Advances in nano research

  • 제17권3호
  • /
  • Pages.197-211
  • /
  • 2024
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On the thermo-mechanical vibration of an embedded short-fiber-reinforced nanobeam

  • Murat Akpinar (Bursa Uludag University, Engineering Faculty, Department of Civil Engineering, Gorukle Campus) ;
  • Busra Uzun (Bursa Uludag University, Engineering Faculty, Department of Civil Engineering, Gorukle Campus) ;
  • Mustafa Ozgur Yayli (Bursa Uludag University, Engineering Faculty, Department of Civil Engineering, Gorukle Campus)
  • 투고 : 2024.04.17
  • 심사 : 2024.08.17
  • 발행 : 2024.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This work investigates the thermo-mechanical vibration frequencies of an embedded composite nano-beam restrained with elastic springs at both ends. Composite nanobeam consists of a matrix and short fibers as reinforcement elements placed inside the matrix. An approach based on Fourier sine series and Stokes' transform is adopted to present a general solution that can examine the elastic boundary conditions of the short-fiber-reinforced nanobeam considered with the Halpin-Tsai model. In addition to the elastic medium effect considered by the Winkler model, the size effect is also considered on the basis of nonlocal strain gradient theory. After creating an eigenvalue problem that includes all the mentioned parameters, this problem is solved to examine the effects of fiber and matrix properties, size parameters, Winkler stiffness and temperature change. The numerical results obtained at the end of the study show that increasing the rigidity of the Winkler foundation, the ratio of fiber length to diameter and the ratio of fiber Young's modulus to matrix Young's modulus increase the frequencies. However, thermal loads acting in the positive direction and an increase in the ratio of fiber mass density to matrix mass density lead to a decrease in frequencies. In this study, it is clear from the eigenvalue solution calculating the frequencies of thermally loaded embbeded short-fiber-reinforced nanobeams that changing the stiffness of the deformable springs provides frequency control while keeping the other properties of the nanobeam constant.

키워드

참고문헌

  1. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M.A. (2023), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct. Mach., 51(10), 5383-5406. https://doi.org/10.1080/15397734.2021.1999263.
  2. Abdullah, S.S., Hosseini-Hashemi, S., Hussein, N.A. and Nazemnezhad, R. (2020), "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. Abrate, S. (1986), "The mechanics of short fiber-reinforced composites: A review", Rubber Chem. Technol., 59(3), 384-404. https://doi.org/10.5254/1.3538207.
  4. Ahmadi, I., Sladek, J. and Sladek, V. (2024), "Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method", Mech. Adv. Mater. Struct., 31(18), 4352-4373. https://doi.org/10.1080/15376494.2023.2195400.
  5. Alfred, P.B., Ossia, C.V. and Big-Alabo, A. (2024), "Free nonlinear vibration analysis of a functionally graded microbeam resting on a three-layer elastic foundation using the continuous piecewise linearization method", Arch. Appl. Mech., 94(1), 57-80. https://doi.org/10.1007/s00419-023-02505-1.
  6. Attia, M.A., Matbuly, M.S., Osman, T. and AbdElkhalek, M. (2024), "Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method", Acta Mech., 235(4), 1961-2012. https://doi.org/10.1007/s00707-023-03797-8.
  7. Barati, M.R. and Zenkour, A. (2018), "Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments", Mech. Adv. Mater. Struct., 25(8), 669-680. https://doi.org/10.1080/15376494.2017.1308603.
  8. Beni, Y.T. (2023), "Size-dependent electro-thermal buckling analysis of flexoelectric microbeams", Int. J. Struct. Stabil. Dyn., 24(8). https://doi.org/10.1142/S0219455424500937.
  9. Chen, J., Qu, W., Ye, C., Zhao, Z. and Wang, H. (2024), "Nonlinear vibration and dynamic stability of dielectric sandwich micro-beams", Int. J. Mech. Sci., https://doi.org/10.1016/j.ijmecsci.2023.108738.
  10. Civalek, O ., Uzun, B. and Yayli, M.O . (2022), "Nonlocal free vibration of embedded short-fiber-reinforced nano-/micro-rods with deformable boundary conditions", Materials, 15(19), 6803. https://doi.org/10.3390/ma15196803.
  11. Civalek, O., Uzun, B. and Yayli, M.O. (2023), "Torsional static and free vibration analysis of noncircular short-fiber-reinforced microwires with arbitrary boundary conditions", Polym. Compos., Early View. https://doi.org/10.1002/PC.27321.
  12. Dean, D., Obore, A.M., Richmond, S. and Nyairo, E. (2006), "Multiscale fiber-reinforced nanocomposites: Synthesis, processing and properties", Compos. Sci. Technol., 66(13), 2135-2142. https://doi.org/10.1016/J.COMPSCITECH.2005.12.015.
  13. Dehkordi, H.R.B. and Beni, Y.T. (2023), "Size-dependent coupled bending-torsional vibration of functionally graded carbon nanotube reinforced composite Timoshenko microbeams", Arch. Civ. Mech. Eng., 23(3), 1-12. https://doi.org/10.1007/s43452-023-00725-4.
  14. 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.
  15. Ebnali Samani, M.S. and Beni, Y.T. (2018), "Size dependent thermo-mechanical buckling of the flexoelectric nanobeam", Mater. Res. Express, 5(8), 085018. https://doi.org/10.1088/2053-1591/AAD2CA.
  16. Ebrahimi, F., Daman, M. and Mahesh, V. (2019), "Thermomechanical 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. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/SEM.2016.59.2.343.
  18. El-Shahrany, H.D. and Zenkour, A.M. (2023), "A nonlocal vibration suppression for a multilayered magneto-viscoelastic nanobeam on a three-parameter-type medium", Mech. Adv. Mater. Struct.. https://doi.org/10.1080/15376494.2023.2278763.
  19. Feo, L., Lovisi, G. and Penna, R. (2023), "Free vibration analysis of functionally graded nanobeams based on surface stress-driven nonlocal model", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2023.2289079.
  20. Frigione, M. and Lettieri, M. (2018), "Durability issues and challenges for material advancements in FRP employed in the construction industry", Polymers., 10(3), 247. https://doi.org/10.3390/polym10030247.
  21. Ghobadi, A., Beni, Y.T. and Golestanian, H. (2020), "Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field", Arch. Appl. Mech., 90(9), 2025-2070. https://doi.org/10.1007/S00419-020-01708-0/FIGURES/11.
  22. Ghobadi, A., Golestanian, H., Beni, Y.T. and Zur, K.K. (2021), "On the size-dependent nonlinear thermo-electro-mechanical free vibration analysis of functionally graded flexoelectric nanoplate", Commun. Nonlinear Sci. Numer. Simul., 95, 105585. https://doi.org/10.1016/J.CNSNS.2020.105585.
  23. Ghorbani Shenas, A., Ziaee, S. and Malekzadeh, P. (2019), "A unified higher-order beam theory for free vibration and buckling of FGCNT-reinforced microbeams embedded in elastic medium based on unifying stress-strain gradient framework", Iran. J. Sci. Technol. Trans. Mech. Eng., 43(1), 469-492. https://doi.org/10.1007/s40997-018-0171-z.
  24. Gul, U. (2024), "Dynamic analysis of short-fiber reinforced composite nanobeams based on nonlocal strain gradient theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 238(7), 2641-2676. https://doi.org/10.1177/09544062241227086.
  25. Gul, U. and Aydogdu, M. (2023), "On the axial vibration of viscously damped short-fiber-reinforced nano/micro-composite rods", J. Vib. Eng. Technol., 11(3), 1327-1341. https://doi.org/10.1007/s42417-022-00643-4.
  26. Guzman de Villoria, R. and Miravete, A. (2007), "Mechanical model to evaluate the effect of the dispersion in nanocomposites", Acta Mater., 55(9), 3025-3031. https://doi.org/10.1016/j.actamat.2007.01.007.
  27. Herisanu, N., Marinca, B. and Marinca, V. (2023), "Longitudinal-transverse vibration of a functionally graded nanobeam subjected to mechanical impact and electromagnetic actuation", Symmetry, 15(7), 1376. https://doi.org/10.3390/sym15071376.
  28. Hosseini, S.M.H. and Beni, Y.T. (2023), "Free vibration analysis of rotating piezoelectric/flexoelectric microbeams", Appl. Phys. A Mater. Sci. Process., 129(5), 1-13. https://doi.org/10.1007/s00339-023-06615-z.
  29. Jena, S.K., Chakraverty, S. and Jena, R.M. (2019), "Propagation of uncertainty in free vibration of Euler-Bernoulli nanobeam", J. Brazilian Soc. Mech. Sci. Eng., 41(10), 1-18. https://doi.org/10.1007/s40430-019-1947-9.
  30. Junaedi, H., Baig, M., Dawood, A., Albahkali, E. and Almajid, A. (2020), "Mechanical and physical properties of short carbon fiber and nanofiller-reinforced polypropylene hybrid nanocomposites", Polym, 12(12), 2851. https://doi.org/10.3390/POLYM12122851.
  31. Karmakar, S. and Chakraverty, S. (2022), "Thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation", Eng. Anal. Bound. Elem., 140, 581-591. https://doi.org/10.1016/j.enganabound.2022.04.020.
  32. Khan, S.U., Li, C.Y., Siddiqui, N.A. and Kim, J.K. (2011), "Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes", Compos. Sci. Technol., 71(12), 1486-1494. https://doi.org/10.1016/j.compscitech.2011.03.022.
  33. Ladmek, M., Belkacem, A., Daikh, A.A., Bessaim, A., Garg, A., Houari, M.S.A., Belarbi, M.O. and Ouldyerou, A. (2023a), "Free vibration of functionally graded carbon nanotubes reinforced composite nanobeams", Adv. Mater. Res., 12(2), 161-177. https://doi.org/10.12989/amr.2023.12.2.161.
  34. Ladmek, M., Belkacem, A., Houari, M.S.A., Daikh, A.A., Bessaim, A., Belarbi, M.O., Tounsi, A., Khdair, A.I. and Eltaher, M.A. (2023b), "On vibration responses of advanced functionally graded carbon nanotubes reinforced composite nanobeams", J. Nano Res., 80, 49-63. https://doi.org/10.4028/p-u9eXPt.
  35. Lal, R. and Dangi, C. (2020), "Comprehensive effect of in-plane load and nonlinear thermal field on dynamic response of embedded bi-directional functionally graded tapered thick nanobeams", J. Therm. Stress., 43(12), 1577-1600. https://doi.org/10.1080/01495739.2020.1831416.
  36. Lei, H.F., Zhang, Z.Q. and Liu, B. (2012), "Effect of fiber arrangement on mechanical properties of short fiber reinforced composites", Compos. Sci. Technol., 72(4), 506-514. https://doi.org/10.1016/j.compscitech.2011.12.011.
  37. Li, C. and Qing, H. (2024), "Theoretical thermal damping vibration analysis of functionally graded viscoelastic Timoshenko microbeam with integral nonlocal strain gradient model", Mech. Based Des. Struct. Mach., 52(7), 4337-4360. https://doi.org/10.1080/15397734.2023.2227702.
  38. 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.
  39. Lin, Y., Min, J., Teng, H., Lin, J., Hu, J. and Xu, N. (2020), "Flexural performance of Steel-FRP composites for automotive applications", Automot. Innov., 3(3), 280-295. https://doi.org/10.1007/s42154-020-00109-x.
  40. Lovisi, G., Feo, L., Lambiase, A. and Penna, R. (2024), "Application of surface stress-driven model for higher vibration modes of functionally graded nanobeams", Nanomaterials, 14(4), 350. https://doi.org/10.3390/nano14040350.
  41. Marinca, B., Herisanu, N. and Marinca, V. (2023), "Investigating nonlinear forced vibration of functionally graded nanobeam based on the nonlocal strain gradient theory considering mechanical impact, electromagnetic actuator, thickness effect and nonlinear foundation", Eur. J. Mech. A/Solids, 102, 105119. https://doi.org/10.1016/j.euromechsol.2023.105119.
  42. Modanloo, V., Mashayekhi, A., Taghipour Lahijani, Y. and Akhoundi, B. (2023), "Prediction of large deflection of chromium nanobeams using a hybrid meta-heuristic algorithm", J. Eng. Res., In Press. https://doi.org/10.1016/J.JER.2023.12.004.
  43. Mohammadi, M., Farajpour, A. and Rastgoo, A. (2023), "Coriolis effects on the thermo-mechanical vibration analysis of the rotating multilayer piezoelectric nanobeam", Acta Mech., 234(2), 751-774. https://doi.org/10.1007/s00707-022-03430-0.
  44. Mojahedi, M. (2024), "Analytical and Numerical Investigation of a Nonlinear Nanobeam Model", J. Vib. Eng. Technol., 12(3), 3471-3485. https://doi.org/10.1007/s42417-023-01058-5.
  45. Moradi, Z., Ebrahimi, F. and Davoudi, M. (2023), "On the vibration and energy harvesting of the piezoelectric MEMS/NEMS via nonlocal strain gradient theory", Adv. Nano Res., 15(3), 203-213. https://doi.org/10.12989/anr.2023.15.3.203.
  46. Murin, J., Aminbaghai, M. and Kutis, V. (2010), "Exact solution of the bending vibration problem of FGM beams with variation of material properties", Eng. Struct., 32(6), 1631-1640. https://doi.org/10.1016/j.engstruct.2010.02.010.
  47. Nalbant, M.O., Bagdatli, S.M. and Tekin, A. (2023), "Investigation of nonlinear vibration behavior of the stepped nanobeam", Adv. Nano Res., 15(3), 215-224. https://doi.org/10.12989/anr.2023.15.3.215.
  48. Pan, N. (1993), "Theoretical determination of the optimal fiber volume fraction and fiber-matrix property compatibility of short fiber composites", Polym. Compos., 14(2), 85-93. https://doi.org/10.1002/PC.750140202.
  49. Penna, R., Lambiase, A., Lovisi, G. and Feo, L. (2023), "Investigating hygrothermal bending behavior of FG nanobeams via local/nonlocal stress gradient theory of elasticity with general boundary conditions", Mech. Adv. Mater. Struct., 1-10. https://doi.org/10.1080/15376494.2023.2269938.
  50. Qing, H. (2023), "Size-dependent nonlinear forced vibration of microbeam using two-phase local/nonlocal viscoelastic integral model with thermal effects", J. Vib. Control., 10775463231210030. https://doi.org/10.1177/10775463231210030.
  51. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  52. Shafiei, N., Ghadiri, M. and Mahinzare, M. (2019), "Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment", Mech. Adv. Mater. Struct., 26(2), 139-155. https://doi.org/10.1080/15376494.2017.1365982.
  53. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., 63(3), 401-415. https://doi.org/10.12989/sem.2017.63.3.401.
  54. Sreejith, M. and Rajeev, R.S. (2021), "Fiber reinforced composites for aerospace and sports applications", Fiber Reinf. Compos. Const. Compat. Perspect. Appl., 821-859. https://doi.org/10.1016/B978-0-12-821090-1.00023-5.
  55. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001.
  56. Tuyen, B. Van, and Du, N.D. (2023), "Analytic solutions for static bending and free vibration analysis of FG nanobeams in thermal environment", J. Therm. Stress., 46(9), 871-894. https://doi.org/10.1080/01495739.2023.2211642.
  57. Usmani, A.S., Rotter, J.M., Lamont, S., Sanad, A.M. and Gillie, M. (2001), "Fundamental principles of structural behaviour under thermal effects", Fire Saf. J., 36(8), 721-744. https://doi.org/10.1016/S0379-7112(01)00037-6.
  58. Uzun, B., Civalek, O . and Yayli, M.O . (2023), "A hardening nonlocal approach for vibration of axially loaded nanobeam with deformable boundaries", Acta Mech., 234(5), 2205-2222. https://doi.org/10.1007/s00707-023-03490-w.
  59. Uzun, B. and Yayli, M.O . (2024), "Rotary inertia effect on dynamic analysis of embedded FG porous nanobeams under deformable boundary conditions with the effect of neutral axis", J. Brazilian Soc. Mech. Sci. Eng., 46(2), 1-20. https://doi.org/10.1007/s40430-023-04605-z.
  60. Vahidi-Moghaddam, A., Rajaei, A., Azadi Yazdi, E., Eghtesad, M. and Necsulescu, D.S. (2023), "Nonlinear forced vibrations of nonlocal strain gradient microbeams", Mech. Based Des. Struct. Mach., 51(2), 1035-1053. https://doi.org/10.1080/15397734.2020.1860773.
  61. 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.
  62. Wei, D., Zhang, N., Jiao, Y., Fan, Y., Yu, H. and Koochakianfard, O. (2024), "Magneto-hygro-thermo-mechanical vibration analysis of spinning nanobeams with axisymmetric cross-sections incorporating surface, rotary inertia, and thickness effects", Eng. Struct., 305, 117702. https://doi.org/10.1016/j.engstruct.2024.117702.
  63. Yang, W., Wang, S., Kang, W., Yu, T. and Li, Y. (2023), "A unified high-order model for size-dependent vibration of nanobeam based on nonlocal strain/stress gradient elasticity with surface effect", Int. J. Eng. Sci., 182, 103785. https://doi.org/10.1016/j.ijengsci.2022.103785.
  64. Yayli, M.O., Uzun, B. and Deliktas, B. (2022), "Buckling analysis of restrained nanobeams using strain gradient elasticity", Wave Random Complex Med., 32(6), 2960-2979. https://doi.org/10.1080/17455030.2020.1871112.
  65. Yuan, Y., Niu, Z. and Smitt, J. (2023), "Magneto-hygro-thermal vibration analysis of the viscoelastic nanobeams reinforcedwith carbon nanotubes resting on Kerr's elastic foundation based on NSGT", Adv. Compos. Mater., 32(4), 568-590. https://doi.org/10.1080/09243046.2022.2122766.
  66. Zaman, A., Gutub, S.A. and Wafa, M.A. (2013), "A review on FRP composites applications and durability concerns in the construction sector", J. Reinf. Plast. Compos., 32(24), 1966-1988. https://doi.org/10.1177/0731684413492868.
  67. Zhao, X., Zheng, S. and Li, Z. (2022), "Bending, free vibration and buckling analyses of AFG flexoelectric nanobeams based on the strain gradient theory", Mech. Adv. Mater. Struct., 29(4), 548-563. https://doi.org/10.1080/15376494.2020.1779880.