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Small scale computational vibration of double-walled CNTs: Estimation of nonlocal shell model

  • Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed Amine (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Naeem, Muhammad N. (Department of Mathematics, Govt. College University Faisalabad) ;
  • Ghamkhar, Madiha (Mathematics and Statistics Department, University of Agriculture) ;
  • Khedher, Khaled Mohamed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Bouzgarrou, Souhail Mohamed (Civil Engineering Department, Faculty of Engineering, Jazan University) ;
  • Ali, Zainab (Department of Mathematics, Govt. College University Faisalabad) ;
  • Iqbal, Zafar (Department of Mathematics, University of Sargodha) ;
  • Mahmoud, S.R. (GRC Department, Faculty of Applied studies, King Abdulaziz University) ;
  • Algarni, Ali (Statistics Department, Faculty of Science, King Abdulaziz University) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department)
  • Received : 2020.07.10
  • Accepted : 2020.09.22
  • Published : 2020.10.25
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Abstract

In this paper, vibration characteristics of double-walled carbon nanotubes (CNTs) is studied based upon nonlocal elastic shell theory. The significance of small scale is being perceived by developing nonlocal Love shell model. The wave propagation approach has been utilized to frame the governing equations as eigen value system. The influence of nonlocal parameter subjected to diverse end supports has been overtly analyzed. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of changing mechanical parameter Poisson's ratio has been investigated in detail. The dominance of boundary conditions via nonlocal parameter is shown graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

Keywords

References

  1. Alibeigloo, A. and Shaban, M. (2013), "Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity", Acta Mechanica, 224(7), 1415-1427. https://doi.org/10.1007/s00707-013-0817-2.
  2. Alijani, M. and Bidgoli, M.R. (2018), "Agglomerated $SiO_2$ nanoparticles reinforced-concrete foundations based on higher order shear deformation theory: Vibration analysis", Adv. Concrete Constr., 6(6), 585. http://dx.doi.org/10.12989/acc.2018.6.6.585.
  3. Aminikhah, H. and Hemmatnezhad, M. (2011), "Nonlinear vibrations of multiwalled carbon nanotubes under various boundary conditions", Int. J. Differ. Eq., 2011, Article ID 343576. https://doi.org/10.1155/2011/343576.
  4. Ansari, R., Hemmatnezhad, M. and Rezapour, J. (2011), "The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions", Curr. Appl. Phys., 11(3), 692-697. https://doi.org/10.1016/j.cap.2010.11.034.
  5. 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.
  6. Basirjafari, S., Esmaeilzadeh Khadem, S. and Malekfar, R. (2013), "Validation of shell theory for modeling the radial breathing mode of a single-walled carbon nanotube", Int. J. Eng. Trans. A, 26(4), 447-454.
  7. 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.2016.18.5.1053.
  8. Bisen, H.B., Hirwani, C.K., Satankar, R.K., Panda, S.K., Mehar, K. and Patel, B. (2018), "Numerical study of frequency and deflection responses of natural fiber (Luffa) reinforced polymer composite and experimental validation", J. Nat. Fiber., 1-15. https://doi.org/10.1080/15440478.2018.1503129.
  9. 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., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.
  10. Budiansky, B. (1963), "On the'best'first-order linear shell theory", Prager Anniversary Volume-Progress in Applied Mechanics.
  11. Cirak, F., Ortiz, M. and Pandolfi, A. (2005), "A cohesive approach to thin-shell fracture and fragmentation", Comput. Meth. Appl. Mech. Eng., 194(21-24), 2604-2618. https://doi.org/10.1016/j.cma.2004.07.048.
  12. Demir, A.D. and Livaoglu, R. (2019), "The role of slenderness on the seismic behavior of ground-supported cylindrical silos", Adv. Concrete Constr., 7(2), 65. http://dx.doi.org/10.12989/acc.2019.7.2.065.
  13. Dewangan, H.C., Panda, S.K. and Sharma, N. (2020), "Experimental validation of role of cut-out parameters on modal Responses of laminated composite-A coupled Fe approach", Int. J. Appl. Mech., 2050068. https://doi.org/10.1142/S1758825120500684.
  14. Dewangan, H.C., Sharma, N., Hirwani, C.K. and Panda, S.K. (2020), "Numerical eigenfrequency and experimental verification of variable cutout (square/rectangular) borne layered glass/epoxy flat/curved panel structure", Mech. Bas. Des. Struct. Mach., 1-18. https://doi.org/10.1080/15397734.2020.1759432.
  15. 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.
  16. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Science and Business Media, New York.
  17. Fakhrabadi, M.M.S., Rastgoo, A. and Ahmadian, M.T. (2015), "Application of electrostatically actuated carbon nanotubes in nanofluidic and bio-nanofluidic sensors and actuators", Measure., 73, 127-136. https://doi.org/10.1016/j.measurement.2015.05.009.
  18. 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.
  19. Hernandez, E., Goze, C., Bemier, P. and Rubio, A. (1998), "Elastic properties of C and BxCyNz composite nanotubes", Phys. Rev. Lett., 80, 4502-505. https://doi.org/10.1103/PhysRevLett.80.4502.
  20. 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.
  21. Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B: Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  22. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(1), 56-58. https://doi.org/10.1038/354056a0.
  23. Kagimoto, H., Yasuda, Y. and Kawamura, M. (2015), "Mechanisms of ASR surface cracking in a massive concrete cylinder", Adv. Concrete Constr., 3(1), 39. http://dx.doi.org/10.12989/acc.2015.3.1.039.
  24. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016.
  25. Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  26. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x.
  27. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032.
  28. Kolahchi, R., Hosseini, H., Fakhar, M.H., Taherifar, R. and Mahmoudi, M. (2019), "A numerical method for magneto-hygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Comput. Math. Appl., 78(6), 2018-2034. https://doi.org/10.1016/j.camwa.2019.03.042.
  29. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2020), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw Struct. Mater., 22(1), 3-27. https://doi.org/10.1177/1099636217731071.
  30. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023.
  31. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.
  32. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A. N. (2017), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016.
  33. Krishnan, A., Dujardin, E., Ebbesen, T.W., Yianilos, P.N. and Treacy, M.M.J. (1998), "Young's modulus of single-walled nanotubes", Phys. Rev. B, 58(20), 14013. https://doi.org/10.1103/PhysRevB.58.14013.
  34. Kunche, M.C., Mishra, P.K., Nallala, H.B., Hirwani, C.K., Katariya, P.V., Panda, S. and Panda, S.K. (2019), "Theoretical and experimental modal responses of adhesive bonded T-joints", Wind Struct., 29(5), 361-369. https://doi.org/10.12989/was.2019.29.5.361.
  35. Li, C. and Chou, T.W (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-249992. https://doi.org/10.1016/S0020-7683(03)00056-8.
  36. Liew, K.M. and Wang, Q. (2007), "Analysis of wave propagation in carbon nanotubes via elastic shell theories", Int. J. Eng. Sci., 45(2-8), 227-241. https://doi.org/10.1016/j.ijengsci.2007.04.001.
  37. Love, A.E.H. (1888), "The small free vibrations and deformation of a thin elastic shell", Philos. Tran. Roy. Soc. London A, 179, 491-546. https://doi.org/10.1098/rsta.1888.0016
  38. Love, A.E.H. (2013), A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
  39. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889.
  40. Malhari Ramteke, P., Mehar, K., Sharma, N. and Panda, S. (2020a), "Numerical prediction of deflection and stress responses of functionally graded structure for grading patterns (Power-law, sigmoid and exponential) and variable porosity (Even/Uneven)", Scientia Iranica. 10.24200/SCI.2020.55581.4290.
  41. Markus, S. (1988), Mechanics of Vibrations of Cylindrical Shells, Amsterdam.
  42. Mehar et al. (2016), "Modeled mathematically based on the higher order shell theory. The material properties of carbon nanotube reinforced composite plate are assumed to be temperature dependent and graded in the thickness direction using different grading rules".
  43. Mehar, K. and Kumar Panda, S. (2018), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266.
  44. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181. http://dx.doi.org/10.12989/anr.2019.7.3.181.
  45. Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519.
  46. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Solid., 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  47. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017b), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057.
  48. Mehar, K., Panda, S.K. and Patle, B.K. (2018), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809. https://doi.org/10.1002/pc.24409.
  49. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324.
  50. Mesbah, H.A. and Benzaid, R. (2017), "Damage-based stress-strain model of RC cylinders wrapped with CFRP composites", Adv. Concrete Constr., 5(5), 539. http://dx.doi.org/10.12989/acc.2017.5.5.539.
  51. Mohsen, M. and Eyvazian A. (2020), "Post-buckling analysis of Mindlin Cut out-plate reinforced by FG-CNTs", Steel Compos. Struct., 34(2), 289. https://doi.org/10.12989/scs.2020.34.2.289.
  52. Motezaker, M. and Eyvazian, A. (2020), "Buckling load optimization of beam reinforced by nanoparticles", Struct. Eng. Mech., 73(5), 481-486 https://doi.org/10.12989/sem.2020.73.5.481.
  53. Motezaker, M. and Kolahchi, R. (2017a), "Seismic response of concrete columns with nanofiber reinforced polymer layer", Comput. Concrete, 20(3), 361-368. https://doi.org/10.12989/cac.2017.20.3.361.
  54. Motezaker, M. and Kolahchi, R. (2017b), "Seismic response of $SiO2_{2}$ nanoparticles-reinforced concrete pipes based on DQ and newmark methods", Comput. Concrete, 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745.
  55. Motezaker, M., Jamali, M. and Kolahchi, R. (2020), "Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory", J. Comput. Appl. Math., 369, 112625. https://doi.org/10.1016/j.cam.2019.112625.
  56. Pandey, H.K., Hirwani, C.K., Sharma, N., Katariya, P.V., Dewangan, H.C. and Panda, S.K. (2019), "Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses-An FEM approach and experimental verification", Adv. Nano Res., 7(6), 419-429. https://doi.org/10.12989/anr.2019.7.6.419.
  57. Pine, P., Yaish, Y.E. and Adler, J. (2011), "The effect of boundary conditions on the vibrations of armchair, zigzag, and chiral single-walled carbon nanotubes", J. Appl. Phys., 110(12), 124311. https://doi.org/10.1063/1.3667290.
  58. Qian, D., Wagner, G.J., Liu, W.K., Yu, M.F. and Ruoff, R.S. (2002), "Mechanics of carbon nanotubes", Appl. Mech. Rev, 55(6), 495-533. https://doi.org/10.1115/1.1490129
  59. Rabczuk, T., Areias, P.M.A. and Belytschko, T. (2007), "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Meth. Eng., 72(5), 524-548. https://doi.org/10.1002/nme.2013.
  60. Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020b), "Static deflection simulation study of 2D Functionally graded porous structure", Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2020.03.537.
  61. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  62. Rayleigh, L. (1882), "On the equilibrium of liquid conducting masses charged with electricity", London, Edinburgh, Dublin Philos. Mag. J. Sci., 14(87), 184-186. https://doi.org/10.1080/14786448208628425.
  63. Samadvand, H. and Dehestani, M. (2020), "A stress-function variational approach toward CFRP-concrete interfacial stresses in bonded joints", Adv. Concrete Constr., 9(1), 43-54. https://doi.org/10.12989/acc.2020.9.1.043.
  64. Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P. (1999), "Ab-initio structural, elastic, and vibrational properties of carbon nanotubes", Phys. Rev. B, 59, 12678-2688. http://dx.doi.org/10.1103/PhysRevB.59.12678
  65. Soldano, C. (2015), "Hybrid metal-based carbon nanotubes", "Novel platform for multifunctional applications", Prog. Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001.
  66. Sosa, E.D., Darlington, TK., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., Article ID 705687, 12. http://dx.doi.org/10.1155/2014/705687.
  67. Torkaman-Asadi, M.A., Rahmanian, M. and Firouz-Abadi, R.D. (2015), "Free vibrations and stability of high-speed rotating carbon nanotubes partially resting on Winkler foundations", Compos. Struct., 126, 52-61. https://doi.org/10.1016/j.compstruct.2015.02.037.
  68. Vodenitcharova, T. and Zhang, L.C. (2003), "Effective wall thickness of single walled carbon nanotubes", Phy. Rev. B, 68, 165401. https://doi.org/10.1103/PhysRevB.68.165401.
  69. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnol., 18(10), 105401. https://doi.org/10.1088/0957-4484/18/10/105401
  70. 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.
  71. Wang, Y.Z. (2017), "Nonlinear internal resonance of double-walled nanobeams under parametric excitation by nonlocal continuum theory", Appl. Math. Model., 48, 621-634. https://doi.org/10.1016/j.apm.2017.04.018.
  72. Wang, Y.Z., Cui, H.T., Li, F.M. and Kishimoto, K. (2011), "Effects of viscous fluid on wave propagation in carbon nanotubes", Phys. Lett. A., 375(24), 2448-2451. https://doi.org/10.1016/j.physleta.2011.05.016.
  73. Wang, Y.Z., Wang, Y.S. and Ke, L.L. (2016), "Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory", Physica E: Lowdimens. Syst. Nanostr., 83, 195-200. https://doi.org/10.1016/j.physe.2016.05.020.
  74. Yakobson, B.I., Brabec, C.J. and Bernholc, J. (1996), "Nano-mechanics of carbon tubes: instabilities beyond linear response", Phy. Rev. Lett., 76, 2511-2514. https://doi.org/10.1103/PhysRevLett.76.2511.
  75. Yakobson, B.I., Campbell, M.P., Brabec, C.J. and Bemholc J. (1997), "High strain rate fracture and C-chain unravelling in carbon nanotubes", Comput. Mater. Sei., 8(4), 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5.
  76. Yoon, J., Ru, C.Q. and Mioduchowski. A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sei. Tech., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.
  77. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043.
  78. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. http://dx.doi.org/10.12989/sem.2015.54.4.693.
  79. Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Vibration analysis of thin cylindrical shells using wave propagation approach", J. Sound Vib., 239(3), 397-403. https://doi.org/10.1006/jsvi.2000.3139.
  80. 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. Math. Mech., 1(1), 89-106.