Advances in nano research

  • 제17권1호
  • /
  • Pages.19-32
  • /
  • 2024
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An innovative approach for analyzing free vibration in functionally graded carbon nanotube sandwich plates

  • Shahabeddin Hatami (Department of Civil Engineering, Yasouj University) ;
  • Mohammad J. Zarei (Department of Civil Engineering, Yasouj University) ;
  • Seyyed H. Asghari Pari (Department of Civil Engineering, Yasouj University)
  • 투고 : 2023.10.14
  • 심사 : 2024.06.18
  • 발행 : 2024.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

Functionally graded-carbon nanotube (FG-CNT) is expected to be a new generation of materials with a wide range of potential applications in technological fields such as aerospace, defense, energy, and structural industries. In this paper, an exact finite strip method for functionally graded-carbon nanotube sandwich plates is developed using first-order shear deformation theory to get the exact natural frequencies of the plates. The face sheets of the plates are made of FG-CNT with continuous and smooth grading based on the power law index. The equations of motion have been generated based on the Hamilton principle. By extracting the exact stiffness matrix for any strip of the sandwich plate as a non-algebraic function of natural frequencies, it is possible to calculate the exact free vibration frequencies. The accuracy and efficiency of the current method is established by comparing its findings to the results of the literature works. Examples are presented to prove the efficiency of the generated method to deal with various problems, such as the influence of the length-to-height ratio, the power law index, and a core-to-face sheet thickness of the single and multi-span sandwich plates with various boundary conditions on the natural frequencies. The exact results obtained from this analysis can check the validity and accuracy of other numerical methods.

키워드

참고문헌

  1. Bahrami, M.R. and Hatami, S. (2016), "Free and forced transverse vibration analysis of moderately thick orthotropic plates using spectral finite element method", J. Solid Mech., 8(4), 895-915. https://doi.org/20.1001.1.20083505.2016.8.4.15.9. 1001.1.20083505.2016.8.4.15.9
  2. Barati, A., Hadi, A., Nejad, M.Z. and Noroozi, R. (2022), "On vibration of bi-directional functionally graded nanobeams under magnetic field", Mech. Based Des Struct. Mach., 50(2), 468-485. https://doi.org/10.1080/15397734.2020.1719507.
  3. Boscolo, M. and Banerjee, J.R. (2011), "Dynamic stiffness elements and their applications for plates using first order shear deformation theory", Comput. Struct., 89(3-4), 395-410. https://doi.org/10.1016/j.compstruc.2010.11.005.
  4. Cheung, Y.K. (1968), "The finite strip method in the analys of elastic plates with two opposite simply supported ends", Proceedings of the Institution of Civil Engineers, 40(1), 1-7. https://doi.org/10.1680/iicep.1968.7709
  5. Chiker, Y., Bachene, M., Attaf, B., Hafaifa, A. and Guemana, M. (2023), "Uncertainty influence of nanofiller dispersibilities on the free vibration behavior of multi-layered functionally graded carbon nanotube-reinforced composite laminated plates", Acta Mechanica, 234, 1687-1711. https://doi.org/10.1007/s00707-022-03438-6.
  6. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure. Structural Engineering and Mechanics", Struct. Eng. Mech., 68(6), 721-733. https://doi.org/10.12989/sem.2018.68.6.721.
  7. Eghbali, M. and Hosseini, S.A. (2023), "On moving harmonic load and dynamic response of carbon nanotube-reinforced composite beams using higher-order shear deformation theories", Mech. Adv. Compos. Struct., 10(2), 257-270. https://doi.org/10.22075/MACS.2022.28205.1431.
  8. El Meiche, N., Tounsi, A., Ziane, N. and Mechab, I. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004.
  9. Gao, W., Liu, Y., Qin, Z. and Chu, F. (2022), "Wave propagation in smart sandwich plates with functionally graded nanocomposite porous core and piezoelectric layers in multi-physics environment", Int. J. Appl. Mech., 14(7), 2250071. https://doi.org/10.1142/S1758825122500715.
  10. Garg, A., Chalak, H.D., Zenkour, A.M., Belarbi, M.O. and Sahoo, R. (2022), "Bending and free vibration analysis of symmetric and unsymmetric functionally graded CNT reinforced sandwich beams containing softcore", Thin Wall. Struct., 170, 108626. https://doi.org/10.1016/j.tws.2021.108626.
  11. Gholami, M., Gorji Azandariani, M., Najat Ahmed, A. and Abdolmaleki, H. (2023), "Proposing a dynamic stiffness method for the free vibration of bi-directional functionally-graded timoshenko nanobeams", Adv. Nano Res., 14(2), 127-139. https://doi.org/10.12989/.2023.14.2.127.
  12. Hadji, L. and Avcar, M. (2021), "Free vibration analysis of FG porous sandwich plates under various boundary conditions", J. Appl. Comput. Mech., 7(2), 505-519. https://doi.org/10.22055/JACM.2020.35328.2628.
  13. Hatami, S., Ronagh, H.R. and Azhari, M. (2008), "Exact free vibration analysis of axially moving viscoelastic plates", Comput. Struct., 86(17-18), 1738-1746. https://doi.org/10.1016/j.compstruc.2008.02.002.
  14. Hosseini, H.S., Khorshidi, K. and Payandeh, H. (2009), "Vibration analysis of moderately thick rectangular plates with internal line support using the Rayleigh-Ritz approach", Scientia Iranica, 16(1), 22-39.
  15. Kumar, V., Singh, S.J., Saran, V.H. and Harsha, S.P. (2021), "Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov's method", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(4), 880-897. https://doi.org/10.1177/1464420720980491.
  16. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  17. Malik, M. and Bert, C.W. (1998), "Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method", Int. J. Solids Struct., 35(3-4), 299-318. https://doi.org/10.1016/S0020-7683(97)00073-5.
  18. Marandi, S.M. and Karimipour, I. (2023), "Free vibration analysis of a nanoscale FG-CNTRCs sandwich beam with flexible core: Implementing an extended high order approach", Eng. Struct., 276, 115320. https://doi.org/10.1016/j.engstruct.2022.115320.
  19. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  20. Mousavi, S.B., Amir, S., Jafari, A. and Arshid, E. (2021), "Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories", Adv. Nano Res., 10(3), 235-251. https://doi.org/10.12989/anr.2021.10.3.235.
  21. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
  22. Riahi, F., Mamghaderi, V., Zirakian, T. and Sanaati, B. (2019), "Further assessment of buckling stability of steel plates", Int. J. Civil Eng. Technol., 10(4), 1715-1721.
  23. Rout, M. and Hota, S.S. (2023), "Geometrically nonlinear free vibration of CNTs reinforced sandwich conoidal shell in thermal environment", Acta Mechanica, 1-18. https://doi.org/10.1007/s00707-023-03508-3.
  24. Soltani, M.R., Hatami, S., Azhari, M. and Ronagh, H.R. (2016), "Dynamic stiffness method for free vibration of moderately thick functionally graded plates", Mech. Adv. Compos. Struct., 3(1), 15-30. https://doi.org/10.22075/macs.2016.404.
  25. Soni, S.K., Thomas, B., Swain, A. and Roy, T. (2022), "Functionally graded carbon nanotubes reinforced composite structures: An extensive review", Compos. Struct., 299, 116075. https://doi.org/10.1016/j.compstruct.2022.116075.
  26. Talebi, S., Arvin, H. and Beni, Y.T. (2023), "Thermal free vibration examination of sandwich piezoelectric agglomerated randomly oriented CNTRC Timoshenko beams regarding pyroelectricity", Eng. Anal. Bound. Elem., 146, 500-516. https://doi.org/10.1016/j.enganabound.2022.11.013.
  27. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech. A Solids, 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008.
  28. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-hill, New York.
  29. Wittrick, W.H. and Williams, F.W. (1974), "Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings", Int. J. Mech. Sci., 16(4), 209-239. https://doi.org/10.1016/0020-7403(74)90069-1.
  30. Wolfram Research, Inc. (2024), Mathematica, Version 14.0, Champaign, IL, U.S.A. https://www.wolfram.com
  31. Wu, H., Kitipornchai, S. and Yang, J. (2015), "Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets", Int. J. Struct. Stabil. Dyn., 15(7), 1540011. https://doi.org/10.1142/S0219455415400118.
  32. Wu, X. and Fang, T. (2022), "Intelligent computer modeling of large amplitude behavior of FG inhomogeneous nanotubes", Adv. Nano Res., 12(6), 617-627. https://doi.org/10.12989/anr.2022.12.6.617.
  33. Yang, Z. and He, D. (2019), "Vibration and buckling of functionally graded sandwich micro-plates based on a new size-dependent model", Int. J. Appl. Mech., 11(1), 1950004. https://doi.org/10.1142/S1758825119500042.
  34. Yang, Z., Wu, P., Liu, W. and Fang, H. (2020), "Analytical solutions for functionally graded sandwich plates bonded by viscoelastic interlayer based on kirchhoff plate theory", Int. J. Appl. Mech., 12(6), 2050062. https://doi.org/10.1142/S1758825120500623.
  35. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  36. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct, 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.