DOI QR코드

DOI QR Code

Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation

  • Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bedia, E.A. Adda (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2019.06.28
  • Accepted : 2020.03.31
  • Published : 2020.06.25

Abstract

This paper, presents the dynamic and stability analysis of the simply supported single walled Carbon Nanotubes (SWCNT) reinforced concrete beam on elastic-foundation using an integral first-order shear deformation beam theory. The condition of the zero shear-stress on the free surfaces of the beam is ensured by the introduction of the shear correction factors. The SWCNT reinforcement is considered to be uniform and variable according to the X, O and V forms through the thickness of the concrete beam. The effective properties of the reinforced concrete beam are calculated by employing the rule of mixture. The analytical solutions of the buckling and free vibrational behaviors are derived via Hamilton's principle and Navier method. The analytical results of the critical buckling loads and frequency parameters of the SWCNT-RC beam are presented in the form of explicit tables and graphs. Also the diverse parameters influencing the dynamic and stability behaviors of the reinforced concrete beam are discussed in detail.

Keywords

References

  1. Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: A micromechanical approach", Iran. J. Sc.i Technol. Tran. Mech. Eng., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y.
  2. Abdou, M.A., Othman, M.I.A., Tantawi, R.S. and Mansour, N.T. (2019), "Exact solutions of generalized thermoelastic medium with double porosity under L-S theory", Ind. J. Phys., 94, 725-736. https://doi.org/10.1007/s12648-019-01505-8.
  3. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  4. Akbas, S.D. (2019a), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091.
  5. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.
  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. Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.
  8. Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. https://doi.org/10.12989/cac.2019.24.1.037.
  9. Alibeigloo, A. and Liew, K.M. (2015), "Elasticity solution of free vibration and bending behavior of functionally graded carbon nanotube-reinforced composite beam with thin piezoelectric layers using differential quadrature method", Int. J. Appl. Mech., 7(1), 1550002. https://doi.org/10.1142/s1758825115400025.
  10. Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods", J. Mech. Sci. Technol., 25(3), 809-820. https://doi.org/10.1007/s12206-011-0127-3.
  11. Arani, A.G., Pourjamshidian, M., Arefi, M. and Arani, M.R. (2019), "Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak's foundation based on higher order shear deformation theory", Struct. Eng. Mech., 69(4), 439-455. https://doi.org/10.12989/sem.2019.69.4.439.
  12. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. http://dx.doi.org/10.12989/cac.2016.17.5.567.
  13. Arhamnamazi, S.A., Bani Mostafa Arab, N., Oskouei, A.R. and Aymerich, F, (2019), "Accuracy assessment of ultrasonic C-scan and X-ray radiography methods for impact damage detection in glass fiber reinforced polyester composites", J. Appl. Comput. Mech., 5(2), 258-268. http://dx.doi.org/10.22055/JACM.2018.26297.1318.
  14. Avcar, M. (2016a), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A., 130(1), 375-378. http://dx.doi.org/10.12693/APhysPolA.130.375.
  15. Avcar, M. (2016b), "Free vibration of non-homogeneous beam subjected to axial force resting on pasternak foundation", J. Polytech., 19(4), 507-512. http://dx.doi.org/10.2339/2016.19.4.507-512.
  16. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  17. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  18. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  19. Bajc, U., Saje, M., Planinc, I. and Bratina, S. (2015), "Semi-analytical buckling analysis of reinforced concrete columns exposed to fire", Fire Saf. J., 71, 110-122. https://doi.org/10.1016/j.firesaf.2014.11.018.
  20. Bakhshi, N. and Taheri-Behrooz, F. (2019), "Length effect on the stress concentration factor of a perforated orthotropic composite plate under in-plane loading", Compos. Mater. Eng., 1(1), 71-90. https://doi.org/10.12989/cme.2019.1.1.071.
  21. Bakhshi, N. and Taheri-Behrooz, F. (2019), "Length effect on the stress concentration factor of a perforated orthotropic composite plate under in-plane loading", Compos. Mater. Eng., 1(1), 71-90. https://doi.org/10.12989/cme.2019.1.1.071.
  22. Barati, M.R. (2018), "Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity", Eur. Phys. J. Plus., 133, 170. https://doi.org/10.1140/epjp/i2018-11993-0.
  23. Barati, M.R. and Shahverdi, H. (2020). "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J Braz. Soc. Mech. Sci. Eng., 42, 33. https://doi.org/10.1007/s40430-019-2118-8.
  24. Barati, M.R. and Zenkour, A.M. (2018), "Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions", Mech. Adv. Mater. Struct., 26(18), 1580-1588. https://doi.org/10.1080/15376494.2018.1444235.
  25. Barati, M.R. and Zenkour, A.M. (2019), "Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection", Mech. Adv. Mater. Struct., 26(6), 503-511. https://doi.org/10.1080/15376494.2017.1400622.
  26. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Des., 3(3), 213-232. https://doi.org/10.12989/acd.2017.2.3.165.
  27. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircraft Spacecraft Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.
  28. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517.
  29. Bensaid, I. and Kerboua, B. (2019), "Improvement of thermal buckling response of FG-CNT reinforced composite beams with temperature-dependent material properties resting on elastic foundations", Adv. Aircraft Spacecraft Sci., 6(3), 207-223. https://doi.org/10.12989/aas.2019.6.3.207.
  30. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339.
  31. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
  32. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
  33. Chen, B., Kondoh, K., Umeda, J., Li, S., Jia, L. and Li, J. (2019), "Interfacial in-situ $Al_{2}O_{3}$ nanoparticles enhance load transfer in carbon nanotube (CNT)-reinforced aluminum matrix composites", J. Alloy. Compound., 789, 25-29. https://doi.org/10.1016/j.jallcom.2019.03.063.
  34. Civalek, O. and Ozturk, B. (2010), "Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation", Geomech. Eng., 2(1), 45-56. https://doi.org/10.12989/gae.2010.2.1.045.
  35. Daghigh, H. and Daghigh, V. (2018), "Free vibration of size and temperature-dependent carbon nanotube (CNT)-reinforced composite nanoplates with CNT agglomeration", Polym. Compos., 40(S2), E1479-E1494. https://doi.org/10.1002/pc.25057.
  36. Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Des., 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  37. Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335.
  38. Ebrahimi, F. and Barati, M.R. (2017a), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518.
  39. Ebrahimi, F. and Barati, M.R. (2017b), "Vibration analysis of nonlocal strain gradient embedded single-layer graphene sheets under nonuniform in-plane loads", J. Vib. Control., 107754631773408. https://doi.org/10.1177/1077546317734083.
  40. Ebrahimi, F. and Barati, M.R. (2018a), "Hygro-thermal vibration analysis of bilayer graphene sheet system via nonlocal strain gradient plate theory", J. Brazil. Soc. Mech. Sci. Eng., 40(9), 428. https://doi.org/10.1007/s40430-018-1350-y.
  41. Ebrahimi, F. and Barati, M.R. (2018b), "A nonlocal strain gradient refined plate model for thermal vibration analysis of embedded graphene sheets via DQM", Struct. Eng. Mech., 66(6), 693-701. https://doi.org/10.12989/sem.2018.66.6.693.
  42. Ebrahimi, F., Barati, M.R. and Civalek, O. (2019), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366-019-00742-z.
  43. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022.
  44. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  45. Faleh, N.M., Fenjan, R.M. and Ahmed, R.A. (2020), "Forced vibrations of multi-phase crystalline porous shells based on strain gradient elasticity and pulse load effects", J. Vib. Eng. Technol., 1-9. https://doi.org/10.1007/s42417-020-00203-8.
  46. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R. (2017), "Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates", Compos. Part B. Eng., 115, 384-408. https://doi.org/10.1016/j.compositesb.2016.09.021.
  47. Fenjan, R.M., Ahmed, R.A and Faleh, N.M. (2019), "Investigating dynamic stability of metal foam nanoplates under periodic in-plane loads via a three-unknown plate theory", Adv. Aircraft Spacecraft Sci., 6(4), 297-314. https://doi.org/10.12989/aas.2019.6.4.297.
  48. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019b), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupl. Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.
  49. Fladr, J., Bily, P. and Broukalova, I. (2019), "Evaluation of steel fiber distribution in concrete by computer aided image analysis", Compos. Mater. Eng., 1(1), 49-70. https://doi.org/10.12989/cme.2019.1.1.049.
  50. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329(10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  51. Forsat, M., Badnava, S., Mirjavadi, S.S., Barati, M.R. and Hamouda, A. (2020), "Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory", Eur. Phys. J. Plus., 135, 81. https://doi.org/10.1140/epjp/s13360-019-00042-x.
  52. Frikha, A., Zghal, S. and Dammak, F. (2018), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Technol., 78, 438-451. https://doi.org/10.1016/j.ast.2018.04.048.
  53. Ghadimi, M.G. (2020), "Buckling of non-sway Euler composite frame with semi-rigid connection", Compos. Mater. Eng., 2(1), 13-24. https://doi.org/10.12989/cme.2020.2.1.013.
  54. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Modeling and evaluation of rectangular hole effect on nonlinear behavior of imperfect composite plates by an effective simulation technique", Compos. Mater. Eng., 2(1), 25-41. https://doi.org/10.12989/cme.2020.2.1.025.
  55. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  56. Hajlaoui, A., Chebbi, E. and Dammak, F. (2019), "Buckling analysis of carbon nanotube reinforced FG shells using an efficient solid-shell element based on a modified FSDT", Thin Wall. Struct., 144, 106254. https://doi.org/10.1016/j.tws.2019.106254.
  57. Hamad, L.B., Khalaf, B.S. and Faleh, N.M. (2019), "Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials", Adv. Mater. Res., 8(3), 179. https://doi.org/10.12989/amr.2019.8.3.179.
  58. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75. https://doi.org/10.12989/scs.2020.34.1.075.
  59. 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.
  60. Heshmati, M., Yas, M.H. and Daneshmand, F. (2015), "A comprehensive study on the vibrational behavior of CNT-reinforced composite beams", Compos. Struct., 125, 434-448. https://doi.org/10.1016/j.compstruct.2015.02.033.
  61. Jafari Mehrabadi, S., Sobhani Aragh, B., Khoshkhahesh, V. and Taherpour, A. (2012), "Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes", Compos. Part B: Eng., 43(4), 2031-2040. https://doi.org/10.1016/j.compositesb.2012.01.067.
  62. Kamarian, S., Shakeri, M., Yas, M., Bodaghi, M. and Pourasghar, A. (2015), "Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs", J. Sandw. Struct. Mater., 17(6), 632-665. https://doi.org/10.1177/1099636215590280.
  63. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024.
  64. Khater, H.M., El Nagar, A.M., Ezzat, M. and Lottfy, M. (2020), "Fabrication of sustainable geopolymer mortar incorporating granite waste", Compos. Mater. Eng., 2(1), 1-12. https://doi.org/10.12989/cme.2020.2.1.001.
  65. Kiani, Y. (2016), "Shear buckling of FG-CNT reinforced composite plates using Chebyshev-Ritz method", Compos. Part B: Eng., 105, 176-187. https://doi.org/10.1016/j.compositesb.2016.09.001.
  66. Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Comput. Des., 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165.
  67. Lei, J., He, Y., Li, Z., Guo, S. and Liu, D. (2018), "Postbuckling analysis of bi-directional functionally graded imperfect beams based on a novel third-order shear deformation theory", Compos. Struct., 209, 811-829. https://doi.org/10.1016/j.compstruct.2018.10.106.
  68. Lin, F. and Xiang, Y. (2014), "Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories", Appl. Math. Modell., 38, 3741-3754. https://doi.org/10.1016/j.apm.2014.02.008.
  69. Majeed, W.I. and Sadiq, I.A. (2018), "Buckling and pre stressed vibration analysis of laminated plates using new shear deformation", IOP Conf. Ser.: Mater. Sci. Eng., 454, 012006. https://doi.org/10.1088/1757-899X/454/1/012006
  70. Mandi, A., Kundu, S., Pati, P. and Pal, P.C. (2019), "Love wave propagation in a fiber-reinforced layer with corrugated boundaries overlying heterogeneous half-space", J. Appl. Comput. Mech., 5(5), 926-934. https://doi.org/10.22055/JACM.2019.27062.1413.
  71. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng., 095441001876119. https://doi.org/10.1177/0954410018761192.
  72. Mercan, K., Baltacioglu, A.K. and Civalek, O. (2018), "Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method", Compos. Struct., 186, 139-153. https://doi.org/10.1016/j.compstruct.2017.12.008.
  73. Mirjavadi, S., Yahya, Y.Z., Forsat, M., Khan, I., Hamouda, A. and Reza Barati, M. (2020), "Magneto-electric effects on nonlocal nonlinear dynamic characteristics of imperfect multi-phase magneto-electro-elastic beams", J. Magnet. Magnet. Mater., 166649. https://doi.org/10.1016/j.jmmm.2020.166649.
  74. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda A.M.S. (2019c), "Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection", Microsyst. Technol., 25, 3137-3150. https://doi.org/10.1007/s00542-018-4277-4.
  75. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A. (2018a), "Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load", Mater. Res. Express., 6(3), 035029. https://doi.org/10.1088/2053-1591/aaf5a2.
  76. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2018b), "Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", Eur. J. Mech.-A/Solid., 74, 210-220. https://doi.org/10.1016/j.euromechsol.2018.11.004.
  77. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity", Int. J. Mech. Mater. Des., 1-12. https://doi.org/10.1007/s10999-019-09452-2.
  78. Mirjavadi, S.S., Forsat, M. and Badnava, S. (2019), "Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models", Biomech. Model. Mechanobiol., 1-13. https://doi.org/10.1007/s10237-019-01265-8.
  79. Mirjavadi, S.S., Forsat, M., Hamouda, A. and Barati, M.R. (2019a), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express., 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552.
  80. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431.
  81. Mohseni, A. and Shakouri, M. (2019), "Vibration and stability analysis of functionally graded CNT reinforced composite beams with variable thickness on elastic foundation", Proc. Inst. Mech. Eng., Part L: J. Mater.: Des. Appl., 146442071986622. https://doi.org/10.1177/1464420719866222.
  82. Narwariya, M., Choudhury, A. and Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Comput. Des., 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113.
  83. Natarajan, S., Haboussi, M. and Manickam, G. (2014). "Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets", Compos. Struct., 113, 197-207. https://doi.org/10.1016/j.compstruct.2014.03.007.
  84. Othman, I.A.M. and Mahdy, A.S.M. (2018), "Numerical studies for solving a free convection boundary-layer flow over a vertical plate", Mech. Mech. Eng., 22(1), 35-42.
  85. Othman, M.I.A., Abouelregal, A.E. and Said, S.M. (2019), "The effect of variable thermal conductivity on an infinite fiber-reinforced thick plate under initial stress", J. Mech. Mater. Struct., 14(2), 277-293. https://doi.org/10.2140/jomms.2019.14.277.
  86. Ouakad, H.M., Sedighi, H.M. and Younis, M.I. (2017), "One-to-one and three-to-one internal resonances in MEMS shallow arches", J. Comput. Nonlin. Dyn., 12(5), 051025. https://doi.org/10.1115/1.4036815.
  87. Oucif, C., Ouzaa, K. and Mauludin, L.M. (2019), "Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns", J. Appl. Comput. Mech., 5, 517-525. https://doi.org/10.22055/JACM.2017.23514.1159.
  88. Qin, Z., Pang, X., Safaei, B. and Chu, F. (2019), "Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions", Compos. Struct., 220, 847-860. https://doi.org/10.1016/j.compstruct.2019.04.046.
  89. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams", Comput. Math. Appl., 66(7), 1147-1160. https://doi.org/10.1016/j.camwa.2013.04.031.
  90. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  91. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Comput. Des., 3(2), 165-190. https://doi.org/10.12989/acd.2018.3.2.165.
  92. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329.
  93. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  94. Sayyad, A.S. and Ghugal, Y.M. (2018), "An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation", Adv. Aircraft Spacecraft Sci., 5(6), 671-689. https://doi.org/10.12989/aas.2018.5.6.671.
  95. Sedighi, H.M. and Bozorgmehri, A. (2016), "Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory", Acta. Mech., 227(6), 1575-1591. https://doi.org/10.1007/s00707-016-1562-0.
  96. Sedighi, H.M., Koochi, A., Daneshmand, F. and Abadyan, M. (2015), "Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow", Int. J. Nonlin. Mech., 77, 96-106. https://doi.org/10.1016/j.ijnonlinmec.2015.08.002.
  97. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.
  98. Setoodeh, A.R. and Shojaee, M. (2017), "Critical buckling load optimization of functionally graded carbon nanotube-reinforced laminated composite quadrilateral plates", Polym. Compos., 39(S2), 853-868. https://doi.org/10.1002/pc.24289.
  99. Shahverdi, H., Barati, M.R. and Hakimelahi, B. (2019), "Post-buckling analysis of honeycomb core sandwich panels with geometrical imperfection and graphene reinforced nano-composite face sheets", Mater. Res. Express., 6(9), 095017. https://doi.org/10.1088/2053-1591/ab2b74.
  100. Sharma, J.N., Chand, R. and Othman, M.I.A. (2009), "On the propagation of Lamb waves in viscothermoelastic plates under fluid loadings", Int. J. Eng. Sci., 47(3), 391-404. https://doi.org/10.1016/j.ijengsci.2008.10.008.
  101. Shen, H.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.
  102. Shen, H.S., He, X.Q. and Yang, D.Q. (2017), "Vibration of thermally postbuckled carbon nanotube-reinforced composite beams resting on elastic foundations", Int. J. Nonlin. Mech., 91, 69-75. https://doi.org/10.1016/j.ijnonlinmec.2017.02.010.
  103. Shokrieh, M.M. and Kondori, M.S. (2020), "Effects of adding graphene nanoparticles in decreasing of residual stresses of carbon/epoxy laminated composites", Compos. Mater. Eng., 2(1), 53-64. https://doi.org/10.12989/cme.2020.2.1.053.
  104. Thostenson, E.T., Ren, Z. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 61(13), 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X.
  105. Timesli, A. (2020), "An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory", SN Appl. Sci., 2, 407. https://doi.org/10.1007/s42452-020-2182-9
  106. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B: Eng., 89, 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016.
  107. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  108. Wang, Z.X., Xu, J. and Qiao, P. (2014), "Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates", Compos. Struct., 108, 423-434. https://doi.org/10.1016/j.compstruct.2013.09.024.
  109. 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
  110. Wu, C.P. and Li, H.Y. (2014), "Three-dimensional free vibration analysis of functionally graded carbon nanotube-reinforced composite plates with various boundary conditions", J. Vib. Control., 2(1), 89-107. https://doi.org/10.1177/1077546314528367.
  111. Wu, H., Kitipornchai, S. and Yang, J. (2016), "Thermo-electro-mechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections", Smart Mater. Struct., 25(9), 095022. https://doi.org/10.1088/0964-1726/25/9/095022.
  112. Xiang, H.J. and Shi, Z.F. (2011), "Vibration attenuation in periodic composite Timoshenko beams on Pasternak foundation", Struct. Eng. Mech., 40(3), 373-392. https://doi.org/10.12989/sem.2011.40.3.373.
  113. 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. Vess. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  114. Yazdani, R. and Mohammadimehr, M. (2019), "Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution", Comput. Concrete, 24(6), 499-511. https://doi.org/10.12989/cac.2019.24.6.499.
  115. Zarei, H., Fallah, M., Bisadi, H., Daneshmehr, A. and Minak, G. (2017), "Multiple impact response of temperature-dependent carbon nanotube-reinforced composite (CNTRC) plates with general boundary conditions", Compos. Part B: Eng., 113, 206-217. https://doi.org/10.1016/j.compositesb.2017.01.021.
  116. Zghal, S., Frikha, A. and Dammak, F. (2018), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B: Eng., 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037.
  117. Zhang, L.W. and Selim, B.A. (2017), "Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy's higher-order shear deformation theory", Compos. Struct., 160, 689-705. https://doi.org/10.1016/j.compstruct.2016.10.102.
  118. 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.
  119. Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177.

Cited by

  1. Impacts of PU Foam Stand-Off Layer on the Vibration Damping Performance of Stand-Off Free Layer Damping Cantilever Beams vol.2020, 2020, https://doi.org/10.1155/2020/8871562
  2. Design Optimization of Concrete Aqueduct Structure considering Temperature Effects vol.2020, 2020, https://doi.org/10.1155/2020/6679047
  3. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2020, https://doi.org/10.12989/amr.2020.9.4.265
  4. Dynamic analysis of a laminated composite beam under harmonic load vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.563
  5. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  6. Experimental and analytical study on continuous GFRP-concrete decks with steel bars vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.737
  7. Effect of boundary conditions on thermal buckling of laminated composite shallow shell vol.42, pp.p5, 2021, https://doi.org/10.1016/j.matpr.2020.12.501
  8. New Finite Modeling of Free and Forced Vibration Responses of Piezoelectric FG Plates Resting on Elastic Foundations in Thermal Environments vol.2021, 2020, https://doi.org/10.1155/2021/6672370
  9. Geometrical Influences on the Vibration of Layered Plates vol.2021, 2020, https://doi.org/10.1155/2021/8843358
  10. Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments vol.2021, 2020, https://doi.org/10.1155/2021/5533920
  11. A Refined Model for Analysis of Beams on Two-Parameter Foundations by Iterative Method vol.2021, 2021, https://doi.org/10.1155/2021/5562212
  12. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2020, https://doi.org/10.12989/anr.2021.10.1.025
  13. On thermally induced instability of FG-CNTRC cylindrical panels vol.10, pp.1, 2021, https://doi.org/10.12989/anr.2021.10.1.043
  14. Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain vol.77, pp.3, 2020, https://doi.org/10.12989/sem.2021.77.3.315
  15. Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.151
  16. Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.175
  17. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2020, https://doi.org/10.12989/csm.2021.10.1.061
  18. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2020, https://doi.org/10.12989/csm.2021.10.1.061
  19. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2020, https://doi.org/10.12989/anr.2021.10.3.271
  20. Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets vol.27, pp.4, 2020, https://doi.org/10.12989/cac.2021.27.4.369
  21. Computational analysis of the nonlinear vibrational behavior of perforated plates with initial imperfection using NURBS-based isogeometric approach vol.8, pp.5, 2020, https://doi.org/10.1093/jcde/qwab043
  22. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157
  23. Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder vol.79, pp.5, 2020, https://doi.org/10.12989/sem.2021.79.5.593