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Young's modulus distribution as intelligent control estimation with smart structure

  • Ikram Ahmad (Department of Chemistry, University of Sahiwal) ;
  • Sana Shahzadi (Department of Chemistry, University of Sahiwal) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Hamdi Ayed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Rana Muhammad Akram Muntazir (Department of Mathematics, Lahore Leads University) ;
  • Muzamal Hussain (Department of Mathematics, University of Sahiwal) ;
  • Abir Mouldi (Department of Industrial Engineering, College of Engineering, King Khalid University) ;
  • Sehar Asghar (Department of Mathematics, Government College University Faisalabad) ;
  • Bazal Fatima (Department of Chemistry, University of Sahiwal) ;
  • Waheed Iqbal (Department of Mathematics, Government College University Faisalabad) ;
  • Fatima Zahra (School of Science, Department of Mathematics, University of Management and Technology (UMT)) ;
  • Essam Mohammed Banoqitah (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University)
  • Received : 2023.08.06
  • Accepted : 2024.07.17
  • Published : 2024.03.25

Abstract

The calculation of the natural frequencies versus Young's modulus of carbon nanotubes with modified continuum shell is the subject of current research. When designing these tubes, it is important to understand their frequencies because excessive vibrations might cause fatigue. These tubes are designed and built to meet specific needs and have been suitably modified to investigate their vibratory response. There are numerous uses for carbon nanotube free vibration analysis in the mechanical sciences. The fundamental frequency with Young's modulus for clamped-free and simply supported end conditions, which is connected to the carbon nanotubes, is calculated theoretically for chiral single carbon nanotubes. When Young's modulus rises, so does the frequency curve pattern. Young's modulus influences the single-walled carbon nanotube's dynamic response by simulating it as a modified continuum shell. The Young's modulus of chiral tube and the value of frequency increased as the chiral tube's index increased. The results are checked against past studies to ensure the problem's validity and are determined to be accurate.

Keywords

Acknowledgement

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/95/45.

References

  1. Adali, S. (2009), "Variational principles for multi-walled carbon nanotubes undergoing non-linear vibrations by semi-inverse method", Micro Nano Lett., 4(4), 198-203. https://doi.org/10.1049/mnl.2009.0084
  2. Al-Shamma, F., Majeed, W.I. and Ali, H.A.K. (2018), "Experimental responses of MWCNTs reinforced cross-ply thin composite shells under transverse impact and thermal loads", J. Eng. Sustain. Develop., 22(3), 34-49. https://doi.org/10.31272/jeasd.2018.3.4
  3. Alwabli, A.S., Kaci, A., Bellifa, H., Bousahla, A.A., Tounsi, A., Alzahrani, D.A., Abulfaraj, A.A., Bourada, F., Benrahou, K.H., Tounsi, A. and Mahmoud, S.R. (2021), "The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory", Adv. Nano Res., Int. J., 10(1), 15-24. https://doi.org/10.12989/anr.2021.10.1.015
  4. Ansari, R., Sahmani, S. and Arash, B. (2010), "Nonlocal plate model for free vibrations of single-layered graphene sheets", Phys. Lett. A., 375(1), 53-62. https://doi.org/10.1016/j.physleta.2010.10.028
  5. Asghar, S., Naeem, M.N., Khadimallah, M.A., Hussain, M., Iqbal, Z. and Tounsi, A. (2020), "Effect of chiral structure for free vibration of DWCNTs: Modal analysis", Adv. Concrete Constr., Int. J., 9(6), 577-588. https://doi.org/10.12989/acc.2020.9.6.577
  6. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
  7. Budarapu, P.R., Yb, S.S., Javvaji, B. and Mahapatra, D.R. (2014), "Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium", Front. Struct. Civil Eng., 8, 151-159. https://doi.org/10.1007/s11709-014-0247-9
  8. Chandraseker, K., Mukherjee, S., Paci, J.T. and Schatz, G.C. (2009), "An atomistic-continuum Cosserat rod model of carbon nanotubes", J. Mech. Phys. Solids, 57(6), 932-958. https://doi.org/10.1016/j.jmps.2009.02.005
  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. Nano Res., Int. J., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193
  10. Eslami, M. and Javaheri, R. (1999), "Buckling of composite cylindrical shells under mechanical and thermal loads", J. Thermal Stress., 22(6), 527-545. https://doi.org/10.1080/014957399280733
  11. Fatahi-Vajari, A., Azimzadeh, Z. and Hussain, M. (2019), "Nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes using homotopy perturbation method", Micro Nano Lett., 14(14), 1366-1371. https://doi.org/10.1049/mnl.2019.020
  12. Fu, Y.M., Hong, J.W. and Wang, X.Q. (2006), "Analysis of nonlinear vibration for embedded carbon nanotubes", J. Sound Vib., 296(4-5), 746-756. https://doi.org/10.1016/j.jsv.2006.02.024
  13. Fuller, R.B. (1970), Utopia or Oblivion, Bantam Books, New York.
  14. Gao, Q., Ding, Z. and Liao, W. (2022), "Effective elastic properties of irregular auxetic structures", Compos. Struct., 287, 115269. https://doi.org/10.1016/j.compstruct.2022.115269
  15. Ghasemi, S.E. and Gouran, S. (2022), "Nonlinear analysis on flow-induced vibration of single-walled carbon nanotubes employing analytical methods", Int. J. Struct. Stabil. Dyn., 22(11), 2250115. https://doi.org/10.1142/S0219455422501152
  16. He, H., Shi, J., Yu, S., Yang, J., Xu, K., He, C. and Li, X. (2024), "Exploring green and efficient zero-dimensional carbon-based inhibitors for carbon steel: From performance to mechanism", Constr. Build. Mater., 411, 134334. https://doi.org/10.1016/j.conbuildmat.2023.134334
  17. Hollerer, S. and Celigoj, C.C. (2013), "Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model", Computat. Mech., 51, 765-789. https://doi.org/10.1007/s00466-012-0757-z
  18. Hou, X., Zhang, L., Su, Y., Gao, G., Liu, Y., Na, Z., Xu, Q., Ding, T., Xiao, L., Li, L. and Chen, T. (2023a), "A space crawling robotic bio-paw (SCRBP) enabled by triboelectric sensors for surface identification", Nano Energy, 105, 108013. https://doi.org/10.1016/j.nanoen.2022.108013
  19. Hou, X., Xin, L., Fu, Y., Na, Z., Gao, G., Liu, Y., Xu, Q., Zhao, P., Yan, G., Su, Y. and Cao, K. (2023b), "A self-powered biomimetic mouse whisker sensor (BMWS) aiming at terrestrial and space objects perception", Nano Energy, 118, 109034. https://doi.org/10.1016/j.nanoen.2023.109034
  20. 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.
  21. Huang, H., Huang, M., Zhang, W., Pospisil, S. and Wu, T. (2020), "Experimental investigation on rehabilitation of corroded RC columns with BSP and HPFL under combined loadings", J. Struct. Eng., 146(8), 04020157. https://doi.org/10.1061/(ASCE)ST.1943-541X.000272
  22. Huang, H., Xue, C., Zhang, W. and Guo, M. (2022a), "Torsion design of CFRP-CFST columns using a data-driven optimization approach", Eng. Struct., 251, 113479. https://doi.org/10.1016/j.engstruct.2021.113479
  23. Huang, H., Yao, Y., Liang, C. and Ye, Y. (2022b), "Experimental study on cyclic performance of steel-hollow core partially encased composite spliced frame beam", Soil Dyn. Earthq. Eng., 163, 107499. https://doi.org/10.1016/j.soildyn.2022.107499
  24. Huang, H., Yao, Y., Zhang, W. and Zhou, L. (2023), "A push-out test on partially encased composite column with different positions of shear studs", Eng. Struct., 289, 116343. https://doi.org/10.1016/j.engstruct.2023.116343
  25. Hussain, M. (2024), "Small-scale Computational Vibration of Carbon Nanotubes", Compos. Struct., 9781032656229.
  26. Hussain, M. and Naeem, M.N. (2019), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathe. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  27. Iqbal, W., Jalil, M., Khadimallah, M.A., Hussain, M., Naeem, M.N., Al Naim, A.F. and Tounsi, A. (2021), "Interaction of casson nanofluid with Brownian motion: Temperature profile with shooting method", Adv. Nano Res., Int. J., 10(4), 349-357. https://doi.org/10.12989/anr.2021.10.4.349
  28. Ju, Y., Liu, W., Zhang, Z. and Zhang, R. (2022), "Distributed Three-Phase Power Flow for AC/DC Hybrid Networked Microgrids Considering Converter Limiting Constraints", IEEE Transact. Smart Grid, 13(3), 1691-1708. https://doi.org/10.1109/TSG.2022.3140212
  29. Jweeg, M.J. and Alazzawy, W.I. (2007), "A suggested analytical solution for laminated closed cylindrical shells using General Third Shell Theory (GTT)", Al-Nahrain J. Eng. Sci., 10(1), 11-26.
  30. Jweeg, M.J. and Alazzawy, W.I. (2010), "A study of free vibration and fatigue for cross-ply closed cylindrical shells using General Third shell Theory (GTT)", J. Eng., 16(02), 5170-5184. https://doi.org/10.31026/j.eng.2010.02.29
  31. 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
  32. 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", Computat. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002
  33. Khadimallah, M.A., Safeer, M., Taj, M., Ayed, H., Hussain, M., Bouzgarrou, S.M., Mahmoud, S.R., Ahmad, M. and Tounsi, A. (2020), "The effects of the surrounding viscoelastic media on the buckling behavior of single microfilament within the cell: A mechanical model", Adv. Concrete Constr., Int. J., 10(2), 141-149. https://doi.org/10.12989/acc.2020.10.2.141
  34. Kroto, H.W., Heath, J.R., O'Brien, S.C., Curl, R.F. and Smalley, R.E. (1985), "C60 buckyminsterfullerence", Nature, 318, 162.
  35. Li, F., Gan, J., Zhang, L., Tan, H., Li, E. and Li, B. (2024a), "Enhancing impact resistance of hybrid structures designed with triply periodic minimal surfaces", Compos. Sci. Technol., 245, 110365. https://doi.org/10.1016/j.compscitech.2023.11036
  36. Li, J., Wang, Z., Zhang, S., Lin, Y., Jiang, L. and Tan, J. (2024b), "Task incremental learning-driven Digital-Twin predictive modeling for customized metal forming product manufacturing process", Robot. Comput.-Integr. Manuf., 85, 102647. https://doi.org/10.1016/j.rcim.2023.102647
  37. Lu, D., Ma, C., Du Xiuli, Jin, L. and Gong, Q. (2017), "Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept", Int. J. Geomech., 17(2), 04016058. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000729
  38. Lu, D., Meng, F., Zhou, X., Zhuo, Y., Gao, Z. and Du, X. (2023), "A dynamic elastoplastic model of concrete based on a modeling method with environmental factors as constitutive variables", J. Eng. Mech., 149(12). https://doi.org/10.1061/JENMDT.EMENG-720
  39. Malikan, M. and Eremeyev, V.A. (2020), "Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method", Mater. Res. Express, 7(2), 025005. https://doi.org/10.1088/2053-1591/ab691c10.1088/2053-1591/ab691c
  40. Naidu, S.S., Varun, C. and Satyanarayana, G. (2012), "Fundamental natural frequencies of double-walled carbon nanotubes", Int. J. Eng. Res. Technol. (IJERT), 322(4-5), 652-664. https://doi.org/10.1016/j.jsv.2009.02.037
  41. Natsuki, T., Ni, Q.Q. and Endo, M. (2008), "Vibrational analysis of fluid-filled carbon nanotubes using the wave propagation approach", Appl. Phys. A, 90, 441-445. https://doi.org/10.1007/s00339-007-4297-x
  42. Nogales, E. (2001), "Structural insights into microtubule function", Annual Rev. Biophys. Biomolecul. Struct., 30(1), 397-420. https://doi.org/10.1146/annurev.biophys.30.1.397
  43. Pourasghar, A., Yang, W., Brigham, J. and Chen, Z. (2021), "Nonlocal thermoelasticity: Transient heat conduction effects on the linear and nonlinear vibration of single-walled carbon nanotubes", Mech. Based Des. Struct. Mach., 1-17. https://doi.org/10.1080/15397734.2021.1985516
  44. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  45. Regi, M. (2007), "6-synthesis, characteristics and applications of carbon nanotubes: the case of aerospace engineering", Nanofib. Nanotechnol. Textiles, 113-193. https://doi.org/10.1533/9781845693732.2.113
  46. Reilly, R.M. (2007), "Carbon Nanotubes: Potential benefits and risks of nanotechnology in nuclear medicine", J. Nuclear Med., 48(7), 1039-1042. http://doi.org/10.2967/jnumed.107.041723
  47. Ru, C.Q. (2000), "Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube", J. Appl. Phys., 87(10), 7227-7231. https://doi.org/10.1063/1.372973
  48. Shi, Y., Hou, X., Na, Z., Zhou, J., Yu, N., Liu, S., Xin, L., Gao, G. and Liu, Y. (2023), "Bio-inspired attachment mechanism of dynastes Hercules: Vertical climbing for on-orbit assembly legged robots", J. Bionic Eng., 21(1), 137-148. https://doi.org/10.1007/s42235-023-00423-0
  49. Shima, H. (2011), "Buckling of carbon nanotubes: a state of the art review", Materials, 5(1), 47-84. https://doi.org/10.3390/ma5010047
  50. Soldano, C. (2015), "Hybrid metal-based carbon nanotubes: Novel platform for multifunctional applications", Progress Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001
  51. Su, F.Q., He, X.L., Dai, M.J., Yang, J.N., Hamanaka, A., Yu, Y.H., Li, W. and Li, J.Y. (2023), "Estimation of the cavity volume in the gasification zone for underground coal gasification under different oxygen flow conditions", Energy, 285, 129309. https://doi.org/10.1016/j.energy.2023.129309
  52. 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
  53. Wang, Q., Varadan, V.K. and Quek, S.T. (2006), "Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models", Phys. Lett. A, 357(2), 130-135. https://doi.org/10.1016/j.physleta.2006.04.026.
  54. Xiang, Y., Wang, Z., Zhang, S., Jiang, L., Lin, Y. and Tan, J. (2024), "Cross-sectional performance prediction of metal tubes bending with tangential variable boosting based on parameters-weight-adaptive CNN", Expert Syst. Applicat., 237, 121465. https://doi.org/10.1016/j.eswa.2023.121465
  55. Xu, K.Y., Guo, X.N. and Ru, C.Q. (2006), "Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces", J. Appl. Phys., 99(6), 64303. https://doi.org/10.1063/1.2179970
  56. 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
  57. Xu, S., Jing, X., Zhu, P., Jin, H., Paik, K.W., He, P. and Zhang, S. (2023), "Equilibrium phase diagram design and structural optimization of SAC/Sn-Pb composite structure solder joint for preferable stress distribution", Mater. Characteriz., 206, 113389. https://doi.org/10.1016/j.matchar.2023.113389
  58. Yao, Y., Huang, H., Zhang, W., Ye, Y., Xin, L. and Liu, Y. (2022), "Seismic performance of steel-PEC spliced frame beam", J. Constr. Steel Res., 197, 107456. https://doi.org/10.1016/j.jcsr.2022.107456
  59. Yao, Y., Zhou, L., Huang, H., Chen, Z. and Ye, Y. (2023), "Cyclic performance of novel composite beam-to-column connections with reduced beam section fuse elements", Struct., 50, 842-858. https://doi.org/10.1016/j.istruc.2023.02.054
  60. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Tech., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7
  61. Zhang, C. (2023), "The active rotary inertia driver system for flutter vibration control of bridges and various promising applications", Sci. China Technol. Sci., 66(2), 390-405. https://doi.org/10.1007/s11431-022-2228-0
  62. Zhang, Y.Y., Wang, C.M. and Tan, V.B.C. (2009), "Assessment of Timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics", Adv. Appl. Mathe. Mech., 1(1), 89-106. https://global-sci.org/intro/article_detail/aamm/210.html https://doi.org/10.html
  63. Zhang, C., Duan, C. and Sun, L. (2024a), "Inter-Storey Isolation Versus Base Isolation Using Friction Pendulum Systems", Int. J. Struct. Stabil. Dyn., 24(02), 2450022. https://doi.org/10.1142/S0219455424500226
  64. Zhang, W., Zheng, D., Huang, Y. and Kang, S. (2024b), "Experimental and simulative analysis of flexural performance in UHPC-RC hybrid beams", Constr. Build. Mater., 436, 136889. https://doi.org/10.1016/j.conbuildmat.2024.136889
  65. Zhou, X., Lu, D., Zhang, Y., Du, X. and Rabczuk, T. (2022), "An open-source unconstrained stress updating algorithm for the modified Cam-clay model", Comput. Methods Appl. Mech. Eng., 390, 114356. https://doi.org/10.1016/j.cma.2021.114356
  66. Wang, C., Ru, C. and Mioduchowski, A. (2004), "Applicability and limitations of simplified elastic shell equations for carbon nanotubes", J. Appl. Mech., 71(5), 622631. https://doi.org/10.1115/1.1778415
  67. Wang, C.Y., Ru, C.Q. and Mioduchowski, A. (2005), "Pressure effect on radial breathing modes of multiwall carbon nanotubes", J. Appl. Phys., 97(2), 024310024320. https://doi.org/10.1063/1.1836007
  68. Budiansky, B. (1963), "On the'best'first-order linear shell theory", The Prager Anniversary Volume-Progress in Applied Mechanics.
  69. Flugge, W. (2013), Statik und dynamik der schalen, Springer-Verlag.