DOI QR코드

DOI QR Code

Computational mathematical modeling of the nonlinear vibration characteristics of AFG truncated conical nano pipe based on the nonlocal strain gradient theory

  • Zhang, Ruihua (College of Mechanical Engineering, Nantong Vocational University) ;
  • Cao, Yiqing (School of Mechanical and Electrical Engineering, Putian University)
  • Received : 2021.01.31
  • Accepted : 2022.02.16
  • Published : 2022.03.10

Abstract

In the present paper, the numerical dynamic analysis of a functionally graded nano-scale nonuniform tube was investigated according to the high-order beam theory coupled with the nonlocal gradient strain theory. The supposed cross-section is changed along the pipe length, and the material distribution, which combines both metal and ceramics, is smoothly changed in the pipe length direction, which is called axially functionally graded (AFG) pipe. Moreover, the porosity voids are dispersed in the cross-section and the radial pattern that the existence of both material distribution along the tube length and porosity voids make a two-dimensional functionally graded (2D-FG) truncated conical pipe. On the basis of the Hamilton principle, the governing equations and the associated boundary conditions equations are derived, and then a numerical approach is applied to solve the obtained equations.

Keywords

Acknowledgement

This work was supported by the program of Young and middle-aged academic leaders of University "Blue Project "of Jiangsu Province (QL20200513), the Science and Technology Planning Project of Nantong (JC2020077), the Natural Science Foundation of Fujian Province (2020J01916).

References

  1. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  2. Ahangarnazhad, B.H., Pourbaba, M. and Afkar, A. (2020), "Bond behavior between steel and Glass Fiber Reinforced Polymer (GFRP) bars and ultra high performance concrete reinforced by Multi-Walled Carbon Nanotube (MWCNT)", Steel Compos. Struct., 35(4), 463-474. https://doi.org/10.12989/scs.2020.35.4.463.
  3. Al-Furjan, M.S.H., Habibi, M., Jung, D.w., Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2020), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., https://doi.org/10.1007/s00366-020-01130-8.
  4. Al-Furjan, M.S.H., hatami, A., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  5. Alipour, M., Torabi, M.A., Sareban, M., Lashini, H., Sadeghi, E., Fazaeli, A., Habibi, M. and Hashemi, R. (2020), "Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels", Mech. Based Design Struct. Machines, 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343.
  6. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S.R., Bedia, E.A.A. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. https://doi.org/10.12989/cac.2020.26.2.185.
  7. Ansari, R., Mohammadi, V., Faghih Shojaei, M., Gholami, R. and Rouhi, H. (2014), "Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory", European J. Mech. A/Solids, 45, 143-152. https://doi.org/10.1016/j.euromechsol.2013.11.002.
  8. Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133.
  9. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2016), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123(1), 104. https://doi.org/10.1007/s00339-016-0712-5.
  10. Azimi, M., Mirjavadi, S.S., Shafiei, N., Hamouda, A.M.S. and Davari, E. (2018), "Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution", Mech. Adv. Mater. Struct., 25(6), 467-480. https://doi.org/10.1080/15376494.2017.1285455.
  11. Bagdatli, S.M. (2015), "Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory", Compos. B Eng., 80, 43-52. https://doi.org/10.1016/j.compositesb.2015.05.030.
  12. Bakhti, K., Kaci, A., Bousahla, A., Houari, M., Tounsi, A. and Adda Bedia, E. (2013), "Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory", Steel Compos. Struct., 14(4), 335-347. https://doi.org/10.12989/scs.2013.14.4.335.
  13. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  14. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. https://doi.org/10.12989/cac.2020.26.5.439.
  15. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Bedia, E.A. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  16. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  17. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 191. https://doi.org/10.12989/anr.2019.7.3.191.
  18. Che, H. and Wang, J. (2021), "A Two-Timescale Duplex Neurodynamic Approach to Mixed-Integer Optimization", IEEE Trans. Neural Networks Learning Syst., 32(1), 36-48. https://doi.org/10.1109/TNNLS.2020.2973760.
  19. Cheshmeh, E., Karbon, M., Eyvazian, A., Jung, D.w., Habibi, M. and Safarpour, M. (2020), "Buckling and vibration analysis of FG-CNTRC plate subjected to thermo-mechanical load based on higher order shear deformation theory", Mech. Based Design Struct. Machines, 1-24. https://doi.org/10.1080/15397734.2020.1744005.
  20. Civalek, O. (2020), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", J. Numerical Methods Eng., 121(5), 990-1019. https://doi.org/10.1002/nme.6254.
  21. Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021a), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano Res., 10(2), 175-189. https://doi.org/10.12989/ANR.2021.10.2.175.
  22. Dai, Z., Zhang, L., Bolandi, S.Y. and Habibi, M. (2021b), "On the vibrations of the non-polynomial viscoelastic composite open-type shell under residual stresses", Compos. Struct., 263, 113599. https://doi.org/10.1016/j.compstruct.2021.113599.
  23. Di Sciuva, M. and Sorrenti, M. (2019), "Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory", Compos. Struct., 227, 111324. https://doi.org/10.1016/j.compstruct.2019.111324.
  24. Dong, H., Zhao, B. and Deng, Y. (2018), "Instability phenomenon associated with two typical high speed railway vehicles", J. Non-Linear Mech., 105, 130-145. https://doi.org/10.1016/j.ijnonlinmec.2018.06.006.
  25. Du, H. and Yu, M. (2020), "Probability Distribution of Nonlinear Wave Surface Slope Based on Copula Function", J. Coastal Res., 103(SI), 839-842. https://doi.org/10.2112/SI103-173.1.
  26. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837.
  27. Ebrahimi, F. and Shafiei, N. (2017), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772. https://doi.org/10.1080/15376494.2016.1196781.
  28. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2021), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Waves in Random and Complex Media. 31(6), 1655-1681. https://doi.org/10.1080/17455030.2019.1694729.
  29. Ebrahimi, F., Shafiei, N., Kazemi, M. and Mousavi Abdollahi, S.M. (2017), "Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method", Mech. Adv. Mater. Struct., 24(15), 1257-1273. https://doi.org/10.1080/15376494.2016.1227499.
  30. Ehyaei, J., Akbarshahi, A. and Shafiei, N.J.A.i.n.r. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", 5(2), 141. https://doi.org/10.12989/anr.2017.5.2.141.
  31. Esfahani, S., Esmaeilzade Khadem, S. and Ebrahimi Mamaghani, A. (2019), "Nonlinear vibration analysis of an electrostatic functionally graded nano-resonator with surface effects based on nonlocal strain gradient theory", J. Mech. Sci., 151, 508-522. https://doi.org/10.1016/j.ijmecsci.2018.11.030.
  32. Fazaeli, A., Habibi, M. and Ekrami, A.a. (2016), "Experimental and finite element comparison of mechanical properties and formability of dual phase steel and ferrite - pearlite steel with the same chemical composition %J Metallurgical Engineering", Metallurgical Eng., 19(2), 84-93. https://doi.org/10.22076/me.2017.41458.1064.
  33. Foroutan, K., Ahmadi, H. and Carrera, E. (2019), "Nonlinear vibration of imperfect FG-CNTRC cylindrical panels under external pressure in the thermal environment", Compos. Struct., 227, 111310. https://doi.org/10.1016/j.compstruct.2019.111310.
  34. Gao, Y., Xiao, W.-s. and Zhu, H. (2019), "Nonlinear vibration of different types of functionally graded nanotubes using nonlocal strain gradient theory", European Phys. J. Plus, 134(7), 345. https://doi.org/10.1140/epjp/i2019-12735-6.
  35. Ghabussi, A., Habibi, M., NoormohammadiArani, O., Shavalipour, A., Moayedi, H. and Safarpour, H. (2020), "Frequency characteristics of a viscoelastic graphene nanoplatelet-reinforced composite circular microplate", J. Vib. Control, 27(1-2), 101-118. https://doi.org/10.1177/1077546320923930.
  36. Ghadiri, M. and Shafiei, N. (2016a), "Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen's theory using differential quadrature method", Microsyst. Technol., 22(12), 2853-2867. https://doi.org/10.1007/s00542-015-2662-9.
  37. Ghadiri, M. and Shafiei, N. (2016b), "Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method", J. Vib. Control, 23(19), 3247-3265. https://doi.org/10.1177/1077546315627723.
  38. Ghadiri, M. and Shafiei, N. (2016c), "Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions", Acta Astronautica, 121, 221-240. https://doi.org/10.1016/j.actaastro.2016.01.003.
  39. Ghadiri, M., Hosseini, S.H.S. and Shafiei, N. (2016a), "A power series for vibration of a rotating nanobeam with considering thermal effect", Mech. Adv. Mater. Struct., 23(12), 1414-1420. https://doi.org/10.1080/15376494.2015.1091527.
  40. Ghadiri, M., Mahinzare, M., Shafiei, N. and Ghorbani, K. (2017a), "On size-dependent thermal buckling and free vibration of circular FG Microplates in thermal environments", Microsyst. Technol., 23(10), 4989-5001. https://doi.org/10.1007/s00542-017-3308-x.
  41. Ghadiri, M., Shafiei, N. and Akbarshahi, A. (2016b), "Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam", Appl. Phys. A, 122(7), 673. https://doi.org/10.1007/s00339-016-0196-3.
  42. Ghadiri, M., Shafiei, N. and Alavi, H. (2017b), "Thermo-mechanical vibration of orthotropic cantilever and propped cantilever nanoplate using generalized differential quadrature method", Mech. Adv. Mater. Struct., 24(8), 636-646. https://doi.org/10.1080/15376494.2016.1196770.
  43. Ghadiri, M., Shafiei, N. and Alavi, H. (2017c), "Vibration analysis of a rotating nanoplate using nonlocal elasticity theory", J. Solid Mech., 9(2), 319-337. https://doi.org/20.1001.1.20083505.2017.9.2.8.5.
  44. Ghadiri, M., Shafiei, N. and Alireza Mousavi, S. (2016c), "Vibration analysis of a rotating functionally graded tapered microbeam based on the modified couple stress theory by DQEM", Appl. Phys. A, 122(9), 837. https://doi.org/10.1007/s00339-016-0364-5.
  45. Ghadiri, M., Shafiei, N. and Babaei, R. (2017d), "Vibration of a rotary FG plate with consideration of thermal and Coriolis effects", Steel Compos. Struct., 25(2), 197-207. https://doi.org/10.12989/SCS.2017.25.2.197.
  46. Ghadiri, M., Shafiei, N. and Safarpour, H. (2017e), "Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen's nonlocal elasticity", Microsyst. Technol., 23(4), 1045-1065. https://doi.org/10.1007/s00542-016-2822-6.
  47. Ghadiri, M., Shafiei, N., Salekdeh, S.H., Mottaghi, P. and Mirzaie, T. (2016d), "Investigation of the dental implant geometry effect on stress distribution at dental implant-bone interface", J. Brazilian Soc. Mech. Sci. Eng., 38(2), 335-343. https://doi.org/10.1007/s40430-015-0472-8.
  48. Ghazanfari, A., Assempour, A., Habibi, M. and Hashemi, R.J.M.M.E. (2016), "Investigation on the effective range of the through thickness shear stress on forming limit diagram using a modified Marciniak-Kuczynski model", Modares Mech. Eng., 16(1), 137-143.
  49. Ghazanfari, A., Soleimani, S.S., Keshavarzzadeh, M., Habibi, M., Assempuor, A. and Hashemi, R. (2020), "Prediction of FLD for sheet metal by considering through-thickness shear stresses", Mech. Based Design Struct. Machines, 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.
  50. Gheshlaghi, B. and Hasheminejad, S.M. (2011), "Surface effects on nonlinear free vibration of nanobeams", Compos. B Eng., 42(4), 934-937. https://doi.org/10.1016/j.compositesb.2010.12.026.
  51. Gholipour, A. and Ghayesh, M.H. (2020), "Nonlinear coupled mechanics of functionally graded nanobeams", J. Eng. Sci., 150, 103221. https://doi.org/10.1016/j.ijengsci.2020.103221.
  52. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., AlZahrani, M.M., Hussain, M. and Mahmoud, S. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
  53. Guo, J., Baharvand, A., Tazeddinova, D., Habibi, M., Safarpour, H., Roco-Videla, A. and Selmi, A. (2021a), "An intelligent computer method for vibration responses of the spinning multilayer symmetric nanosystem using multi-physics modeling", Eng. Comput., https://doi.org/10.1007/s00366-021-01433-4.
  54. Guo, Y., Mi, H. and Habibi, M. (2021b), "Electromechanical energy absorption, resonance frequency, and low-velocity impact analysis of the piezoelectric doubly curved system", Mech. Syst. Signal Processing, 157, 107723. https://doi.org/10.1016/j.ymssp.2021.107723.
  55. Habibi, M., Hashemi, R., Fallah Tafti, M. and Assempour, A. (2018), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manufacturing Processes, 31, 310-323. https://doi.org/10.1016/j.jmapro.2017.11.009.
  56. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2016), "Forming limit diagrams by including the M-K model in finite element simulation considering the effect of bending", Proc. Institution of Mech. Engineers, Part L: J. Mater.: Design Appl., 232(8), 625-636. https://doi.org/10.1177/1464420716642258.
  57. Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2021), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Waves Random Complex Media, 31(6), 1340-1366. https://doi.org/10.1080/17455030.2019.1662968.
  58. He, X., Ding, J., Habibi, M., Safarpour, H. and Safarpour, M. (2021), "Non-polynomial framework for bending responses of the multi-scale hybrid laminated nanocomposite reinforced circular/annular plate", Thin-Walled Struct., 166, 108019. https://doi.org/10.1016/j.tws.2021.108019.
  59. Hosseini, S.M.R., HABIBI, M. and ASSEMPOUR, A. (2018), "Experimental and numerical determination of forming limit diagram of steel-copper two-layer sheet considering the interface between the layers", Modares Mech. Eng., 18(6), 174-181. https://www.sid.ir/en/journal/ViewPaper.aspx?id=734559.
  60. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021), "The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation", Eng. Comput., https://doi.org/10.1007/s00366-021-01456-x.
  61. Huang, X., Hao, H., Oslub, K., Habibi, M. and Tounsi, A. (2021a), "Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem", Eng. Comput., https://doi.org/10.1007/s00366-021-01399-3.
  62. Huang, X., Zhang, Y., Moradi, Z. and Shafiei, N. (2021b), "Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform micro-tube", Eng. Comput., https://doi.org/10.1007/s00366-021-01395-7.
  63. Huang, X., Zhu, Y., Vafaei, P., Moradi, Z. and Davoudi, M. (2021c), "An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate", Eng. Comput., https://doi.org/10.1007/s00366-021-01320-y.
  64. Huo, J., Zhang, G., Ghabussi, A. and Habibi, M. (2021), "Bending analysis of FG-GPLRC axisymmetric circular/annular sector plates by considering elastic foundation and horizontal friction force using 3D-poroelasticity theory", Compos. Struct., 276, 114438. https://doi.org/10.1016/j.compstruct.2021.114438.
  65. Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. B Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  66. Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (2020), "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411.
  67. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  68. Jiao, J., Ghoreishi, S.-m., Moradi, Z. and Oslub, K. (2021), "Coupled particle swarm optimization method with genetic algorithm for the static-dynamic performance of the magneto-electro-elastic nanosystem", Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01391-x.
  69. Kaci, A., Tounsi, A., Bakhti, K. and Adda Bedia, E.A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., 12(6), 491-504. https://doi.org/10.12989/scs.2012.12.6.491.
  70. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  71. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35(4), 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  72. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41(11), 495. https://doi.org/10.1007/s40430-019-1996-0.
  73. Ke, L.-L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024.
  74. Khadimallah, M.A., Hussain, M., Khedher, K.M., Naeem, M.N. and Tounsi, A. (2020), "Backward and forward rotating of FG ring support cylindrical shells", Steel Compos. Struct., 37(2), 137-150. http://dx.doi.org/10.12989/scs.2020.37.2.137.
  75. Lee, H.-L. and Chang, W.-J. (2008), "Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory", J. Appl. Phys., 103(2), 024302. https://doi.org/10.1063/1.2822099.
  76. Lee, W.Y., Stinton, D.P., Berndt, C.C., Erdogan, F., Lee, Y.D. and Mutasim, Z. (1996), "Concept of functionally graded materials for advanced thermal barrier coating applications", J. American Ceramic Soc., 79(12), 3003-3012. https://doi.org/10.1111/j.1151-2916.1996.tb08070.x.
  77. Li, J., Tang, F. and Habibi, M. (2020a), "Bi-directional thermal buckling and resonance frequency characteristics of a GNP-reinforced composite nanostructure", Eng. Comput., 2020, https://doi.org/10.1007/s00366-020-01110-y.
  78. Li, Y., Li, S., Guo, K., Fang, X. and Habibi, M. (2020b), "On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach", Eng. Comput., 2020, https://doi.org/10.1007/s00366-020-01166-w.
  79. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  80. Liu, H., Lv, Z. and Wu, H. (2019), "Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory", Compos. Struct., 214, 47-61. https://doi.org/10.1016/j.compstruct.2019.01.090.
  81. Liu, H., Shen, S., Oslub, K., Habibi, M. and Safarpour, H. (2021a), "Amplitude motion and frequency simulation of a composite viscoelastic microsystem within modified couple stress elasticity", Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01316-8.
  82. Liu, H., Zhao, Y., Pishbin, M., Habibi, M., Bashir, M.O. and Issakhov, A. (2021b), "A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method", Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01419-2.
  83. Liu, K., Ke, F., Huang, X., Yu, R., Lin, F., Wu, Y. and Ng, D.W.K. (2021c), "DeepBAN: A Temporal Convolution-Based Communication Framework for Dynamic WBANs", IEEE Transactions on Communications, 69(10), 6675-6690. https://doi.org/10.1109/TCOMM.2021.3094581.
  84. Liu, L., Xiang, H. and Li, X. (2021d), "A novel perturbation method to reduce the dynamical degradation of digital chaotic maps", Nonlinear Dynam., 103(1), 1099-1115. https://doi.org/10.1007/s11071-020-06113-4.
  85. Liu, Y. (2020), "Marine Oil Spill Control Based on Discrete Mathematical Model", J. Coastal Res., 103(SI), 387-391. https://doi.org/10.2112/SI103-079.1.
  86. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021e), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01454-z.
  87. Liu, Z., Meyers, M.A., Zhang, Z. and Ritchie, R.O. (2017), "Functional gradients and heterogeneities in biological materials: Design principles, functions, and bioinspired applications", Progress in Mater. Sci., 88, 467-498. https://doi.org/10.1016/j.pmatsci.2017.04.013.
  88. Liu, Z., Su, S., Xi, D. and Habibi, M. (2020a), "Vibrational responses of a MHC viscoelastic thick annular plate in thermal environment using GDQ method", Mech. Based Design Struct. Machines, 2020, 1-26. https://doi.org/10.1080/15397734.2020.1784201.
  89. Liu, Z., Wu, X., Yu, M. and Habibi, M. (2020b), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings", Mech. Based Design Struct. Machines, 2020, 1-25. https://doi.org/10.1080/15397734.2020.1815544.
  90. Ma, L., Liu, X. and Moradi, Z. (2021), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 2021, https://doi.org/10.1007/s00366-020-01210-9.
  91. Mahmoud, D. and Elbestawi, M.A. (2017), "Lattice structures and functionally graded materials applications in additive manufacturing of orthopedic implants: A review", J. Manufact. Mater. Process., 1(2), 13. https://doi.org/10.3390/jmmp1020013.
  92. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  93. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  94. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A., Kazemi, M. and Structures, C. (2017a), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  95. Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel Afshari, B. (2017b), "Thermal buckling behavior of twodimensional imperfect functionally graded microscale-tapered porous beam", J. Thermal Stresses, 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962.
  96. Mirjavadi, S.S., Mohasel Afshari, B., Shafiei, N., Rabby, S. and Kazemi, M. (2017c), "Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam", J. Vib. Control, 24(18), 4211-4225. https://doi.org/10.1177/1077546317721871.
  97. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017d), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A, 123(5), 315. https://doi.org/10.1007/s00339-017-0918-1.
  98. Moayedi, H., Aliakbarlou, H., Jebeli, M., Noormohammadiarani, O., Habibi, M., Safarpour, H. and Foong, L.K. (2020a), "Thermal Buckling Responses of a Graphene Reinforced Composite Micropanel Structure", 12(01), 2050010. https://doi.org/10.1142/s1758825120500106.
  99. Moayedi, H., Darabi, R., Ghabussi, A., Habibi, M. and Foong, L.K. (2020b), "Weld orientation effects on the formability of tailor welded thin steel sheets", Thin-Walled Struct., 149, 106669. https://doi.org/10.1016/j.tws.2020.106669.
  100. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H. and Foong, L.K.J.E.w.C. (2020c), "Application of nonlocal strain-stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell", Eng. Comput., 37(4), 3359-3374. https://doi.org/10.1007/s00366-020-01002-1.
  101. Mohammadi, M., Hosseini, M., Shishesaz, M., Hadi, A. and Rastgoo, A. (2019), "Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads", European J. Mech. A/Solids, 77, 103793. https://doi.org/10.1016/j.euromechsol.2019.05.008.
  102. Moradi-Dastjerdi, R. and Payganeh, G. (2017), "Thermoelastic dynamic analysis of wavy carbon nanotube reinforced cylinders under thermal loads", Steel Compos. Struct., 25(3), 315-326. https://doi.org/10.12989/scs.2017.25.3.315.
  103. Moradi-Dastjerdi, R. and Payganeh, G. (2018), "Thermoelastic vibration analysis of functionally graded wavy carbon nanotube-reinforced cylinders", Polymer Compos., 39(S2), E826-E834. https://doi.org/10.1002/pc.24278.
  104. Mueller, E., Drasar, C., Schilz, J. and Kaysser, W. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng. A., 362(1-2), 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1.
  105. Murmu, T. and Pradhan, S.C. (2009), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46(4), 854-859. https://doi.org/10.1016/j.commatsci.2009.04.019.
  106. Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.w. and Nabipour, N. (2021), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomolecular Struct. Dynam., 39(7), 2543-2554. https://doi.org/10.1080/07391102.2020.1751297.
  107. Oyarhossein, M.A., Alizadeh, A.a., Habibi, M., Makkiabadi, M., Daman, M., Safarpour, H. and Jung, D.W. (2020), "Dynamic response of the nonlocal strain-stress gradient in laminated polymer composites microtubes", Scientific Reports, 10(1), 5616. https://doi.org/10.1038/s41598-020-61855-w.
  108. Peng, D., Chen, S., Darabi, R., Ghabussi, A. and Habibi, M. (2021), "Prediction of the bending and out-of-plane loading effects on formability response of the steel sheets", Archives Civil Mech. Eng., 21(2), 74. https://doi.org/10.1007/s43452-021-00227-1.
  109. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng. A., 362(1-2), 40-60. https://doi.org/10.1016/S0921-5093(03)00580-X.
  110. Pourasghar, A. and Chen, Z. (2019), "Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs", Polymer Eng. Sci., 59(7), 1362-1370. https://doi.org/10.1002/pen.25119.
  111. Reddy, J.N. and Chin, C.D. (1998), "THERMOMECHANICAL ANALYSIS OF FUNCTIONALLY GRADED CYLINDERS AND PLATES", J. Thermal Stresses, 21(6), 593-626. https://doi.org/10.1080/01495739808956165.
  112. Rezaiee-Pajand, M., Masoodi, A.R. and Rajabzadeh-Safaei, N. (2019), "Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures", Steel Compos. Struct., 30(6), 493-516. https://doi.org/10.12989/scs.2019.30.6.493.
  113. Rouabhia, A., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A., Kouider Halim, B., Tounsi, A. and Al-Zahrani, M.M. (2020), "Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory", Steel Compos. Struct., 37(6), 695-709. https://doi.org/10.12989/scs.2020.37.6.695.
  114. Shafiei, N. and Kazemi, M. (2017a), "Buckling analysis on the bidimensional functionally graded porous tapered nano-/micro-scale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.
  115. Shafiei, N. and Kazemi, M. (2017b), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045.
  116. Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004.
  117. Shafiei, N., Ghadiri, M. and Mahinzare, M. (2019), "Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment", Mech. Adv. Mater. Struct., 26(2), 139-155. https://doi.org/10.1080/15376494.2017.1365982.
  118. Shafiei, N., Ghadiri, M., Makvandi, H. and Hosseini, S.A. (2017a), "Vibration analysis of Nano-Rotor's Blade applying Eringen nonlocal elasticity and generalized differential quadrature method", Appl. Math. Modelling, 43, 191-206. https://doi.org/10.1016/j.apm.2016.10.061.
  119. Shafiei, N., Hamisi, M. and Ghadiri, M. (2020), "Vibration analysis of rotary tapered axially functionally graded Timoshenko nanobeam in thermal environment", J. Solid Mech., 12(1), 16-32.
  120. Shafiei, N., Kazemi, M. and Fatahi, L. (2017b), "Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method", Mech. Adv. Mater. Struct., 24(3), 240-252. https://doi.org/10.1080/15376494.2015.1128025.
  121. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016a), "Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler-Bernoulli microbeams", Physica E: Low-dimensioanl Syst. Nanostruct., 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011.
  122. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016b), "Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen's nonlocal elasticity and DQM", Appl. Phys. A, 122(8), 728. https://doi.org/10.1007/s00339-016-0245-y.
  123. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016c), "Nonlinear vibration of axially functionally graded tapered microbeams", J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007.
  124. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016d), "On sizedependent vibration of rotary axially functionally graded microbeam", J. Eng. Sci., 101, 29-44. https://doi.org/10.1016/j.ijengsci.2015.12.008.
  125. Shafiei, N., Kazemi, M., Safi, M. and Ghadiri, M. (2016e), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009.
  126. Shafiei, N., Mirjavadi, S.S., Afshari, B.M., Rabby, S. and Hamouda, A.M.S. (2017c), "Nonlinear thermal buckling of axially functionally graded micro and nanobeams", Compos. Struct., 168, 428-439. https://doi.org/10.1016/j.compstruct.2017.02.048.
  127. Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017d), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Methods Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  128. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016f), "On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007.
  129. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016g), "Vibration behavior of a rotating non-uniform FG microbeam based on the modified couple stress theory and GDQEM", Compos. Struct., 149, 157-169. https://doi.org/10.1016/j.compstruct.2016.04.024.
  130. Shao, Y., Zhao, Y., Gao, J. and Habibi, M. (2021), "Energy absorption of the strengthened viscoelastic multi-curved composite panel under friction force", Archives Civil Mech. Eng., 21(4), 141. https://doi.org/10.1007/s43452-021-00279-3.
  131. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2021), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. Comput., 37(4), 3629-3648. https://doi.org/10.1007/s00366-020-01024-9.
  132. Shariati, A., Jung, D.w., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020a), "On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams", Materials, 13(7), 1707. https://doi.org/10.3390/ma13071707.
  133. Shariati, A., Jung, D.w., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020b), "Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters", Symmetry, 12(4), 586. https://doi.org/10.3390/sym12040586.
  134. Shen, H.-S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213-216 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  135. Shen, Z.-B., Li, X.-F., Sheng, L.-P. and Tang, G.-J. (2012), "Transverse vibration of nanotube-based micro-mass sensor via nonlocal Timoshenko beam theory", Comput. Mater. Sci., 53(1), 340-346. https://doi.org/10.1016/j.commatsci.2011.09.023.
  136. Shi, X., Li, J. and Habibi, M. (2020), "On the statics and dynamics of an electro-thermo-mechanically porous GPLRC nanoshell conveying fluid flow", Mech. Based Design Struct. Machines, 1-37. https://doi.org/10.1080/15397734.2020.1772088.
  137. Shivanian, E., Ghadiri, M. and Shafiei, N. (2017), "Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation", Appl. Phys. A, 123(5), 329. https://doi.org/10.1007/s00339-017-0955-9.
  138. Simsek, M. (2011), "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Compos. Struct., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059.
  139. Simsek, M. (2019), "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.
  140. Sola, A., Bellucci, D. and Cannillo, V. (2016), "Functionally graded materials for orthopedic applications-an update on design and manufacturing", Biotech. Adv., 34(5), 504-531. https://doi.org/10.1016/j.biotechadv.2015.12.013.
  141. Srinivas, P., Babu, P.R. and Balakrishna, B. (2019), "Effect of silicon carbide, magnesium oxide as reinforcing elements and zinc sterate as binding agent in the characterization of Al functionally graded materials for automotive applications", Mater. Today: Proc., 27, 460-466. https://doi.org/10.1016/j.matpr.2019.11.275.
  142. Tagrara, S., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  143. Tang, Y. and Yang, T. (2018a), "Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics", J. Appl. Mech., 10(04), 1850041. https://doi.org/10.1142/S1758825118500412.
  144. Tang, Y. and Yang, T. (2018b), "Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material", Compos. Struct., 185, 393-400. https://doi.org/10.1016/j.compstruct.2017.11.032.
  145. Tang, Y., Lv, X. and Yang, T. (2019), "Bi-directional functionally graded beams: asymmetric modes and nonlinear free vibration", Compos. B Eng., 156, 319-331. https://doi.org/10.1016/j.compositesb.2018.08.140.
  146. Tang, Y., Ma, Z.-S., Ding, Q. and Wang, T. (2021), "Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: A nano-structure analysis", Compos. Struct., 264, 113746. https://doi.org/10.1016/j.compstruct.2021.113746.
  147. Tang, Y., Yang, T. and Fang, B. (2018a), "Fractional Dynamics of Fluid-Conveying Pipes Made of Polymer-Like Materials", Acta Mechanica Solida Sinica. 31(2), 243-258. https://doi.org/10.1007/s10338-018-0007-9.
  148. Tang, Y., Zhen, Y. and Fang, B. (2018b), "Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid", Appl. Math. Modelling, 56, 123-136. https://doi.org/10.1016/j.apm.2017.11.022.
  149. Thai, H.-T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009.
  150. Vinyas, M. (2019), "A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods", Compos. B Eng., 158, 286-301. https://doi.org/10.1016/j.compositesb.2018.09.086.
  151. Vo-Duy, T., Ho-Huu, V. and Nguyen-Thoi, T. (2019), "Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method", Frontiers Struct. Civil Eng., 13(2), 324-336. https://doi.org/10.1007/s11709-018-0466-6.
  152. Wang, M., Jiang, C., Zhang, S., Song, X., Tang, Y. and Cheng, H.- M. (2018), "Reversible calcium alloying enables a practical room-temperature rechargeable calcium-ion battery with a high discharge voltage", Nature Chem., 10(6), 667-672. https://doi.org/10.1038/s41557-018-0045-4.
  153. Wang, Z.-X. and Shen, H.-S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  154. Wang, Z., Yu, S., Xiao, Z. and Habibi, M. (2020), "Frequency and buckling responses of a high-speed rotating fiber metal laminated cantilevered microdisk", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2020.1824284.
  155. Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultrafast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01396-6.
  156. Xiong, Y.-Z., Gao, R.-N., Zhang, H., Dong, L.-L., Li, J.-T. and Li, X. (2020), "Rationally designed functionally graded porous Ti6Al4V scaffolds with high strength and toughness built via selective laser melting for load-bearing orthopedic applications", J. Mech. Behavior Biomed. Mater., 104, 103673. https://doi.org/10.1016/j.jmbbm.2020.103673.
  157. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021), "Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution", Compos. Struct., 275, 114395. https://doi.org/10.1016/j.compstruct.2021.114395.
  158. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Technol., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.
  159. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Processing, 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373.
  160. Yu, X., Sun, Y., Zhao, D. and Wu, S. (2021), "A revised contact stiffness model of rough curved surfaces based on the length scale", Tribology International, 164, 107206. https://doi.org/10.1016/j.triboint.2021.107206.
  161. Zghal, S., Trabelsi, S., Frikha, A. and Dammak, F. (2019), "Forced Vibration Analysis of Functionally Graded Carbon Nanotubes-Reinforced Composite Plates with Finite Element Strategy", International Conference Design and Modeling of Mechanical Systems, Springer, Cham, Switzerland. 778-785.
  162. Zhang, L., Chen, Z., Habibi, M., Ghabussi, A. and Alyousef, R. (2021a), "Low-velocity impact, resonance, and frequency responses of FG-GPLRC viscoelastic doubly curved panel", Compos. Struct., 269, 114000. https://doi.org/10.1016/j.compstruct.2021.114000.
  163. Zhang, X., Shamsodin, M., Wang, H., NoormohammadiArani, O., Khan, A.M., Habibi, M. and Al-Furjan, M.S.H. (2021b), "Dynamic information of the time-dependent tobullian biomolecular structure using a high-accuracy size-dependent theory", J. Biomolecular Struct. Dynam., 39(9), 3128-3143. https://doi.org/10.1080/07391102.2020.1760939.
  164. Zhang, X., Tang, Y., Zhang, F. and Lee, C.-S. (2016), "A Novel Aluminum-Graphite Dual-Ion Battery", Adv. Energy Mater., 6(11), 1502588. https://doi.org/10.1002/aenm.201502588.
  165. Zhang, Y., Wang, Z., Tazeddinova, D., Ebrahimi, F., Habibi, M. and Safarpour, H. (2021c), "Enhancing active vibration control performances in a smart rotary sandwich thick nanostructure conveying viscous fluid flow by a PD controller", Waves Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1948627.
  166. Zhao, J. and Yu, Z. (2021), "On the modeling and simulation of the nonlinear dynamic response of NEMS via a couple of nonlocal strain gradient theory and classical beam theory", Adv. Nano Res., 11(5), 547-563. https://doi.org/10.12989/ANR.2021.11.5.547.
  167. Zhao, J., Choe, K., Shuai, C., Wang, A. and Wang, Q. (2019), "Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions", Compos. B Eng., 160, 225-240. https://doi.org/10.1016/j.compositesb.2018.09.105.
  168. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. (2021a), "Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory", Eng. Comput., 2021, https://doi.org/10.1007/s00366-020-01242-1.
  169. Zhao, Y., Zhu, Y. and Song, J. (2021b), "Analytical modeling of the linear and nonlinear dynamic characteristics of the nonuniform axially functionally graded cylindrical beam based on the strain gradient theory", Waves Random Complex Media, 1-32. https://doi.org/10.1080/17455030.2021.1965672.
  170. Zhen, Y., Gong, Y. and Tang, Y. (2021), "Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature", Compos. Struct., 268, 113980. https://doi.org/10.1016/j.compstruct.2021.113980.
  171. Zhong, R., Wang, Q., Tang, J., Shuai, C. and Qin, B. (2018), "Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates", Compos. Struct., 194, 49-67. https://doi.org/10.1016/j.compstruct.2018.03.104.
  172. Zhou, C., Zhao, Y., Zhang, J., Fang, Y. and Habibi, M. (2020), "Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system", Adv. Nano Res., 9(4), 295-307. https://doi.org/10.12989/ANR.2020.9.4.295.
  173. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. https://doi.org/10.12989/cac.2020.26.1.063.