DOI QR코드

DOI QR Code

Sport and exercise impact on the therapy with nanomedicine in drug delivery

  • Zhang, Bo (Department of Physical Education and Teaching, Hebei Finance University) ;
  • Jin, Hao (Department of Sports Work, Hebei Agricultural University) ;
  • Duan, Xiaojing (Department of Functional Ultrasound, Affiliated Hospital of Hebei University)
  • Received : 2022.02.22
  • Accepted : 2022.05.24
  • Published : 2022.09.25

Abstract

Nanomachines can be pretty helpful in curing diseases. Nanomototors, thanks to their self-propelled feature, are one of the best structures to be utilized as drug delivery devices. These devices have been employed in biomedical application as they can improve the efficiency of drug delivery. In this study stability of a designed nanomotor in the bloodstream is investigated when the physical activities have been done considering the physical activities. Sports training, as well as exercise enhance the bloodstream, and this factor can significantly impact the drug-delivery quality. The mathematical simulation of nanomotor movement in the condition of the sports is done based on the mechanical sciences, and the impact of various essential parameters is discussed in detail.

Keywords

References

  1. Adamian, A., Safari, K.H., Sheikholeslami, M., Habibi, M., Al-Furjan, M. and Chen, G. (2020), "Critical temperature and frequency characteristics of GPLs-reinforced composite doubly curved panel", Appl. Sci., 10(9), 3251. https://doi.org/10.3390/app10093251.
  2. Al-Furjan, M., Dehini, R., Khorami, M., Habibi, M. and won Jung, D. (2020a), "On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory", Compos. Struct., 112990. https://doi.org/10.1016/j.compstruct.2020.112990.
  3. Al-Furjan, M., Fereidouni, M., Habibi, M., Abd Ali, R., Ni, J. and Safarpour, M. (2020b), "Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01177-7.
  4. Al-Furjan, M., Fereidouni, M., Sedghiyan, D., Habibi, M. and won Jung, D. (2020c), "Three-dimensional frequency response of the CNT-Carbon-Fiber reinforced laminated circular/annular plates under initially stresses", Compos. Struct., 113146. https://doi.org/10.1016/j.compstruct.2020.113146.
  5. Al-Furjan, M., Habibi, M., won Jung, D. and Safarpour, H. (2020d), "Vibrational characteristics of a higher-order laminated composite viscoelastic annular microplate via modified couple stress theory", Compos. Struct., 113152. https://doi.org/10.1016/j.compstruct.2020.113152.
  6. Al-Furjan, M., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2020e), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Seminumerical and finite element modeling", Thin Wall. Struct., 107242. https://doi.org/10.1016/j.tws.2020.107242.
  7. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H. and Jung, D.W. (2020f), "Frequency and critical angular velocity characteristics of rotary laminated cantilever microdisk via twodimensional analysis", Thin Wall. Struct., 157, 107111. https://doi.org/10.1016/j.tws.2020.107111.
  8. 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 Des. Struct., 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343.
  9. Allam, M.N.M. and Radwan, A.F. (2019), "Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium", Adv. Mech. Eng., 11(4), 1687814019837067. https://doi.org/10.1177/1687814019837067.
  10. Apuzzo, A., Barretta, R., Faghidian, S.A., Luciano, R. and Marotti de Sciarra, F. (2018), "Free vibrations of elastic beams by modified nonlocal strain gradient theory", Int. J. Eng. Sci., 133, 99-108. https://doi.org/10.1016/j.ijengsci.2018.09.002.
  11. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057.
  12. 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.
  13. 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.
  14. Bai, Y., Alzahrani, B., Baharom, S. and Habibi, M. (2020), "Seminumerical simulation for vibrational responses of the viscoelastic imperfect annular system with honeycomb core under residual pressure", Eng. Comput., 1-26. https://doi.org/10.1007/s00366-020-01191-9.
  15. Barati, M.R. and Shahverdi, H. (2018), "Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory", Microsyst. Technol., 24(3), 1479-1494. https://doi.org/10.1007/s00542-017-3531-5.
  16. Barretta, R. and Marotti de Sciarra, F. (2018), "Constitutive boundary conditions for nonlocal strain gradient elastic nanobeams", Int. J. Eng. Sci., 130, 187-198. https://doi.org/10.1016/j.ijengsci.2018.05.009.
  17. Behdad, S., Fakher, M., Naderi, A. and Hosseini-Hashemi, S. (2021), "Vibrations of defected local/nonlocal nanobeams surrounded with two-phase Winkler-Pasternak medium: Nonclassic compatibility conditions and exact solution", Wave. Random Complex Med., 1-36. https://doi.org/10.1080/17455030.2021.1918796.
  18. Borjesson, M., Onerup, A., Lundqvist, S. and Dahlof, B. (2016), "Physical activity and exercise lower blood pressure in individuals with hypertension: Narrative review of 27 RCTs", British J. Sports Med., 50(6), 356. https://doi.org/10.1136/bjsports-2015-095786.
  19. Chen, F., Chen, J., Duan, R., Habibi, M. and Khadimallah, M.A. (2022), "Investigation on dynamic stability and aeroelastic characteristics of composite curved pipes with any yawed angle", Compos. Struct., 115195. https://doi.org/10.1016/j.compstruct.2022.115195.
  20. Chen, L., Huang, Y., Yu, X., Lu, J., Jia, W., Song, J., Liu, L., Wang, Y., Huang, Y., Xie, J. and Li, M. (2021), "Corynoxine protects dopaminergic neurons through inducing autophagy and diminishing neuroinflammation in rotenone-induced animal models of parkinson's disease", Front. Pharm., 12. https://doi.org/10.3389/fphar.2021.642900.
  21. 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 Des. Struct., 1-24. https://doi.org/10.1080/15397734.2020.1744005.
  22. Choi, Y., Wang, J., Zhu, Y. and Lai, W.F. (2021), "Students' perception and expectation towards pharmacy education: A qualitative study of pharmacy students in a developing country", Indian J. Pharm. Edu. Res., 55(1), 63-69. https://doi.org/10.5530/ijper.55.1.9.
  23. 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.
  24. Dai, Z., Zhang, L., Bolandi, S.Y. and Habibi, M. (2021b), "On the vibrations of the non-polynomial viscoelastic composite opentype shell under residual stresses", Compos. Struct., 113599. https://doi.org/10.1016/j.compstruct.2021.113599.
  25. Ebrahimi, F. and Barati, M.R. (2017), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 42(5), 1715-1726. https://doi.org/10.1007/s13369-016-2266-4.
  26. Ebrahimi, F. and Dabbagh, A. (2017), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293. https://doi.org/10.1016/j.compstruct.2016.11.058.
  27. Ebrahimi, F., Hajilak, Z.E., Habibi, M. and Safarpour, H. (2019a), "Buckling and vibration characteristics of a carbon nanotubereinforced spinning cantilever cylindrical 3D shell conveying viscous fluid flow and carrying spring-mass systems under various temperature distributions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(13), 4590-4605. https://doi.org/10.1177/0954406219832323.
  28. Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2020a), "Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell", Microsyst. Technol., 26(2), 461-473. https://doi.org/10.1007/s00542-019-04542-9.
  29. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2019b), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Wave. Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1694729.
  30. 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.
  31. 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 higherorder shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772. https://doi.org/10.1080/15376494.2016.1196781.
  32. 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.
  33. Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020b), "Frequency characteristics of a GPL-reinforced composite microdisk coupled with a piezoelectric layer", Eur. Phys. J. Plus, 135(2), 144. https://doi.org/10.1140/epjp/s13360-020-00217-x.
  34. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141.
  35. Eringen, A.C. and Wegner, J. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56(2), B20-B22. https://doi.org/10.1115/1.1553434.
  36. Esmailpoor Hajilak, Z., Pourghader, J., Hashemabadi, D., Sharifi Bagh, F., Habibi, M. and Safarpour, H. (2019), "Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory", Mech. Based Des. Struct., 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743.
  37. Fakher, M., Behdad, S., Naderi, A. and Hosseini-Hashemi, S. (2020), "Thermal vibration and buckling analysis of two-phase nanobeams embedded in size dependent elastic medium", Int. J. Mech. Sci., 171, 105381. https://doi.org/10.1016/j.ijmecsci.2019.105381.
  38. Fu, Y.M., Hong, J.W. and Wang, X.Q. (2006), "Analysis of nonlinear vibration for embedded carbon nanotubes", J. Sound Vib., 296(4), 746-756. https://doi.org/10.1016/j.jsv.2006.02.024.
  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. 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.
  42. 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.
  43. 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 Astronaut., 121, 221-240. https://doi.org/10.1016/j.actaastro.2016.01.003.
  44. 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.
  45. Ghadiri, M., Shafiei, N. and Alavi, H. (2017b), "Thermomechanical 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.
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. 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. Brazil. Soc. Mech. Sci. Eng., 38(2), 335-343. https://doi.org/10.1007/s40430-015-0472-8.
  51. 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 Des. Struct., 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.
  52. Ghorbanpour Arani, A., Abdollahian, M. and Kolahchi, R. (2015), "Nonlinear vibration of a nanobeam elastically bonded with a piezoelectric nanobeam via strain gradient theory", Int. J. Mech. Sci., 100, 32-40. https://doi.org/10.1016/j.ijmecsci.2015.06.002.
  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., 1-22. https://doi.org/10.1007/s00366-021-01433-4.
  54. Guo, J., Kim, K., Lei, K.W. and Fan, D.L. (2015), "Ultra-durable rotary micromotors assembled from nanoentities by electric fields", Nanoscale, 7(26), 11363-11370. https://doi.org/10.1039/C5NR02347E.
  55. 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 Pr., 157, 107723. https://doi.org/10.1016/j.ymssp.2021.107723.
  56. Habibi, M., Ghazanfari, A., Assempour, A., Naghdabadi, R. and Hashemi, R. (2017), "Determination of forming limit diagram using two modified finite element models", Mech Eng. 48(4), 141-144. https://doi.org/10.22060/MEJ.2016.664.
  57. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2018), "Forming limit diagrams by including the M-K model in finite element simulation considering the effect of bending", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 232(8), 625-636. https://doi.org/10.1177/1464420716642258.
  58. Habibi, M., Hashemabadi, D. and Safarpour, H. (2019a), "Vibration analysis of a high-speed rotating GPLRC nanostructure coupled with a piezoelectric actuator", Eur. Phys. J. Plus, 134(6), 307. https://doi.org/10.1140/epjp/i2019-12742-7.
  59. Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019b), "Wave propagation characteristics of the electrically GNPreinforced nanocomposite cylindrical shell", J. Brazil. Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x.
  60. Habibi, M., Mohammadi, A., Safarpour, H. and Ghadiri, M. (2019c), "Effect of porosity on buckling and vibrational characteristics of the imperfect GPLRC composite nanoshell", Mech. Based Des. Struct., 1-30. https://doi.org/10.1080/15397734.2019.1701490.
  61. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019d), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct., 1-19. https://doi.org/10.1080/15397734.2019.1697932.
  62. Habibi, M., Taghdir, A. and Safarpour, H. (2019e), "Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets", Compos. Part B Eng., 175, 107125. https://doi.org/10.1016/j.compositesb.2019.107125.
  63. Habibi, M., Safarpour, M. and Safarpour, H. (2020), "Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods", Mech. Based Des. Struct., 1-22. https://doi.org/10.1080/15397734.2020.1779086.
  64. Habibi, M., Darabi, R., Sa, J.C.d. and Reis, A. (2021), "An innovation in finite element simulation via crystal plasticity assessment of grain morphology effect on sheet metal formability", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(8), 1937-1951. https://doi.org/10.1177/14644207211024686.
  65. Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Wave. Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1662968.
  66. 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 Wall. Struct., 166, 108019. https://doi.org/10.1016/j.tws.2021.108019.
  67. 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., 1-19. https://doi.org/10.1007/s00366-021-01456-x.
  68. Huang, X., Hao, H., Oslub, K., Habibi, M. and Tounsi, A. (2021a), "Dynamic stability/instability simulation of the rotary sizedependent functionally graded microsystem", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01399-3.
  69. 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 microtube", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-021-01395-7.
  70. 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., 38(4), 3137-3149. https://doi.org/10.1007/s00366-021-01320-y.
  71. 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 magnetoelectro- elastic nanosystem", Eng. Comput., 38(3), 2499-2513. https://doi.org/10.1007/s00366-021-01391-x.
  72. Karami, B., Janghorban, M. and Tounsi, A. (2018), "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. https://doi.org/10.1016/j.tws.2018.02.025.
  73. 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.
  74. Li, L., Hu, Y., Li, X. and Ling, L. (2016), "Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory", Microfluid. Nanofluid., 20(5), 76. https://doi.org/10.1007/s10404-016-1739-9.
  75. Li, Y., Li, S., Guo, K., Fang, X. and Habibi, M. (2020), "On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01166-w.
  76. 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. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  77. 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.
  78. 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 Des. Struct., 1-26. https://doi.org/10.1080/15397734.2020.1784201.
  79. 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 Des. Struct., 1-25. https://doi.org/10.1080/15397734.2020.1815544.
  80. 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., 1-15. https://doi.org/10.1007/s00366-021-01316-8.
  81. Liu, H., Zhao, Y., Pishbin, M., Habibi, M., Bashir, M. 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., 1-16. https://doi.org/10.1007/s00366-021-01419-2.
  82. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021c), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-021-01454-z.
  83. Lori, E.S., Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020), "The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-01004-z.
  84. Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 99(7), 073510. https://doi.org/10.1063/1.2189213.
  85. Lu, L., Guo, X. and Zhao, J. (2017a), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006.
  86. Lu, L., Guo, X. and Zhao, J. (2017b), "A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms", Int. J. Eng. Sci., 119, 265-277. https://doi.org/10.1016/j.ijengsci.2017.06.024.
  87. Ma, W.L., Li, X.F. and Lee, K.Y. (2020), "Third-order shear deformation beam model for flexural waves and free vibration of pipes", J. Acoust. Soc. Am., 147(3), 1634-1647. https://doi.org/10.1121/10.0000855.
  88. Ma, L., Liu, X. and Moradi, Z. (2021), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 1-25. https://doi.org/10.1007/s00366-020-01210-9.
  89. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A., Kazemi, M. and Structures, C. (2017a), "Thermal vibration of twodimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  90. 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. Therm. Stress., 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962.
  91. 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.
  92. 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.
  93. Moayedi, H., Habibi, M., Safarpour, H., Safarpour, M. and Foong, L. (2019), "Buckling and frequency responses of a graphene nanoplatelet reinforced composite microdisk", Int. J. Appl. Mech., 11(10), 1950102. https://doi.org/10.1142/S1758825119501023.
  94. Moayedi, H., Aliakbarlou, H., Jebeli, M., Noormohammadiarani, O., Habibi, M., Safarpour, H. and Foong, L. (2020a), "Thermal buckling responses of a graphene reinforced composite micropanel structure", Int. J. Appl. Mech., 12(1), 2050010. https://doi.org/10.1142/S1758825120500106.
  95. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H. and Foong, L.K. (2020b), "Application of nonlocal strain-stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell", Eng. Comput., 1-16. https://doi.org/10.1007/s00366-020-01002-1.
  96. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H. and Foong, L.K. (2021), "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.
  97. Mohammadgholiha, M., Shokrgozar, A., Habibi, M. and Safarpour, H. (2019), "Buckling and frequency analysis of the nonlocal strain-stress gradient shell reinforced with graphene nanoplatelets", J. Vib. Control, 25(19-20), 2627-2640. https://doi.org/10.1177/1077546319863251.
  98. Mohammadi, A., Lashini, H., Habibi, M. and Safarpour, H. (2019), "Influence of viscoelastic foundation on dynamic behaviour of the double walled cylindrical inhomogeneous micro shell using MCST and with the aid of GDQM", J. Solid Mech., 11(2), 440-453. https://doi.org/10.22034/JSM.2019.665264.
  99. Moradi, Z., Davoudi, M., Ebrahimi, F. and Ehyaei, A.F. (2021), "Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller", Wave. Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1926572.
  100. Naderi, A., Behdad, S., Fakher, M. and Hosseini-Hashemi, S. (2020), "Vibration analysis of mass nanosensors with considering the axial-flexural coupling based on the two-phase local/nonlocal elasticity", Mech. Syst. Signal Pr., 145, 106931. https://doi.org/10.1016/j.ymssp.2020.106931.
  101. Naderi, A., Fakher, M. and Hosseini-Hashemi, S. (2021), "On the local/nonlocal piezoelectric nanobeams: Vibration, buckling, and energy harvesting", Mech. Syst. Signal Pr., 151, 107432. https://doi.org/10.1016/j.ymssp.2020.107432.
  102. Naderi, A., Behdad, S. and Fakher, M. (2022), "Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM", Smart Mater. Struct., 31(4), 045007. https://doi.org/10.1088/1361-665x/ac5456.
  103. Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.w. and Nabipour, N. (2020), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomol. Struct. Dyn., 1-12. https://doi.org/10.1080/07391102.2020.1751297.
  104. Nami, M.R. and Janghorban, M. (2015), "Free vibration analysis of rectangular nanoplates based on two-variable refined plate theory using a new strain gradient elasticity theory", J. Brazil. Soc. Mech. Sci. Eng., 37(1), 313-324. https://doi.org/10.1007/s40430-014-0169-4.
  105. 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", Sci. Rep., 10(1), 1-19. https://doi.org/10.1038/s41598-020-61855-w.
  106. Park, S.K. and Gao, X.L. (2006), "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng., 16(11), 2355-2359. https://doi.org/10.1088/0960-1317/16/11/015.
  107. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041.
  108. Putcha, N.S. and Reddy, J.N. (1986), "Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory", J. Sound Vib., 104(2), 285-300. https://doi.org/10.1016/0022-460X(86)90269-5.
  109. Safarpour, H., Ghanizadeh, S.A. and Habibi, M. (2018), "Wave propagation characteristics of a cylindrical laminated composite nanoshell in thermal environment based on the nonlocal strain gradient theory", Eur. Phys. J. Plus, 133(12), 532. https://doi.org/10.1140/epjp/i2018-12385-2.
  110. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019), "A sizedependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation", Int. J. Mech. Mater. Des., 15(3), 569-583. https://doi.org/10.1007/s10999-018-9431-8.
  111. Safarpour, M., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-00949-5.
  112. 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, 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011.
  113. 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.
  114. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016c), "Nonlinear vibration of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007.
  115. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016d), "On sizedependent vibration of rotary axially functionally graded microbeam", Int. J. Eng. Sci., 101, 29-44. https://doi.org/10.1016/j.ijengsci.2015.12.008.
  116. Shafiei, N., Kazemi, M., Safi, M. and Ghadiri, M. (2016e), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", Int. J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009.
  117. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016f), "On sizedependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007.
  118. 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.
  119. Shafiei, N. and Kazemi, M. (2017a), "Buckling analysis on the bidimensional functionally graded porous tapered nano-/microscale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.
  120. 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.
  121. 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. Modell., 43, 191-206. https://doi.org/10.1016/j.apm.2016.10.061.
  122. 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.
  123. 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.
  124. 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. Meth. Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  125. 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.
  126. 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.
  127. 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. 20.1001.1.20083505.2020.12.1.2.8. 20.1001.1.20083505.2020.12.1.2.8
  128. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2020a), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-01024-9.
  129. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020b), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Materials, 13(7), 1707. https://doi.org/10.3390/ma13071707.
  130. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020c), "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.
  131. Shao, Y., Zhao, Y., Gao, J. and Habibi, M. (2021), "Energy absorption of the strengthened viscoelastic multi-curved composite panel under friction force", Arch. Civil Mech. Eng., 21(4), 1-29. https://doi.org/10.1007/s43452-021-00279-3.
  132. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "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.
  133. Shen, J.P., Wang, P.Y., Gan, W.T. and Li, C. (2020), "Stability of vibrating functionally graded nanoplates with axial motion based on the nonlocal strain gradient theory", Int. J. Struct. Stabil. Dyn., 20(08), 2050088. https://doi.org/10.1142/S0219455420500881.
  134. 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.
  135. Shokrgozar, A., Safarpour, H. and Habibi, M. (2020), "Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 234(2), 512-529. https://doi.org/10.1177/0954406219883312.
  136. Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013.
  137. Singh, D.K. and Pal, P. (2021), "Forced vibration analysis of stiffened lock gate structure", J. Sound Vib., 510, 116278. https://doi.org/10.1016/j.jsv.2021.116278.
  138. Sofiyev, A.H., Deniz, A., Akcay, I.H. and Yusufoglu, E. (2006), "The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load", Acta Mech., 183(3), 129-144. https://doi.org/10.1007/s00707-006-0328-5.
  139. Thai, C.H., Ferreira, A.J.M. and Phung-Van, P. (2020), "A nonlocal strain gradient isogeometric model for free vibration and bending analyses of functionally graded plates", Compos. Struct., 251, 112634. https://doi.org/10.1016/j.compstruct.2020.112634.
  140. 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.
  141. Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultrafast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01396-6.
  142. 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., 114395. https://doi.org/10.1016/j.compstruct.2021.114395.
  143. Yan, J., Yao, Y., Yan, S., Gao, R., Lu, W. and He, W. (2020), "Chiral protein supraparticles for tumor suppression and synergistic immunotherapy: An enabling strategy for bioactive supramolecular chirality construction", Nano Lett., 20(8), 5844-5852. https://doi.org/10.1021/acs.nanolett.0c01757.
  144. Yang, Y., Wang, J. and Yu, Y. (2018), "Wave propagation in fluidfilled single-walled carbon nanotube based on the nonlocal strain gradient theory", Acta Mech. Solida Sinica, 31(4), 484-492. https://doi.org/10.1007/s10338-018-0035-5.
  145. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic highorder computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Pr., 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373.
  146. Zare, R., Najaafi, N., Habibi, M., Ebrahimi, F. and Safarpour, H. (2020), "Influence of imperfection on the smart control frequency characteristics of a cylindrical sensor-actuator GPLRC cylindrical shell using a proportional-derivative smart controller", Smart Struct. Syst., 26(4), 469-480. https://doi.org/10.12989/sss.2020.26.4.469.
  147. Zeighampour, H. and Tadi Beni, Y. (2015), "Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory", Appl. Math. Modell., 39(18), 5354-5369. https://doi.org/10.1016/j.apm.2015.01.015.
  148. Zhang, P. and Fu, Y. (2013), "A higher-order beam model for tubes", Eur. J. Mech. A Solids, 38, 12-19. https://doi.org/10.1016/j.euromechsol.2012.09.009.
  149. Zhang, X., Shamsodin, M., Wang, H., NoormohammadiArani, O., Khan, A.M., Habibi, M. and Al-Furjan, M. (2020), "Dynamic information of the time-dependent tobullian biomolecular structure using a high-accuracy size-dependent theory", J. Biomol. Struct. Dyn., 1-16. https://doi.org/10.1080/07391102.2020.1760939.
  150. Zhang, Y., Wang, Z., Tazeddinova, D., Ebrahimi, F., Habibi, M. and Safarpour, H. (2021), "Enhancing active vibration control performances in a smart rotary sandwich thick nanostructure conveying viscous fluid flow by a PD controller", Wave. Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1948627.
  151. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. (2022), "Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.
  152. 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.