress gradient and strain gradient elasticity theories", Eur. J. Mech. A Solids, 49, 430-440. https://doi.org/10.1016/j.euromechsol.2014.08.013.
  32. Polizzotto, C. (2016), "Variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models", Int. J. Solid Struct., 80, 405-419. https://doi.org/10.1016/j.ijsolstr.2015.09.015.
  33. Praveen, G. and Reddy, J. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
  34. Rahmani, O., Hosseini, S., Noroozi Moghaddam, M. and Fakhari Golpayegani, I. (2015), "Torsional vibration of cracked nanobeam based on nonlocal stress theory with various boundary conditions: an analytical study", Int. J. Appl. Mech., 7(3), 1550036. https://doi.org/10.1142/S1758825115500362.
  35. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  36. Reddy, J. and Pang, S. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511. https://doi.org/10.1063/1.2833431.
  37. Setoodeh, A., Rezaei, M. and Shahri, M.Z. (2016), "Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory", Appl. Math. Mech., 37(6), 725-740. https://doi.org/10.1007/s10483-016-2085-6.
  38. Shakhlavi, S.J., Hosseini-Hashemi, S. and Nazemnezhad, R. (2020), "Torsional vibrations investigation of nonlinear nonlocal behaviour in terms of functionally graded nanotubes", Int. J. Non Linear Mech., 103513. https://doi.org/10.1016/j.ijnonlinmec.2020.103513.
  39. Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013.
  40. Wang, Q. and Wang, C. (2007), "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes", Nanotechnology, 18(7), 075702. https://doi.org/10.1088/0957-4484/18/7/075702.
  41. Yao, X. and Han, Q. (2006), "Buckling analysis of multiwalled carbon nanotubes under torsional load coupling with temperature change", J. Eng. Mater. Technol., 128(3), 419-427. https://doi.org/10.1115/1.2203102.
  42. Yayli, M.O., Kandemir, S.Y. and Cercevik, A.E. (2019), "Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen's nonlocal differential model", J. Low Freq. Noise V. A., 38(1), 70-87. https://doi.org/10.1177/1461348418813255.
  43. Zur, K.K., Arefi, M., Kim, J. and Reddy, J. (2020), "Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory", Compos. Part B Eng., 182, 107601. https://doi.org/10.1016/j.compositesb.2019.107601.