DOI QR코드

DOI QR Code

Static stability and vibration response of rotating carbon-nanotube-reinforced composite beams in thermal environment

  • Ozge Ozdemir (Department of Aeronautical Engineering, Istanbul Technical University) ;
  • Huseyin Ural (Department of Aeronautical Engineering, Istanbul Technical University) ;
  • Alexandre de Macedo Wahrhaftig (Department of Construction and Structures, Polytechnic School, Federal University of Bahia)
  • 투고 : 2023.02.23
  • 심사 : 2024.04.01
  • 발행 : 2024.05.25

초록

The objective of this paper is to present free vibration and static stability analyses of rotating composite beams reinforced with carbon nanotubes (CNTs) under uniform thermal loads. Beam structural equations and CNT-reinforced composite (CNTRC) beam formulations are derived based on Timoshenko beam theory (TBT). The temperature-dependent properties of the beam material, such as the elastic modulus, shear modulus, and material density, are assumed to vary over the thickness according to the rule of mixture. The beam material is modeled as a mixture of single-walled carbon nanotubes (SWCNTs) in an isotropic matrix. The SWCNTs are aligned and distributed in the isotropic matrix with different patterns of reinforcement, namely the UD (uniform), FG-O, FG-V, FG- Λ and FG-X distributions, where FG-V and FG- Λ are asymmetric patterns. Numerical examples are presented to illustrate the effects of several essential parameters, including the rotational speed, hub radius, effective material properties, slenderness ratio, boundary conditions, thermal force, and moments due to temperature variation. To the best of the authors' knowledge, this study represents the first attempt at the finite element modeling of rotating CNTRC Timoshenko beams under a thermal environment. The results are presented in tables and figures for both symmetric and asymmetric distribution patterns, and can be used as benchmarks for further validation.

키워드

참고문헌

  1. Akurathi, V.L. and Kolli, L.C. (2017), "Free vibration behavior of FG-CNT reinforced composite plates using higher order shear deformation theory", Int. J. Res. Appl. Sci. Eng. Technol., 5(11), 1408-1418. https://doi.org/10.22214/ijraset.2017.11204
  2. Almitani, K.H. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct. 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643
  3. Ansari, R., Torabi, J. and Hassani, R. (2019), "Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates", Comput. Math. Appl. 77(5), 1294-1311. https://doi.org/10.1016/j.camwa.2018.11.009
  4. Ansari, R., Faghih Shojaei, M., Mohammadi, V., Gholami, R. and Sadeghi, F. (2014), "Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams", Compos. Struct., 113(1), 316-327. https://doi.org/10.1016/j.compstruct.2014.03.015
  5. Arvin, H. and Bakhtiari-Nejad, F. (2013a), "Nonlinear free vibration analysis of rotating composite Timoshenko beams", Compos. Struct., 96, 29-43. https://doi.org/10.1016/j.compstruct.2012.09.009
  6. Arvin, H. and Bakhtiari-Nejad, F. (2013b), "Nonlinear modal interaction in rotating composite Timoshenko beams", Compos. Struct., 96, 121-134. https://doi.org/10.1016/j.compstruct.2012.10.015
  7. Babamiri, B.B., Shahrjerdi, A. and Bayat, M. (2020), "Effect of geometrical imperfection on the thermomechanical behavior of functionally graded material rotating disk", J. Braz. Soc. Mech. Sci. Eng., 42, 271. https://doi.org/10.1007/s40430-020-02360-z
  8. Bhattacharya, S. and Das, D. (2019), "Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory", Compos. Struct. 215, 471-492. https://doi.org/10.1016/j.compstruct.2019.01.080
  9. Chung, J. and Yoo, H.H. (2002), "Dynamic analysis of a rotating cantilever beam by using the finite element method", J. Sound Vib., 249(1), 147-164. https://doi.org/10.1006/jsvi.2001.3856
  10. Demirsoy Karahan, E. and O zdemir, O . (2020), "Finite element formulation and free vibration analyses of rotating functionally graded blades", J. Theor. Appl. Mech., 59(1), 3-15. https://doi.org/10.1016/j.camwa.2018.11.009
  11. Di Sciuva, M. and Sorrenti, M. (2019), "Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory", Compos. Struct., 227, 111324. https://doi.org/10.1016/j.compstruct.2019.111324
  12. Eltaher, M.A., Abdelrahman, A.A. and Esen, I. (2021), "Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load", Eur. Phys. J. Plus 123, 1-21. https://doi.org/10.1140/epjp/s13360-021-01682-8
  13. Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241
  14. Fadelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A, 36, 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  15. Feli, S., Karami, L. and Jafari, S.S. (2019), "Analytical modeling of low velocity impact on carbon nanotube-reinforced composite (CNTRC) plates", Mech. Adv. Mater. Struct. 26(5), 394-406. https://doi.org/10.1080/15376494.2017.1400613
  16. Fu, Y., Zhong, J., Shao, X. and Tao, C. (2016), "Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations", Mech. Adv. Mater. Struct., 23(11), 1284-1289. https://doi.org/10.1080/15376494.2015.1068404
  17. Ghaffari, S.S., Ceballes, S. and Abdelkefi, A. (2020), "Nonlinear dynamical responses of forced carbon nanotube-based mass sensors under the influence of thermal loadings", Nonlinear Dyn 100, 1013-1035. https://doi.org/10.1007/s11071-020-05565-y
  18. Ghasemi, A.R. and Soleymani, M. (2021), "Effects of carbon nanotubes distribution on the buckling of carbon nanotubes/ fiber/polymer/metal hybrid laminates cylindrical shell", J. Sandw. Struct. Mater. 23(6), 2086-2105. https://doi.org/10.1177/1099636220909786
  19. Giannopoulos, G.I., Kakavas, P.A. and Anifantis, N.K. (2008), "Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach", Comput. Mater. Sci. 41(4), 561-569. https://doi.org/10.1016/j.commatsci.2007.05.016
  20. Han, Y. and Elliott, J. (2007), Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  21. Heidari, M. and Arvin, H. (2019), "Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes," J. Vib. Control 25(14), 2063-2078. https://doi.org/10.1177/1077546319847836
  22. Karamanli, A. and Vo, T.C. (2021), "Finite element model for carbon nanotube-reinforced and graphene nanoplatelet-reinforced composite beams", Compos. Struct. 264. https://doi.org/10.1016/j.compstruct.2021.113739
  23. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol. 82-83, 499-512. https://doi.org/10.1016/j.ast.2018.10.001
  24. Khadir, A.I., Daikh, A.A. and Eltaher, M.A. (2021), "Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates", Adv. Nano Res., 11(6), 621-640. https://doi.org/10.12989/anr.2021.11.6.621
  25. Khosravi, S., Arvin, H. and Kiani, Y. (2019a), "Interactive thermal and inertial buckling of rotating temperature-dependent FGCNT reinforced composite beams", Compos. B. Eng. 175, 107178. https://doi.org/10.1016/j.compositesb.2019.107178
  26. Khosravi, S., Arvin, H. and Kiani, Y. (2019b), "Vibration analysis of rotating composite beams reinforced with carbon nanotubes in thermal environment", Int. J. Mech. Sci. 164, 105187. https://doi.org/10.1016/j.ijmecsci.2019.105187
  27. Kilic, B. and O zdemir, O . (2021), "Vibration and stability analyses of functionally graded beams", Arch. Mech. Eng. 68(1), 93-113. https://doi.org/10.24425/ame.2021.137043
  28. Kiani, Y. and Eslami, M.R. (2013), "An exact solution for thermal buckling of annular FGM plates on an elastic medium", Compos. B Eng., 45(1), 101-110. https://doi.org/10.1016/j.compositesb.2012.09.034
  29. Kollar, L.P. and Springer, G.S. (2003), Mechanics of Composite Structures, Cambridge University Press, U.K.
  30. Lin, B., Chen, B., Zhu, B., Li, J., and Li, Y. (2021), "Dynamic stability analysis for rotating pre-twisted FG-CNTRC beams with geometric imperfections restrained by an elastic root in thermal environment", Thin Wall. Struct., 164, 107902. https://doi.org/10.1016/j.tws.2021.107902
  31. Liu, Y., Wang, X., Liu, L., Wu, B. and Yang, Q. (2022), "On the forced vibration of high-order functionally graded nanotubes under the rotation via intelligent modeling", Adv. Nano Res. 13(1), 47-61. https://doi.org/10.12989/anr.2022.13.1.047
  32. Lu, X. and Hu, Z. (2012), "Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling", Compos. B. Eng., 43(4), 1902-1913. https://doi.org/10.1016/j.compositesb.2012.02.002
  33. Mangalasseri, A.S., Mahesh, V., Mukunda, S., Mahesh, V., Ponnusami, S.A., Harursampath, D. and Tounsi, A. (2023), "Vibration based energy harvesting performance of magneto-electro-elastic beams reinforced with carbon nanotubes", Adv. Nano Res., 14(1), 27-43. https://doi.org/10.12989/anr.2023.14.1.027
  34. Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model", Eng. Comput., 37(4), 2823-2836. https://doi.org/10.1007/s00366-020-00976-2
  35. Na, K.S. and Kim, J.H. (2004), "Three-dimensional thermal buckling analysis of functionally graded materials" Compos. B: Eng., 35(5), 429-437. https://doi.org/10.1016/j.compositesb.2003.11.013
  36. Ozdemir, O. (2016), "Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams", J. Theor. App. Mech. 54(4), 1205-1217. https://doi.org/10.15632/jtam-pl.54.4.1205
  37. Ozdemir Ozgumus, O. and Kaya, M.O. (2013), "Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending-bending-torsion coupling", Arch. Appl. Mech., 83, 97-108. https://doi.org/10.1007/s00419-012-0634-4
  38. Peng, X.L. and Li, X.F. (2010), "Thermal stress in rotating functionally graded hollow circular disks", Compos. Struct., 92(8), 1896-1904. https://doi.org/10.1016/j.compstruct.2010.01.008
  39. Piovan, M.T. and Sampaio, R. (2009), "A study on the dynamics of rotating beams with functionally graded properties", J. Sound Vib., 327(1-2), 134-143. https://doi.org/10.1016/j.jsv.2009.06.015
  40. Rahmani, B. (2018), "Adaptive fuzzy sliding mode control for vibration suppression of a rotating carbon nanotube-reinforced composite beam", J. Vib. Control, 24(12), 2447-63. https://doi.org/10.1177/1077546316687937
  41. Rayleigh, J.W.S.B (1877), The Theory of Sound, Dover Publications, New York, U.S.A.
  42. Satankar, R.K., Sharma, N., Ramteke, P.M., Panda S.K. and Mahapatra, S.S. (2020), "Acoustic responses of natural fibre reinforced nanocomposite structure using multiphysics approach and experimental validation", Adv. Nano Res. 9(4), 263-276. https://doi.org/10.12989/anr.2020.9.4.263
  43. Shafiei, H. and Setoodeh, A.R. (2017), "Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation", Steel Compos. Struct. 24(1), 65-77. https://doi.org/10.12989/scs.2017.24.1.065
  44. Shen, H.S.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct. 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  45. Shen, H.S. and Xiang, Y. (2013), "Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments", Eng. Struct., 56, 698-708. https://doi.org/10.1016/j.engstruct.2013.06.002
  46. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  47. Shen, Z., Xia, J. and Cheng, P. (2019), "Geometrically nonlinear dynamic analysis of FG-CNTRC plates subjected to blast loads using the weak form quadrature element method", Compos. Struct., 209, 775-788. https://doi.org/10.1016/j.compstruct.2018.11.009
  48. Sobhy, M. (2019), "Levy solution for bending response of FG carbon nanotube reinforced plates under uniform, linear, sinusoidal and exponential distributed loadings", Eng. Struct., 182, 198-212. https://doi.org/10.1016/j.engstruct.2018.12.071
  49. Tian, J., Zhang, Z. and Hua, H. (2019), "Free vibration analysis of rotating functionally graded double-tapered beam including porosities", Int. J. Mech. Sci. 150, 526-538. https://doi.org/10.1016/j.ijmecsci.2018.10.056
  50. Torabi, J., Ansari, R., and Hassani, R. (2019), "Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory", Eur. J. Mech. A/Solids 73, 144-160. https://doi.org/10.1016/j.euromechsol.2018.07.009
  51. Van Do, V.N., Jeon, J.T.T. and Lee, C.H.H. (2020), "Dynamic analysis of carbon nanotube reinforced composite plates by using Bezier extraction based isogeometric finite element combined with higher-order shear deformation theory", Mech. Mater., 142, 103307. https://doi.org/10.1016/j.mechmat.2019.103307
  52. Vinyas, M. (2019), "A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods", Compos. B. Eng., 158, 286-301. https://doi.org/10.1016/j.compositesb.2018.09.086.
  53. Wahrhaftig, A., Brasil, R.M.L.R.F. and Balthazar, J.M. (2013), "The first frequency of cantilevered bars with geometric effect: A mathematical and experimental evaluation", J. Braz. Soc. Mech. Sci. Eng. 35, 457-467. https://doi.org/10.1007/s40430-013-0043-9
  54. Wahrhaftig, A. de M. and Magalhaes, K.M.M. (2021), "Bifurcation analysis of columns of composite materials with thermal variation", Mater. Res., 24. https://doi.org/10.1590/1980-5373-MR-2021-0266
  55. Wang, C.Y. and Zhang, L.C. (2008), "A critical assessment of the elastic properties and effective wall thickness of single-walled carbon nanotubes", Nanotechnology, 19(7), 75705. https://doi.org/10.1088/0957-4484/19/7/075705
  56. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Compos. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028
  57. Wu, Z., Zhang, Y. and Yao, G. (2020), "3/2 superharmonic resonance and 1/2 subharmonic resonance of functionally graded carbon nanotube reinforced composite beams", Compos. Struct. 241, 112056. https://doi.org/10.1016/j.compstruct.2020.112056
  58. Wu, Z., Zhang, Y., Yao, G. and Yang, Z. (2019), "Nonlinear primary and super-harmonic resonances of functionally graded carbon nanotube reinforced composite beams", Int. J. Mech. Sci. 153-154, 321-340. https://doi.org/10.1016/j.ijmecsci.2019.06.039
  59. Wu, H.L, Yang, J. and Kitipornchaj, S. (2016) "Nonlinear vibration of functionally graded carbon nanotube reinforced composite beams with geometric imperfections", Compos. B Eng., 90, 86-96. https://doi.org/10.1016/j.compositesb.2015.12.007
  60. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71, 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011
  61. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Vessels Pip. 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012
  62. Zhang, D.G. (2014) "Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory", Meccanica, 49(2), 283-293. doi:10.1007/s11012-013-9793-9
  63. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015), "State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory", Compos. Struct., 134, 989-1003. https://doi.org/10.1016/j.compstruct.2015.08.138
  64. Zhou, T. and Song, Y. (2019), "Three-dimensional nonlinear bending analysis of FG-CNTs reinforced composite plates using the element-free Galerkin method based on the S-R decomposition theorem", Compos. Struct., 207, 519-530. https://doi.org/10.1016/j.compstruct.2018.09.026
  65. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010