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An accurate analytical exploration for dynamic response of thermo-electric CNTRC beams under driving harmonic and constant loads resting on Pasternak foundation

  • Received : 2021.12.27
  • Accepted : 2024.04.26
  • Published : 2024.06.25

Abstract

This paper aims to analyze the dynamic response of thermoelectric carbon nanotube-reinforced composite (CNTRC) beams under moving harmonic load resting on Pasternak elastic foundation. The governing equations of thermoelectric CNTRC beam are obtained based on the Karama shear deformation beam theory. The beams are resting on the Pasternak foundation. Previous articles have not performed the moving load mode with the analytical method. The exact solution for the transverse and axial dynamic response is presented using the Laplace transform. A comparison of previous studies has been published, where a good agreement is observed. Finally, some examples were used to analyze, such as excitation frequency, voltage, temperature, spring constant factors, the volume fraction of Carbon nanotubes (CNTs), the velocity of a moving harmonic load, and their influence on axial and transverse dynamic and maximum deflections. The advantages of the proposed method compared to other numerical methods are zero reduction of the error percentage that exists in numerical methods.

Keywords

References

  1. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2021.1999263
  2. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389
  3. Alizade Hamidi, B., Hosseini, S.A.H., Hassannejad, R. and Khosravi, F. (2019), "An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories", J. Therm. Stress., 43(2), 157-174. https://doi.org/1010.1080/01495739.2019.1666694
  4. Alizadeh-Hamidi, B., Hassannejad, R. and Omidi, Y. (2021), "Size-dependent thermo-mechanical vibration of lipid supramolecular nano-tubules via nonlocal strain gradient Timoshenko beam theory", Comput. Biol. Med., 134, 104475. https://doi.org/10.1016/j.compbiomed.2021.104475
  5. Alizadeh Hamidi, B., Khosravi, F., Hosseini, S.A. and Hassannejad, R. (2020), "Closed form solution for dynamic analysis of rectangular nanorod based on nonlocal strain gradient", Waves Random Complex Med., 1-17. https://doi.org/10.1080/17455030.2020.1843737
  6. Babaei, H. (2022), "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation", Appl. Math. Comput., 413, 126606. https://doi.org/10.1016/j.amc.2021.126606
  7. Babaei, H., Kiani, Y. and Eslami, M.R. (2021a), "Vibrational behavior of thermally pre-/post-buckled FG-CNTRC beams on a nonlinear elastic foundation: a two-step perturbation technique", Acta Mechanica, 232(10), 3897-3915. https://doi.org/10.1007/s00707-021-03027-z
  8. Babaei, H., Kiani, Y. and Reza Eslami, M. (2021b), "Perturbation method for thermal post-buckling analysis of shear deformable FG-CNTRC beams with different boundary conditions", Int. J. Struct. Stabil. Dyn., 21(13), 2150175. https://doi.org/10.1142/S0219455421501753
  9. Behrouz, S.J., Rahmani, O. and Hosseini, S.A. (2019), "On nonlinear forced vibration of nano cantilever-based biosensor via couple stress theory", Mech. Syst. Signal Pr., 128, 19-36. https://doi.org/10.1016/j.ymssp.2019.03.020
  10. Bensattalah, T., Daouadji, T., Zidour, M., Tounsi, A. and Bedia, E. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568. https://doi.org/10.1007/s11029-016-9606-z
  11. Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical buckling load of triple-walled carbon nanotube based on nonlocal elasticity theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/JNanoR.62.108
  12. Bensattalah, T., Zidour, M., Daouadji, T.H. and Bouakaz, K. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
  13. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209
  14. Chalak, H., Zenkour, A. and Garg, A. (2021), "Free vibration and modal stress analysis of FG-CNTRC beams under hygrothermal conditions using zigzag theory", Mech. Based Des. Struct., 1-22. https://doi.org/10.1080/15397734.2021.1977659
  15. Civalek, O., Akbas, S.D., Akgoz, B. and Dastjerdi, S. (2021a), "Forced vibration analysis of composite beams reinforced by carbon nanotubes", Nanomaterials. 11(3), 571. https://doi.org/10.3390/nano11030571
  16. Civalek, O., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021b), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Meth. Appl. Sci., Special Issue Paper. https://doi.org/10.1002/mma.7069
  17. Ebrahimi, F., Salari, E. and Hosseini, S. (2015), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccanica, 1-27. https://doi.org/10.1007/s11012-015-0248-3
  18. Ebrahimi, F., Farazmandnia, N., Kokaba, M.R. and Mahesh, V. (2021a), "Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory", Eng. Comput., 37(2), 921-936.https://doi.org/10.1007/s00366-019-00864-4
  19. Ebrahimi, F., Seyfi, A. and Dabbagh, A. (2021b), "The effects of thermal loadings on wave propagation analysis of multi-scale hybrid composite beams", Wave Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1956015
  20. Ebrahimi, F., Seyfi, A. and Teimouri, A. (2021c), "Torsional vibration analysis of scale-dependent non-circular graphene oxide powder-strengthened nanocomposite nanorods", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-021-01528-y
  21. Eghbali, M., Hosseini, S.A. and Rahmani, O. (2021), "Free vibration of axially functionally graded nanobeam with an attached mass based on nonlocal strain gradient theory via new ADM numerical method", Amirkabir J. Mech. Eng., 53(2), 8-8. https://doi.org/10.22060/mej.2020.17013.6495
  22. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
  23. Garg, A., Chalak, H., Zenkour, A., 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
  24. Ghadiri, M., Hosseini, S., Karami, M. and Namvar, M. (2018), "In-plane and out of plane free vibration of U-shaped AFM probes based on the nonlocal elasticity", J. Solid Mech., 10(2), 285-299.
  25. Ghadiri Rad, M.H., Shahabian, F. and Hosseini, S.M. (2021), "Two-dimensional geometrically nonlinear hyperelastic wave propagation analysis in FG thick hollow cylinders using MLPG method", AUT J. Civil Eng., 5(3), 465-480. https://doi.org/10.22060/ajce.2021.19911.5752
  26. Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
  27. Hamidi, B.A., Hosseini, S.A. and Hayati, H. (2020), "Forced torsional vibration of nanobeam via nonlocal strain gradient theory and surface energy effects under moving harmonic torque", Wave Random Complex Med., 1-16. https://doi.org/10.1080/17455030.2020.1772523
  28. Hayati, H., Hosseini, S.A. and Rahmani, O. (2017), "Coupled twist-bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory", Microsyst. Technol., 23(7), 2393-2401. https://doi.org/10.1007/s00542-016-2933-0
  29. Heidari, Y., Arefi, M. and Irani-Rahaghi, M. (2021), "Free vibration analysis of cylindrical micro/nano-shell reinforced with CNTRC patches", Int. J. Appl. Mech., 2150040. https://doi.org/10.1142/S175882512150040X
  30. Hosseini, S. and Rahmani, O. (2016), "Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model", Int. J. Struct. Stabil. Dyn., 16(10), 1550077. https://doi.org/10.1142/S0219455415500777
  31. Hosseini, S. and Rahmani, O. (2017), "Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory", Meccanica, 52(6), 1441-1457. https://doi.org/10.1007/s11012-016-0491-2
  32. Hosseini, S., Moghaddam, M. and Rahmani, O. (2020), "Exact solution for axial vibration of the power, exponential and sigmoid FG nonlocal nanobeam", Adv. Aircr. Spacecr. Sci., 7(6), 517-536. https://doi.org/10.12989/aas.2020.7.6.517
  33. Kaiser, J.P., Roesslein, M., Buerki-Thurnherr, T. and Wick, P. (2011), "Carbon nanotubes-curse or blessing", Curr. Med. Chem., 18(14), 2115-2128. https://doi.org/10.2174/092986711795656171
  34. Khosravi, F. and Hosseini, S.A. (2020), "On the viscoelastic carbon nanotube mass nanosensor using torsional forced vibration and Eringen's nonlocal model", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2020.1744001
  35. Khosravi, F., Hosseini, S.A. and Hamidi, B.A. (2020a), "Torsional Vibration of nanowire with equilateral triangle cross section based on nonlocal strain gradient for various boundary conditions: comparison with hollow elliptical cross section", Eur. Phys. J. Plus, 135(3), 1-20. https://doi.org/10.1140/epjp/s13360-020-00312-z
  36. Khosravi, F., Simyari, M., Hosseini, S. and Ghadiri, M. (2020b), "An analytical solution on size dependent longitudinal dynamic response of SWCNT under axial moving harmonic load", J. Solid Mech., 12(3), 586-599. https://doi.org/10.22034/jsm.2019.1875642.1476
  37. Madenci, E. (2021), "Free vibration analysis of carbon nanotube RC nanobeams with variational approaches", Adv. Nano Res., 11(2), 157-171.https://doi.org/10.12989/anr.2021.11.2.157
  38. Mantari, J., Bonilla, E. and Soares, C.G. (2014), "A new tangential-exponential higher order shear deformation theory for advanced composite plates", Compos. Part B Eng., 60, 319-328. https://doi.org/10.1016/j.compositesb.2013.12.001
  39. Mohammadjani, R. and Shariyat, M. (2020), "Nonlinear thermomechanical vibration mitigation analysis in rotating fractional-order viscoelastic bidirectional FG annular disks under nonuniform shocks", J. Therm. Stress., 43(7), 829-873. https://doi.org/10.1080/01495739.2020.1748555
  40. Nielsen, L.E. (1974), "The thermal and electrical conductivity of two-phase systems", Ind. Eng. Chem. Fund., 13(1), 17-20. https://doi.org/10.1021/i160049a004
  41. Serajzadeh, F. and Malekzadeh, P. (2021), "Two-dimensional low-velocity impact analysis of curved sandwich beams with FG-CNTRC face sheets and porous core", Mech. Based Des. Struct. Mach., 1-22. https://doi.org/10.1080/15397734.2021.2013879
  42. Shariyat, M. and Abedi, S. (2022), "An accurate hyper-elasticity-based plate theory and nonlinear energy-based micromechanics for impact and shock analyses of compliant particle-reinforced FG hyperelastic plates", ZAMM J. Appl. Math. Mech., e202100099. https://doi.org/10.1002/zamm.202100099
  43. 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
  44. Simsek, M. and Reddy, J. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", Int. J. Eng. Sci., 64, 37-53. https://doi.org/10.1016/j.ijengsci.2012.12.002
  45. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Advances in nano research. 8(2), 135-148.https://doi.org/10.12989/anr.2020.8.2.135
  46. Tounsi, A., Benguediab, S., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1. https://doi.org/10.12989/anr.2013.1.1.001
  47. Van Quyen, N., Van Thanh, N., Quan, T.Q. and Duc, N.D. (2021), "Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson's ratio auxetic honeycombs core and CNTRC face sheets", Thin Wall. Struct., 162, 107571. https://doi.org/10.1016/j.tws.2021.107571
  48. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028
  49. Xu, J., Yang, Z., Yang, J. and Li, Y. (2021a), "Free vibration analysis of rotating FG-CNT reinforced composite beams in thermal environments with general boundary conditions", Aerosp. Sci. Technol., 118, 107030. https://doi.org/10.1016/j.ast.2021.107030.
  50. Xu, X., Zhang, C., Khan, A., Sebaey, T.A. and Alkhedher, M. (2021b), "Free vibrations of rotating CNTRC beams in thermal environment", Case Stud. Therm. Eng., 28, 101355. https://doi.org/10.1016/j.csite.2021.101355
  51. Zerrouki, R., Karas, A. and Zidour, M. (2020), "Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam", Adv. Nano Res., 9(3), 211-220. https://doi.org/10.12989/anr.2020.9.3.211
  52. Zhang, M. and Li, J. (2009), "Carbon nanotube in different shapes", Mater. Today, 12(6), 12-18. https://doi.org/10.1016/S1369-7021(09)70176-2
  53. Zheng, J., Zhang, C., Musharavati, F., Khan, A., Sebaey, T.A. and Eyvazian, A. (2021), "Forced vibration characteristics of embedded graphene oxide powder reinforced metal foam nanocomposite plate in thermal environment", Case Stud. Therm. Eng., 101167. https://doi.org/10.1016/j.csite.2021.101167