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On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model

  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Janghorban, Maziar (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2018.10.11
  • 심사 : 2019.01.13
  • 발행 : 2019.03.10

초록

Rapid advances in the engineering applications can bring further areas to provide the opportunity to manipulate anisotropic structures for direct productivity in design of micro/nano-structures. For the first time, magnetic affected wave characteristics of nanosize plates made of anisotropic material is investigated via the three-dimensional bi-Helmholtz nonlocal strain gradient theory. Three small scale parameters are used to predict the size-dependent behavior of the nanoplates more accurately. After owing governing equations of wave motion, an analytical approach based harmonic series is utilized to fine the wave frequency as well as phase velocity. It is observed that the small scale parameters, magnetic field and wave number have considerable influence on the wave characteristics of anisotropic nanoplates. Due to the lack of any study on the mechanics of three-dimensional bi-Helmholtz gradient plates made of anisotropic materials, it is hoped that the present exact model may be used as a benchmark for future works of such nanostructures.

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참고문헌

  1. Aguiar, A.R., Bravo-Castillero, J. and Da Silva, U.P. (2018), "Application of Mori-Tanaka method in 3-1 porous piezoelectric medium of crystal class 6", Int. J. Eng. Sci., 123, 36-50. https://doi.org/10.1016/j.ijengsci.2017.11.009
  2. Alibeigloo, A. and Liew, K. (2014), "Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity", Compos. Struct., 113, 23-30. https://doi.org/10.1016/j.compstruct.2014.03.004
  3. Barati, M.R. (2017a), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11. https://doi.org/10.1016/j.ijengsci.2017.03.007
  4. Barati, M.R. (2017b), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/SEM.2017.64.6.683
  5. Barati, M.R. (2018), "Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity", Acta Mech., 229(3), 1183-1196. https://doi.org/10.1007/s00707-017-2032-z
  6. Barretta, R., Faghidian, S.A. and Luciano, R. (2018), "Longitudinal vibrations of nano-rods by stress-driven integral elasticity", Mech. Adv. Mater. Struct., 1-9.
  7. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  8. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/SSS.2017.19.6.601
  9. Besseghier, A., Tounsi, A., Houari, M.S.A., Benzair, A., Boumia, L. and Heireche, H. (2011), "Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity", Phys. E: Low-Dimens. Syst. Nanostruct., 43(7), 1379-1386. https://doi.org/10.1016/j.physe.2011.03.008
  10. Boumia, L., Zidour, M., Benzair, A. and Tounsi, A. (2014), "A Timoshenko beam model for vibration analysis of chiral singlewalled carbon nanotubes", Phys. E Low-Dimens. Syst. Nanostruct., 59, 186-191. https://doi.org/10.1016/j.physe.2014.01.020
  11. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  12. Brach, S., Dormieux, L., Kondo, D. and Vairo, G. (2017), "Strength properties of nanoporous materials: a 3-layered based non-linear homogenization approach with interface effects", Int. J. Eng. Sci., 115, 28-42. https://doi.org/10.1016/j.ijengsci.2017.03.001
  13. Ebrahimi, F. and Barati, M.R. (2018), "Wave propagation analysis of smart strain gradient piezo-magneto-elastic nonlocal beams", Struct. Eng. Mech., 66(2), 237-248. https://doi.org/10.12989/SEM.2018.66.2.237
  14. Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments", Struct. Eng. Mech., 65(6), 645-656. https://doi.org/10.12989/SEM.2018.65.6.645
  15. Ehyaei, J. and Akbarizadeh, M.R. (2017), "Vibration analysis of micro composite thin beam based on modified couple stress", Struct. Eng. Mech., 64(4), 403-411. https://doi.org/10.12989/SEM.2017.64.4.403
  16. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  17. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  18. 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
  19. Ghayesh, M.H. (2018a), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004
  20. Ghayesh, M.H. (2018b), "Functionally graded microbeams: Simultaneous presence of imperfection and viscoelasticity", Int. J. Mech. Sci., 140, 339-350. https://doi.org/10.1016/j.ijmecsci.2018.02.037
  21. Ghayesh, M.H. (2018c), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Math. Modell., 59, 583-596. https://doi.org/10.1016/j.apm.2018.02.017
  22. Ghayesh, M.H. and Farokhi, H. (2015), "Chaotic motion of a parametrically excited microbeam", Int. J. Eng. Sci., 96, 34-45. https://doi.org/10.1016/j.ijengsci.2015.07.004
  23. Gholipour, A., Farokhi, H. and Ghayesh, M.H. (2015), "In-plane and out-of-plane nonlinear size-dependent dynamics of microplates", Nonlin. Dyn., 79(3), 1771-1785. https://doi.org/10.1007/s11071-014-1773-7
  24. Kaghazian, A., Hajnayeb, A. and Foruzande, H. (2017), "Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory", Struct. Eng. Mech., 61(5), 617-624. https://doi.org/10.12989/sem.2017.61.5.617
  25. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Mod. Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  26. Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  27. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/SCS.2018.28.1.099
  28. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/SCS.2017.25.3.361
  29. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 1-20.
  30. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/SCS.2018.27.2.201
  31. Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264.
  32. Karami, B., Shahsavari, D. and Janghorban, M. (2018f), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol., 82, 499-512. https://doi.org/10.1016/j.ast.2018.10.001
  33. Karami, B., Shahsavari, D. and Janghorban, M. (2018g), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  34. Karami, B., Shahsavari, D., Janghorban, M., Dimitri, R. and Tornabene, F. (2019a), "Wave propagation of porous nanoshells", Nanomater., 9(1), 22. https://doi.org/10.3390/nano9010022
  35. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018h), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111. https://doi.org/10.1016/j.tws.2017.10.004
  36. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018i), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
  37. Karami, B., Shahsavari, D. and Li, L. (2018j), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Phys. E: Low-Dimens. Syst. Nanostruct., 97, 317-327. https://doi.org/10.1016/j.physe.2017.11.020
  38. Karami, B., Shahsavari, D. and Li, L. (2018k), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781
  39. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2019b), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(1), 287-301. https://doi.org/10.1177/0954406218756451
  40. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018l), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/SCS.2018.29.3.349
  41. Katariya, P.V. and Panda, S.K. (2018), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: A finite element approach", Arab. J. Sci. Eng., 1-18.
  42. Khaniki, H.B. (2018), "On vibrations of nanobeam systems", Int. J. Eng. Sci., 124, 85-103. https://doi.org/10.1016/j.ijengsci.2017.12.010
  43. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  44. Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., 46(3), 417-431. https://doi.org/10.12989/sem.2013.46.3.417
  45. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  46. Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mater. Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044
  47. Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  48. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021
  49. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Sol., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  50. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007
  51. Malekzadeh, P. and Heydarpour, Y. (2015), "Mixed Navierlayerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates", Meccan., 50(1), 143-167. https://doi.org/10.1007/s11012-014-0061-4
  52. 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
  53. Mehar, K. and Panda, S.K. (2018a), Dynamic esponse of Functionally Graded Carbon Nanotube Reinforced Sandwich Plate, IOP Conference Series: Materials Science and Engineering, IOP Publishing.
  54. Mehar, K. and Panda, S.K. (2018b), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B: Eng.
  55. Mehrabian, A. (2018), "The poroelastic constants of multipleporosity solids", Int. J. Eng. Sci., 132, 97-104. https://doi.org/10.1016/j.ijengsci.2018.08.002
  56. Mehralian, F. and Beni, Y.T. (2018), "Vibration analysis of sizedependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory", J. Brazil. Soc. Mech. Sci. Eng., 40(1), 27. https://doi.org/10.1007/s40430-017-0938-y
  57. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Phys. B: Condens. Matt., 514, 61-69. https://doi.org/10.1016/j.physb.2017.03.030
  58. Mohammadi, K., Mahinzare, M., Ghorbani, K. and Ghadiri, M. (2018), "Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory", Microsyst. Technol., 24(2), 1133-1146. https://doi.org/10.1007/s00542-017-3476-8
  59. Mouli, C.B., Ramji, K., Kar, V.R., Panda, S.K., Anil, L.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527
  60. Murmu, T., McCarthy, M. and Adhikari, S. (2013), "In-plane magnetic field affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach", Compos. Struct., 96, 57-63. https://doi.org/10.1016/j.compstruct.2012.09.005
  61. Nami, M.R. and Janghorban, M. (2014a), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. https://doi.org/10.1016/j.compstruct.2014.01.012
  62. Nami, M.R. and Janghorban, M. (2014b), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Mod. Phys. Lett. B, 28(3), 1450021.
  63. Sahmani, S. and Aghdam, M. (2017a), "Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams", Compos. Struct., 179, 77-88. https://doi.org/10.1016/j.compstruct.2017.07.064
  64. Sahmani, S. and Aghdam, M. (2017b), "A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells", Compos. Struct., 178, 97-109. https://doi.org/10.1016/j.compstruct.2017.06.062
  65. Sahmani, S. and Aghdam, M. (2018), "Nonlocal strain gradient beam model for postbuckling and associated vibrational response of lipid supramolecular protein micro/nano-tubules", Math. Biosci., 295, 24-35. https://doi.org/10.1016/j.mbs.2017.11.002
  66. Sahmani, S., Bahrami, M. and Aghdam, M. (2015), "Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions", Int. J. Mech. Sci., 100, 1-22. https://doi.org/10.1016/j.ijmecsci.2015.06.004
  67. Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", Int. J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004
  68. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sciv Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  69. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018a), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mech., 229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7
  70. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Expr., 4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  71. Shahsavari, D., Karami, B. and Li, L. (2018b), "Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model", Compt. Rend. Mecaniq., 346(12), 1216-1232. https://doi.org/10.1016/j.crme.2018.08.011
  72. Shahsavari, D., Karami, B. and Li, L. (2018c), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053
  73. Shahsavari, D., Karami, B. and Mansouri, S. (2018d), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Sol., 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  74. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018e), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  75. Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Sci., 120, 82-99. https://doi.org/10.1016/j.ijengsci.2017.06.008
  76. She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018a), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009
  77. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018b), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  78. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005
  79. She, G.L., Yuan, F.G. and Ren, Y.R. (2018c), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002
  80. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018d), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063
  81. 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.ijengsci.2017.09.005
  82. Srinivas, S., Rao, C.J. and Rao, A. (1970), "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates", J. Sound Vibr., 12(2), 187-199. https://doi.org/10.1016/0022-460X(70)90089-1
  83. Trofimov, A., Abaimov, S., Akhatov, I. and Sevostianov, I. (2018), "On the bounds of applicability of two-step homogenization technique for porous materials", Int. J. Eng. Sci., 123, 117-126. https://doi.org/10.1016/j.ijengsci.2017.11.017
  84. Xu, X.J., Zheng, M.L. and Wang, X.C. (2017), "On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics", Int. J. Eng. Sci., 119, 217-231. https://doi.org/10.1016/j.ijengsci.2017.06.025
  85. Zeighampour, H., Beni, Y.T. and Dehkordi, M.B. (2018), "Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory", Thin-Wall. Struct., 122, 378-386. https://doi.org/10.1016/j.tws.2017.10.037
  86. Zhu, X. and Li, L. (2017), "On longitudinal dynamics of nanorods", Int. J. Eng. Sci., 120, 129-145. https://doi.org/10.1016/j.ijengsci.2017.08.003

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