Computers and Concrete

  • 제31권1호
  • /
  • Pages.1-7
  • /
  • 2023
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Validity assessment of aspect ratios based on Timoshenko-beam model: Structural design

  • Emad, Ghandourah (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Muzamal, Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed A., Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Mashhour, Alazwari (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed R., Ali (Faculty of Engineering and Technology, Future University in Egypt New Cairo) ;
  • Mohammed A., Hefni (Mining Engineering Department, Faculty of Engineering, King Abdulaziz University)
  • 투고 : 2022.07.29
  • 심사 : 2022.11.01
  • 발행 : 2023.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clamped-clamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.

키워드

과제정보

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant No. (G: 550-135-1439). The authors, therefore, gratefully acknowledge the DSR for their technical and financial support.

참고문헌

  1. Ansari, R. and Rouhi, H. (2012), "Nonlocal analytical Flugge shell model for the axial buckling of double-walled carbon nanotubes with different end conditions", Int. J. Nano Dimens., 7(3), 1250081. https://doi.org/10.1142/S179329201250018X.
  2. Aydogdu, M. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Physica E, 41, 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014.
  3. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B: Eng., 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020.
  4. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.6.1053.
  5. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and El Abbas, A.B. (2014), "Thermal effect on buckling of multiwalled carbon nanotubes using different gradient elasticity theories", Nanosci. Nanotechnol., 4(2), 27-33. https://doi.org/10.5923/j.nn.20140402.02.
  6. Brischetto, S. (2014), "A continuum elastic three-dimensional model for natural frequencies of single walled carbon nanotubes", Compos. Part B: Eng., 61, 222-228. https://doi.org/10.1016/j.compositesb.2014.01.046.
  7. Chang, T., Li, G. and Gua, X. (2005), "Elastic axial buckling of carbon nanotubes via molecular mechanics model", Carbon, 43, 287-294. https://doi.org/10.1016/j.carbon.2004.09.012.
  8. Chang, W.J. and Lee, H.L. (2009), "Free vibration of single-walled carbon nanotubes containing a fluid flow using a Timoshenko beam model", Phys. Lett. A, 373(10), 982-985. https://doi.org/10.1016/j.physleta.2009.01.011.
  9. Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load chiral double-walled carbon nanotubes using non-local elasticity theory", Adv. Neno Res., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193.
  10. Cornwell, C.F and Wille, L.T. (1997), "Elastic properties of single-walled carbon nanotubes in compression", Solid State Commun., 101(8), 555-558. https://doi.org/10.1016/S0038-1098(96)00742-9.
  11. Eltaher, M.A., Eman, S.A. and Mahmoud, F.F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030.
  12. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  13. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  14. Eringen, A.C. and Wegner, J.L. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56(2), B20-B22. https://doi.org/10.1007/b97697.
  15. Ghavanloo, E. and Fazelzadeh, S.A. (2009), "Vibrations characteristics of single walled carbon nanotubes based on the nonlocal Flugge shell theory", ASME J. Eng. Mate.r Technol., 134, 011008. https://doi.org/10.1016/j.apm.2011.12.036.
  16. Gohardani, O., Elola, M.C. and Elizetxea, C. (2014), "Potential and prospective implementation of carbon nanotubes on next generation aircraft and space vehicle: A review of current and expected applications in aerospace sciences", Progr. Aerosp. Sci., 77, 42-68. https://doi.org/10.1016/j.paerosci.2014.05.002.
  17. Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431.
  18. Hao, X., Qiang, H. and Xiaouh,Y. (2008), "Buckling of defective single-walled and double-walled carbon nanotubes under axial compression by molecular dynamic simulation", Compos. Sci. Technol., 68(7-8), 1809-1814. https://doi.org/10.1016/j.compscitech.2008.01.013.
  19. Hashemi, S.H., Ilkhani, M.R. and Fadaee, M. (2012), "Identification of the validity of the Donnell and Sanders shell theories using an exact vibration analysis of the functionally graded thick cylindrical shell panel", Acta Mechanica, 223(5), 1101-1118. https://doi.org/10.1007/s00707-011-0601-0.
  20. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and AddaBedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E: Lowdimens. Syst. Nanostruct., 40(8), 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021.
  21. Hu, Y.G., Liew, K.M. and Wang, Q. (2012), "Modeling of vibrations of carbon nanotubes", Procedia Eng., 31, 343-347. https://doi.org/10.1016/j.proeng.2012.01.1034.
  22. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q. and Yakobson, B.I. (2008), "Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes", J. Mech. Phys. Solid., 56(12), 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010.
  23. Jorio, A. Saito, R., Hafner, J.H., Lieber, C.M., Hunter, M., McClure, T., Dresselhaus, G. and Dresselhaus, M.S. (2001), "Structural (n,m) determination of isolated single-wall carbon nanotubes by resonant raman scattering", Phys. Rev. Lett., 86(6), 1118-1121.https://doi.org/10.1103/PhysRevLett.86.1118.
  24. Jung, N.Y. and Han, S.C. (2013), "Analysis of sigmoid functionally materials (S-FGM) nanoscale plates using nonlocal elasticity theory", Math. Prob. Eng., 476, 131. http://doi.org/10.1155/2013/476131
  25. Karami, B., Janghorban, M., Shahsavari, D., Dimitri, R. and Tornabene, F. (2019), "Nonlocal buckling analysis of composite curved beams reinforced with functionally graded carbon nanotubes", Molecul., 24, 2750. https://doi.org/10.3390/molecules24152750.
  26. Kasas, S., Cibert, C., Kis, A., De Rios, P.L., Riederer, B.M., Forro, L., Dietler, G. and Catsicas, S. (2004), "Oscillation modes of microtubules", Biol. Cell, 96(9), 697-700. https://doi.org/10.1016/j.biolcel.2004.09.002.
  27. Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Non linear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", Comput. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002.
  28. Kolohchi, R., Bidholi, M.M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55, 1001-1014. http://doi.org/10.12989/sem.2015.55.5.1001.
  29. Kostarelos, K., Bianco, A. and Prato, M. (2009), "Promises, facts and challenges for carbon nanotubes in imaging and therapeutics", Nat. Nanotechnol., 4(10), 627-633. https://doi.org/10.1038/nnano.2009.241.
  30. Lal, A. and Markad, K. (2018), "Deflection and stress behaviour of multi-walled carbon nanotube reinforced laminated composite beams", Comput. Concrete, 22(6), 501-514. https://doi.org/10.12989/cac.2018.22.6.501.
  31. Lau, K.T. and Hui, D. (2002), "The revolutionary creation of new advanced materials-carbon nanotube composites", Compos. Part B: Eng., 33(4), 263-277. https://doi.org/10.1016/S1359-8368(02)00012-4.
  32. Li, R. and Kardomateas, G.A. (2007), "Vibration characteristics of multiwalled carbon nanotubes embedded in elastic media by a nonlocal elastic shell model", J. Appl. Mech., 74(6), 1087-1094. https://doi.org/10.1115/1.2722305.
  33. Lieber, C,M. (2003), "Nanoscale science and technology building", MRS Bull., 446-456. https://doi.org/10.1557/mrs2003.144.
  34. Liew, K.M., Wong, C.H., He, X.Q. and Tan, M.J. (2005), "Thermal stability of single and multi-walled carbon nanotubes", Phys. Rev. B, 71, 075424. https://doi.org/10.1103/PhysRevB.71.075424.
  35. Liu, L. and Zang, Y. (2004), "Multi-wall carbon nanotubes as a new infrared detected material", Sensor. Actuator. A: Phys., 116(3), 394-39. https://doi.org/10.1016/j.sna.2004.05.016.
  36. Loghman, A., Arani, A.G. and Barzoki, A.A.M. (2017), "Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates", Comput. Concrete, 19(6), 677-687. https://doi.org/10.12989/cac.2017.19.6.677.
  37. Lu, Y.J., Wang, X. and Lu, G. (2007), "Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading", Int. J. Solid. Struct., 44(1), 336-351. https://doi.org/10.1016/j.ijsolstr.2006.04.031.
  38. Mori, H., Hirai, Y., Ogata, S., Akita, S. and Nakayama, Y. (2005), "Chirality dependence of mechanical properties of single walled cabon nanotubes under axial tensile strain", JPN J. Appl. Phys., 44(2), 42-45. https://doi.org/10.1143/JJAP.44.L1307.
  39. Mousavi, M., Mohammadimehr, M. and Rostami, R. (2019), "Analytical solution for buckling analysis of micro sandwich hollow circular plate", Comput. Concrete, 24(3), 185-192. https://doi.org/10.12989/cac.2019.24.3.185.
  40. Mumrmu, T. and Pradhan, S.C. (2010), "Thermal effects on the stability of embedded carbon nanotubes", Comput. Mater. Sci., 47(3), 721-726. https://doi.org/10.1016/j.commatsci.2009.10.015.
  41. Nejad, M.Z., Hadi, A. and Rastgoo, A. (2016), "Buckling analysis of arbitrary two-directional functionally graded Euler-Bernonllinano-beams based on non-local elasticity theory", Eng. Sci., 103, 1-10. https://doi.org/10.1016/j.ijengsci.2016.03.001.
  42. Nogales, E. (2001), "Structural insights into microtubule function", Ann. Rev. Biophys. Biomolec. Struct., 30(1), 397-420. https://doi.org/10.1146/annurev.biophys.30.1.397.
  43. Pradhan, S.C. and Reddy, G.K. (2011), "Thermo mechanical buckling analysis of carbon nanotubes on Winkler foundation using non-local elasticity theory and DTM", Sadhana, 36(6), 1009-1019. https://doi.org/10.1007/s12046-011-0052-2.
  44. Rafiee, R. and Moghadam, R.M. (2014), "On the modeling of carbon nanotubes: A critical review", Compos. Part B: Eng., 56, 435-449. https://doi.org/10.1016/j.compositesb.2013.08.037.
  45. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res, 4(1), 31-44. http://doi.org/10.12989/anr.2016.4.1.031.
  46. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  47. Regi, M. (2007), "6-synthesis, characteristics and applications of carbon nanotubes: The case of aerospace engineering", Nanofib. Nanotechnol. Textil., 113-193. https://doi.org/10.1533/9781845693732.2.113.
  48. Reilly, R.M. (2007), "Carbon nanotubes: Potential benefits and risks of nanotechnology in nuclear medicine", J. Nucl. Medic., 48(7), 1039-1042. http://doi.org/10.2967/jnumed.107.041723.
  49. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv Nano Res., 7, 265-275. https://doi.org/10.12989/anr.2019.7.4.265.
  50. Sayin, E. and Calayir, Y. (2015), "Comparison of linear and nonlinear earthquake response of masonry walls", Comput. Concrete, 16(1), 17-35. https://doi.org/10.12989/cac.2015.16.1.017.
  51. Soldano, C. (2015), "Hybrid metal-based carbon nanotubes: Novel platform for multifunctional applications", Progr. Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001.
  52. Sosa, E.D., Darlington, T.K., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., 2014, Article ID 705687. http://doi.org/10.1155/2014/705687.
  53. Timoshenko, S. (1974), Vibration Problems in Engineering, Wiley, New York.
  54. Wang, C.M., Ma, Y.Q., Zhang, Y.Y. and Ang, K.K. (2006), "Buckling of double-walled carbon nanotubes modeled by solid shell elements", J. Appl. Phys., 99(11), 114317-114312. https://doi.org/10.1063/1.2202108.
  55. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnol., 18(10), 105401. https://doi.org/10.1016/j.compositesb.2018.08.051.
  56. Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures", Phys. Lett. A, 363, 236-242. https://doi.org/10.1016/j.physleta.2006.10.093.
  57. Xu, K.Y., Aifantis, E.C. and Yan, Y.H. (2008), "Vibrations of double walled carbon nanotubes with different boundary conditions between inner and outer tubes", J. Appl. Mech., 75(2), 021013. https://doi.org/10.1115/1.2793133.
  58. Zamani, A., Kolahchi, R. and Bidgoli, M.R. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concrete, 20(6), 671-682. https://doi.org/10.12989/cac.2017.20.6.671.
  59. Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B, 71(19), 195404. https://doi.org/10.1103/PhysRevB.71.195404.
  60. Zhao, J., Buldum, A., Lu, J.P. and Han, J. (2002), "Gas Molecule adsorption in carbon nanotubes and nanotubes bundles", Nanotechnol., 13(2), 195. https://doi.org/10.1088/0957-4484/13/2/312.
  61. Zidour, M., Benrahou, K., Semmah, A.W., Naceri, M., Belhadj, H.A., Bakhti, K. and Tounsi, A. (2012), "The thermal effect on vibration of single walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Comput. Mater. Sci., 51(1), 252-260. https://doi.org/10.1016/j.commatsci.2011.07.021.
  62. Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., AddaBedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0