Steel and Composite Structures

  • 제34권5호
  • /
  • Pages.657-670
  • /
  • 2020
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Three dimensional free vibration analysis of functionally graded nano cylindrical shell considering thickness stretching effect

  • Dehsaraji, Maryam Lori (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arefi, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Loghman, Abbas (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2019.04.17
  • 심사 : 2020.01.27
  • 발행 : 2020.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, vibration analysis of functionally graded nanoshell is studied based on the sinusoidal higher-order shear and normal deformation theory to account thickness stretching effect. To account size-dependency, Eringen nonlocal elasticity theory is used. For more accurate modeling the problem and corresponding numerical results, sinusoidal higher-order shear and normal deformation theory including out of plane normal strain is employed in this paper. The radial displacement is decomposed into three terms to show variation along the thickness direction. Governing differential equations of motion are derived using Hamilton's principle. It is assumed that the cylindrical shell is made of an arbitrary composition of metal and ceramic in which the local material properties are measured based on power law distribution. To justify trueness and necessity of this work, a comprehensive comparison with some lower order and lower dimension works and also some 3D works is presented. After presentation of comparative study, full numerical results are presented in terms of significant parameters of the problem such as small scale parameter, length to radius ratio, thickness to radius ratio, and number of modes.

키워드

참고문헌

  1. Ansari, R., Rouhi, H. and Rajabiehfard, R.. (2012), "Free vibration analysis of single-walled carbon nanotubes using semi-analytical finite element", Int J Comput Meth Eng Sci Mech., 13,1-8. https://doi.org/10.1080/15502287.2012.660234.
  2. Ansari, R., Rouhi, H. and Sahmani, S. (2011),"Calibration of the analytical nonlocal shell model for vibrations of double-walled carbon nanotubes with arbitrary boundary conditions using molecular dynamics", Int J Mech Sci., 53, 786-792. https://doi.org/10.1016/j.ijmecsci.2011.06.010..
  3. Alibeigloo, A. and Shaban, M. (2013),"Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity", Acta Mech., 224(7), 1415-1427. https://doi.org/10.1007/s00707-013-0817-2.
  4. Ansari, R., Sahmani, S. and Rouhi, H. (2011), "Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions", Phys. Lett. A, 375 ,1255-1263. https://doi.org/10.1016/j.physleta.2011.01.046.
  5. Arash, B and Wang, Q. (2012), "A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes", Comput. Mater. Sci., 51, 303-313. https://doi.org/10.1007/978-3-319-01201-8_2.
  6. Arefi, M and Zenkour, A.M. (2016), "Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory", Mater, Res, Express., 3, 115704. https://doi.org/10.1088/2053-1591/3/11/115704.
  7. Arefi, M. and Zenkour, A.M. (2017a), "Thermo-electro-mechanical bending behavior of sandwich nanoplate integrated with piezoelectric face-sheets based on trigonometric plate theory", Compos Struct., 162, 108-122. https://doi.org/10.1016/j.compstruct.2016.11.071.
  8. Arefi, M., Kiani, M. and Zenkour, A.M. (2017b), "Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezo magnetic face sheets resting on Pasternak's foundation via MCST", Sandw. Struct. Mater., https://doi.org/10.1177/1099636217734279.
  9. Arefi, M. and Zenkour, A.M. (2017c), "Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation", Phys. B: Cond. Matter., 521, 188-197. https://doi.org/10.1016/j.physb.2017.06.066.
  10. Arefi, M. and Zenkour, A.M. (2017d), "Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam", Acta. Mech., 228(10), 3657-3674. https://doi.org/10.1007/s00707-017-1892-6.
  11. Arefi, M. and Zenkour, A.M. (2019), "Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory", J. Sandw. Struct. Mater., 21(8), 2751-2778. https://doi.org/10.1177/1099636217723186.
  12. Amiri, F., Millan, D., Shen, Y., Rabczuk, T. and Arroyo, M. (2014), "Phase-field modeling of fracture in linear thin shells", Theor. Appl. Fract. Mech., 69, 102-109., https://doi.org/10.1016/j.tafmec.2013.12.002
  13. Areias, P., Rabczuk, T. and Msekh, M.A. (2016), "Phase-field analysis of finite-strain plates and shells including element Subdivision", Comput. Method. Appl. M., 312, 322-235. http://dx.doi.org/10.1016/j.cma.2016.01.020.
  14. Baghani, M., MohammadSalehi, M. and Dabaghian, P.H. (2016), "Analytical couple-stress solution for size-dependent large-amplitude vibrations of FG tapered-nanobeams", Solids Struct., 13(1). http://dx.doi.org/10.1590/1679-78252175.
  15. Belkorissat, I., Ahmed Houari, M.S., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable mode", Steel Compos. Struct., 18, 1063-1081. http://dx.doi.org/10.12989/scs.2015.18.4.1063.
  16. Budarapu, P.R. Reinoso, J. and Paggi, M. (2017a), "Concurrently coupled solid shell-based adaptive multiscale method for fracture", Comput. Method. Appl. M., 319(1), 338-365. https://doi.org/10.1016/j.cma.2017.02.023.
  17. Budarapu, P.R. and Rabczuk, T. (2017b), "Multiscale methods for fracture: A review". J. Ind. Inst. Sci., 97(3), 339-376. https://doi.org/10.1007/s41745-017-0041-5.
  18. Budarapu, P.R., Gracie, R., Yang, S.W., Zhuang, X. and Rabczuk, T. (2014), "Efficient Coarse Graining in Multiscale Modeling of Fracture", Theor. Appl. Fract. Mech., 69, 126-143. https://doi.org/10.1016/j.tafmec.2013.12.004.
  19. Chen, W.Q., Ying, J. and Yang, Q.D. (2008), "Free vibrations of transversely isotropic cylinders and cylindrical shells", Pressure Vessel Technol., 120(4). https://doi.org/10.1115/1.2842338.
  20. Duan, W.H., Wang, C.M. and Zhang, Y.Y. (2007), "Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics", J. Appl. Phys., 101, 024305. https://doi.org/10.1063/1.2423140.
  21. Daneshmand, F., Rafiei, M., Mohebpour, S. and Heshmati, M. (2013), "Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory", Appl. Math. Model., 37, 7983-8003. https://doi.org/10.1016/j.apm.2013.01.052.
  22. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. ttps://doi.org/10.1063/1.332803.
  23. Gurtin, M.E. and Murdoch, A. (1975), "A continuum theory of elastic material surfaces", Arch. Rat. Mech. Anal., 57, 291-323. https://doi.org/10.1007/BF00261375.
  24. Gurtin, M.E and Murdoch, A. (1978), "Surface stress in solids". Int. J. Solids Struct., 14, 431-440., .https://doi.org/10.1007/BF00261375
  25. Gurtin, M.E., Issmuller, W.E and Larche, J. (1998), "A general theory of curved deformable interfaces in solids at equilibrium", Philos. Mag., 78(5), 1093-1109. https://doi.org/10.1080/01418619808239977.
  26. Ghavanloo, E. and Fazelzadeh, A. (2013), "Nonlocal elasticity theory for radial vibration of nanoscale spherical shells", Mech. A/Solids, 41, 37-42., https://doi.org/10.1016/j.euromechsol.2013.02.003,
  27. Gholami, R., Darvizeh, A., Ansari, A. and Sadeghi, F. (2016), "Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlin's strain gradient elasticity theory", Mech. -A/Solids., 58,76-88., https://doi.org/10.1016/j.euromechsol.2016.01.014.
  28. Guo, H., Zhuang, X. and Rabczuk, T. (2019), "A deep collocation method for the bending analysis of kirchhoff plate", Comput. Mater. Continu., 59, 433-456. doi:10.32604/cmc.2019.06660.
  29. Hosseini Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., 26(5), 607., https://doi.org/10.12989/scs.2018.26.5.607.
  30. Javvaji, B., Budarapu, P.R., Paggi, M., Zhuang, X. and Rabczuk, T. (2018), "Fracture Properties of Graphene-Coated Silicon for Photovoltaics", Adv. Theory. Simulation., 1(12), 1800097, https://doi.org/10.1002/adts.201800097.
  31. Koutsoumaris, C.C., et al. (2015), "Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes", AIP Publishing LLC., 3, 28-42., https://doi.org/10.1063/1.4938978.
  32. Lam, D., Yang, F., Chong, A., Wang, J and Tong, P. (2003) ,"Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids., 51,1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  33. Li, C., Liu, J.J., Cheng, M. and Fan, X.L. (2017), "Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces", Compos. Part B: Eng,, 116, 153-69., https://doi.org/10.1016/j.compositesb.2017.01.071.
  34. Moradi-Dastjerdi, R., Pourasghar, A. and Foroutan, M. (2014), "Vibration analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube based on mesh-free method". Compos. Mater., 48(15)., https://doi.org/10.1177/0021998313491617.
  35. Murmu, T., Adhikari, S and Wang, C.Y. (2011), "Torsional vibration of carbon nanotube-buckyball systems based on nonlocal elasticity theory". Physica E, 43, 1276-1280., https://doi.org/10.1016/j.physe.2011.02.017.
  36. Nguyen-Thanh, N., Zhou, K., Zhuang, X., Areias, P., Nguyen-Xuan, H., Bazilevs, Y and Rabczuk, T. (2017), "Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling", Comput. Method. Appl. M., 316, 1157-1178., http://dx.doi.org/10.1016/j.cma.2016.12.002.
  37. Pourasghar, A. and Chen, Z. (2016), "Thermoelastic response of CNT reinforced cylindrical panel resting on elastic foundation using theory of elasticity", Compos. Part B Eng., 99, 436-444. https://doi.org/10.1016/j.compositesb.2016.06.028.
  38. Pradhan, S.C and Phadikar, J.K. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett., 373, 1062-1069. https://doi.org/10.1016/j.physleta.2009.01.030.
  39. Reddy, J. (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.
  40. Rabczuk, T., Gracie, R., Song, J.H. and Belytschko, T. (2010), "Immersed particle method for fluid-structure interaction", Numer, Method Eng., 81, 48-71. 10.1002/nme.2670, 2010.
  41. 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, 524-548. https://doi.org/10.1002/nme.2013.
  42. Shojaeefard, M.H., Mahinzare, M., Safarpour, H., Ghadiri, M. and Googarchin, H. (2018), "Free vibration of an ultra-fast-rotating induced cylindrical nano-shell resting on a Winkler foundation under thermo-electro-magneto-elastic condition", Appl. Math. Model., 61, 255-279. https://doi.org/10.1016/j.apm.2018.04.015.
  43. Shaat, M and Abdelkefi, A. (2017), "New insights on the applicability of Eringen's nonlocal theory", Int J Mech Sci., 121, 67-75., https://doi.org/10.1016/j.ijmecsci.2016.12.013.
  44. She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijmecsci.2016.12.013.
  45. Safaei, B., Moradi-Dastjerdi, R., Qin, Z.H. and Chu, F. (2018), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B Eng., 18, 148-176. https://doi.org/10.1016/j.compositesb.2018.10.049.
  46. Salehipour, H., Nahvi, H. and Shahidi, A.R. (2015), "Exact closed-form free vibration analysis for functionally graded micro/nano plates based on modified couple stress and three-dimen-sional elasticity theories", Compos. Struct., 124, 283-291. https://doi.org/10.1016/j.compstruct.2015.01.015.
  47. Soleimani, I., Tadi Beni, Y. and Dehkordi, M.B. (2018), "Finite element vibration analysis of nanoshell based on new cylindrical shell element", Struct. Eng. Mech., 65(1), 33-41. https://doi.org/10.12989/sem.2018.65.1.033.
  48. Tadi Beni, Y. (2016b), "Size-dependent electro mechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams", J. Intel. Mat. Syst. Str., 27, 2199-2215. https://doi.org/10.1177/1045389X15624798.
  49. Tadi Beni, Y. (2016c), "Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling", Mech. Res. Commun., 75, 67-80. https://doi.org/10.1016/j.mechrescom.2016.05.011.
  50. Tadi Beni, Y., Mehralian, F. and Razavi, H. (2015), "Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory", Compos. Struct., 120, 65-106. https://doi.org/10.1016/j.compstruct.2014.09.065.
  51. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124-130. https://doi.org/10.1063/1.2141648 .
  52. Wang, Y.G., Lin, W.H. and Liu, N. (2013), "Large amplitude free vibration of size-dependent circular micro-plates based on the modified couple stress theory", Int. J. Mech. Sci., 71, 51-57. https://doi.org/10.1016/j.ijmecsci.2013.03.008.
  53. Wang, K., Wang, B. and Kitamura, T. (2015), "A review on the application of modified continuum models in modeling and simulation of nanostructures", Acta Mech. Sinica, 32, 83-100. https://doi.org/10.1007/s10409-015-0508-4.
  54. Xiang, H.J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Compos Part B-.Eng., 39(2), 292-303., https://doi.org/10.1016/j.compositesb.2007.01.005.
  55. Yildirm V. (1999), "A numerical study on the free vibration of symmetric cross-ply laminated cylindrical helical springs", Appl. Mech., 66, 1040-1043. http://dx.doi:10.1115/1.2791780.
  56. Yang, F., Chong, A., Lam, D. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39, 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  57. Yan, Z. and Jiang, L.Y. (2012), "Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints", Math.. Phys. Eng. Sci., https://doi.org/10.1098/rspa.2012.0214
  58. Zhu, C.S., Fang, X.Q., Liu, J.X and Li, H.Y. (2017), "Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells", Mech. - A/Solids, 66, 423-432. https://doi.org/10.1016/j.euromechsol.2017.08. 001.
  59. Zeighampour, H. and Tadi Beni, Y. (2014), "Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory", Phys. E, 61, 28-39. https://doi.org/10.1016/j.physe.2014.03.011.
  60. Zhang, Y., Wang, C. and Tan, V. (2009), "Assessment of Timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics", Adv. Appl. Math. Mech., 1, 89-106. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  61. Zeighampour, H. and Tadi Beni, Y. (2015), "A shear deformable cylindrical shell model based on couple stress theory", Arch. Appl. Mech., 85, 539-553. https://doi.org/10.1007/s00419-014-0929-8.
  62. Zenkour, A.M. (2013), "Bending of FGM plates by a simplified four-unknown shear and normal deformations theory", Int. J. Appl. Mech., 5, 1-15,. https://doi.org/10.1142/S1758825113500208.
  63. Zenkour, A.M. (2013), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Model., 37, 9041-9051., https://doi.org/10.1016/j.apm.2013.04.022.

피인용 문헌

  1. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2020, https://doi.org/10.12989/scs.2021.40.3.355