Advances in concrete construction

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Optimization of the cross-section regarding the stability of nanostructures according to the dynamic analysis

  • Qiuyang Cheng (School of Civil, Architecture and Environment, Hubei University of Technology) ;
  • H. Elhosiny Ali (Department of Physics, Faculty of Science, King Khalid University) ;
  • Ibrahim Albaijan (Mechanical Engineering Department, College of Engineering at Al Kharj, Prince Sattam Bin Abdulaziz University)
  • Received : 2022.07.31
  • Accepted : 2023.03.12
  • Published : 2023.04.25
⟨ Previous Next ⟩

Abstract

The vibrational behavior of nanoelements is critical in determining how a nanostructure behaves. However, combining vibrational analysis with stability analysis allows for a more comprehensive knowledge of a structure's behavior. As a result, the goal of this research is to characterize the behavior of nonlocal nanocyndrical beams with uniform and nonuniform cross sections. The nonuniformity of the beams is determined by three distinct section functions, namely linear, convex, and exponential functions, with the length and mass of the beams being identical. For completely clamped, fully pinned, and cantilever boundary conditions, Eringen's nonlocal theory is combined with the Timoshenko beam model. The extended differential quadrature technique was used to solve the governing equations in this research. In contrast to the other boundary conditions, the findings of this research reveal that the nonlocal impact has the opposite effect on the frequency of the uniform cantilever nanobeam. Furthermore, since the mass of the materials employed in these nanobeams is designed to remain the same, the findings may be utilized to help improve the frequency and buckling stress of a resonator without requiring additional material, which is a cost-effective benefit.

Keywords

References

  1. Alameh, A.H., Gratuze, M. and Nabki, F. (2019), "Impact of geometry on the performance of cantilever-based piezoelectric vibration energy harvesters", IEEE Sensors J., 19(22), 10316-10326. https://doi.org/10.1109/JSEN.2019.2932341
  2. Alcheikh, N., Kosuru, L., Kazmi, S. and Younis, M.I. (2020), "Inplane air damping of micro-and nano-mechanical resonators", J. Micromech. Microeng., 30(3), 035007. https://doi.org/10.1088/1361-6439/ab68b0
  3. 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. Mach., 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343
  4. Atmane Hassen, A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  5. Attia, A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  6. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  7. 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
  8. 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
  9. Bazant, Z. and Jirasek, M. (2002), "Nonlocal integral formulations of plasticity and damage: a survey on recent results", J. Eng. Mech., 128, 1129-1239. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)
  10. Bellifa, H., Bakora, A., Tounsi, A., Bousahla Abdelmoumen, A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  11. Bellman, R. and Casti, J. (1971), "Differential quadrature and long-term integration", J. Mathe. Anal. Applicat., 34(2), 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
  12. Bellman, R., Kashef, B. and Casti, J. (1972), "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", J. Computat. Phys., 10(1), 40-52. https://doi.org/10.1016/0021-9991(72)90089-7
  13. Bennai, R., Atmane Hassen, A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  14. Carrozza, M.C., Eisinberg, A., Menciassi, A., Campolo, D., Micera, S. and Dario, P. (2000), "Towards a force-controlled microgripper for assembling biomedical microdevices", J. Micromech. Microeng., 10(2), 271. https://doi.org/10.1088/0960-1317/10/2/328
  15. Caruntu, D.I., Botello, M.A., Reyes, C.A. and Beatriz, J.S. (2019), "Voltage-amplitude response of superharmonic resonance of second order of electrostatically actuated MEMS cantilever resonators", J. Computat. Nonlinear Dyn., 14(3). https://doi.org/10.1115/1.4042017
  16. Caruntu, D.I. and Martinez, I. (2014), "Reduced order model of parametric resonance of electrostatically actuated MEMS cantilever resonators", Int. J. Non-Linear Mech., 66, 28-32. https://doi.org/10.1016/j.ijnonlinmec.2014.02.007
  17. Chaht Fouzia, L., Kaci, A., Houari Mohammed Sid, A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  18. Chen, H., Rosengarten, G., Li, M. and Nordon, R.E. (2012), "Design of microdevices for long-term live cell imaging", J. Micromech. Microeng., 22(6), 065033. https://doi.org/10.1088/0960-1317/22/6/065033
  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. Cheng, F., Wang, H., Zong, G., Niu, B. and Zhao, X. (2023), "Adaptive Finite-Time Command-Filtered Control for Switched Nonlinear Systems with Input Quantization and Output Constraints", Circuits Syst. Signal Process., 42(1), 147-172. https://doi.org/10.1007/s00034-022-02088-2
  21. Cooley, W.G. (2005), "Application of functionally graded materials in aircraft structures", Thesis; Air Force Institue of Technology.
  22. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., Int. J., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  23. 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
  24. 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
  25. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. Comput., 35(4), 1375-1389. https://doi.org/10.1007/s00366-018-0669-4
  26. Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2020), "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
  27. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., Int. J., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141
  28. 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. Mach., 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743
  29. Fang, Q., Liu, X., Zeng, K., Zhang, X., Zhou, M. and Du, J. (2022), "Centrifuge modelling of tunnelling below existing twin tunnels with different types of support", Undergr. Space, 7(6), 1125-1138. https://doi.org/10.1016/j.undsp.2022.02.007
  30. Fang, Q., Wang, G., Du, J., Liu, Y. and Zhou, M. (2023), "Prediction of tunnelling induced ground movement in clay using principle of minimum total potential energy", Tunnell. Undergr. Space Technol., 131, 104854. https://doi.org/10.1016/j.tust.2022.104854
  31. Gao, N. and Li, X.J. (2021), Controlled Drug Delivery using Microdevices, Elsevier.
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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. 20.1001.1.20083505.2017.9.2.8.5 1001.1.20083505.2017.9.2.8.5
  42. Ghadiri, M., Shafiei, N. and Babaei, R. (2017d), "Vibration of a rotary FG plate with consideration of thermal and Coriolis effects", Steel Compos. Struct., Int. J., 25(2), 197-207. https://doi.org/10.12989/scs.2017.25.2.197
  43. 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
  44. Guan, C., Zhu, X. and Feng, C. (2021), "DNA nanodevice-based drug delivery systems", Biomolecules, 11(12), 1855. https://doi.org/10.3390/biom11121855
  45. Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Perform., 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1
  46. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2018a), "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: J. Mater.: Des. Applicat., 232(8), 625-636. https://doi.org/10.1177/1464420716642258
  47. Habibi, M., Hashemi, R., Tafti, M.F. and Assempour, A. (2018b), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manuf. Process., 31, 310-323. https://doi.org/10.1016/j.jmapro.2017.11.009
  48. 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
  49. Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019b), "Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell", J. Brazil. Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x
  50. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019c), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct. Mach., 1-19. https://doi.org/10.1080/15397734.2019.1697932
  51. Habibi, M., Taghdir, A. and Safarpour, H. (2019d), "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
  52. Hashemian, M., Foroutan, S. and Toghraie, D. (2019), "Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects", Mech. Mater., 139, 103209. https://doi.org/10.1016/j.mechmat.2019.103209
  53. He, Y., Chang, X.-H., Wang, H. and Zhao, X. (2022), "Command-Filtered Adaptive Fuzzy Control for Switched MIMO Nonlinear Systems with Unknown Dead Zones and Full State Constraints", Int. J. Fuzzy Syst., 25(2), 544-560. https://doi.org/10.1007/s40815-022-01384-y
  54. Hosseini-Hashemi, S. and Nazemnezhad, R. (2013), "An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects", Compos. Part B: Eng., 52, 199-206. https://doi.org/10.1016/j.compositesb.2013.04.023
  55. Hosseini-Hashemi, S., Behdad, S. and Fakher, M. (2020), "Vibration analysis of two-phase local/nonlocal viscoelastic nanobeams with surface effects", Eur. Phys. J. Plus, 135(2), 1-18. https://doi.org/10.1140/epjp/s13360-020-00148-7
  56. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021a), "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
  57. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021b), "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
  58. Houari Mohammed Sid, A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  59. Hu, K.-M., Zhang, W.-M., Peng, Z.-K. and Meng, G. (2016), "Transverse vibrations of mixed-mode cracked nanobeams with surface effect", J. Vib. Acoust., 138(1), 011020. https://doi.org/10.1115/1.4031832
  60. Huang, X., Zhang, Y., Moradi, Z. and Shafiei, N. (2021a), "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., 38, 2481-2498. https://doi.org/10.1007/s00366-021-01395-7
  61. 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., 1-18. https://doi.org/10.1007/s00366-021-01395-7
  62. Hwang, H.H., Zhu, W., Victorine, G., Lawrence, N. and Chen, S. (2018), "3D-Printing of functional biomedical microdevices via light-and extrusion-based approaches", Small Methods, 2(2), 1700277. https://doi.org/10.1002/smtd.201700277
  63. 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. https://doi.org/10.1007/s00366-021-01391-x
  64. Kar Vishesh, R. and Panda Subrata, K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  65. Karami, B., Janghorban, M. and Rabczuk, T. (2020), "Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory", Compos. Part B: Eng., 182, 107622. https://doi.org/10.1016/j.compositesb.2019.107622
  66. Koyama-Ito, H., Wada, E. and Ito, A. (1987), "A cyclotron microbeam and its application to biomedical samples", Nuclear Instrum. Methods Phys. Res. Section B: Beam Interact. Mater. Atoms, 22(1-3), 205-209. https://doi.org/10.1016/0168-583X(87)90328-4
  67. Kumar, S., Reddy, K.M., Kumar, A. and Devi, G.R. (2013), "Development and characterization of polymer-ceramic continuous fiber reinforced functionally graded composites for aerospace application", Aerosp. Sci. Technol., 26(1), 185-191. https://doi.org/10.1016/j.ast.2012.04.002
  68. Lal, R. and Dangi, C. (2021), "Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen's nonlocal theory incorporating the surface effect", Appl. Mathe. Computat., 395, 125857. https://doi.org/10.1016/j.amc.2020.125857
  69. Lam, K.H., Li, Y., Lee, C., Zhou, Q. and Shung, K.K. (2012). "Ultrahigh frequency ultrasound microbeam for biomedical applications", Proceedings of 2012 IEEE International Ultrasonics Symposium, Dresden, Germany, October. https://doi.org/10.1109/ULTSYM.2012.0499
  70. 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. Am. Ceram. Soc., 79(12), 3003-3012. https://doi.org/10.1111/j.1151-2916.1996.tb08070.x
  71. Lee, W.-B., Weng, C.-H., Cheng, F.-Y., Yeh, C.-S., Lei, H.-Y. and Lee, G.-B. (2009), "Biomedical microdevices synthesis of iron oxide nanoparticles using a microfluidic system", Biomed. Microdev., 11(1), 161-171. https://doi.org/10.1007/s10544-008-9221-4
  72. Lee, M.-s., Kim, C.-i., Park, W.-i., Cho, J.-h., Paik, J.-h. and Jeong, Y.H. (2019), "Energy harvesting performance of unimorph piezoelectric cantilever generator using interdigitated electrode lead zirconate titanate laminate", Energy, 179, 373-382. https://doi.org/10.1016/j.energy.2019.04.215
  73. Li, P., Yang, M. and Wu, Q. (2021), "Confidence interval based distributionally robust real-time economic dispatch approach considering wind power accommodation risk", IEEE Transact. Sustain. Energy, 12(1), 58-69. https://doi.org/10.1109/TSTE.2020.2978634
  74. Liu, C., Ke, L.-L., Yang, J., Kitipornchai, S. and Wang, Y.-S. (2018), "Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory", Mech. Adv. Mater. Struct., 25(15-16), 1252-1264. https://doi.org/10.1080/15376494.2016.1149648
  75. Mahmoud, D. and Elbestawi, M.A. (2017), "Lattice structures and functionally graded materials applications in additive manufacturing of orthopedic implants: a review", J. Manuf. Mater. Process., 1(2), 13. https://doi.org/10.3390/jmmp1020013
  76. Malankowska, M. (2018), Membrane integration in biomedical microdevices, Universidade NOVA de Lisboa, Portugal.
  77. Mehrali, M., Shirazi, F.S., Mehrali, M., Metselaar, H.S.C., Kadri, N.A.B. and Osman, N.A.A. (2013), "Dental implants from functionally graded materials", J. Biomed. Mater. Res. Part A: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials. 101(10), 3046-3057. https://doi.org/10.1002/jbm.a.34588
  78. 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., Int. J., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415
  79. Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel Afshari, B. (2017b), "Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam", J. Thermal Stress., 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962
  80. 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
  81. 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
  82. 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", Waves Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1926572
  83. Mousavi, S.M., Shafiei, N. and Dadvand, A. (2017), "Numerical simulation of subsonic turbulent flow over NACA0012 airfoil: evaluation of turbulence models", Sigma J. Eng. Natural Sci., 35(1), 133-155. https://dergipark.org.tr/en/pub/sigma/issue/65585/1016455#article_cite 1016455#article_cite
  84. 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
  85. Nematollahi, M.S. and Mohammadi, H. (2019), "Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory", Int. J. Mech. Sci., 156, 31-45. https://doi.org/10.1016/j.ijmecsci.2019.03.022
  86. Nisar, A., Afzulpurkar, N., Mahaisavariya, B. and Tuantranont, A. (2008), "MEMS-based micropumps in drug delivery and biomedical applications", Sensors Actuators B: Chem., 130(2), 917-942. https://doi.org/10.1016/j.snb.2007.10.064
  87. Omidi, S., Oskooee, M.B. and Shafiei, N. (2013), "Finite element analysis of an ultra-fine grained Titanium dental implant covered by different thicknesses of hydroxyapatite layer", Indian J. Dentist., 4(1), 1-4. https://doi.org/10.1016/j.ijd.2012.10.002
  88. Ouakad, H.M., El-Borgi, S., Mousavi, S.M. and Friswell, M.I. (2018), "Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory", Appl. Mathe. Modell., 62, 207-222. https://doi.org/10.1007/s00339-016-0245-y
  89. Phan, M.T., Trinh, X.T., Le, Q.C., Ngo, V.K.T. and Nguyen, C.C. (2021), "Effect of environmental conditions on quality factors of MEMS cantilever beam resonator in gas rarefaction", Sens. Imag., 22(1), 1-27. https://doi.org/10.1007/s11220-020-00329-9
  90. Pinto, E., Faustino, V., Rodrigues, R.O., Pinho, D., Garcia, V., Miranda, J.M. and Lima, R. (2014), "A rapid and low-cost nonlithographic method to fabricate biomedical microdevices for blood flow analysis", Micromachines, 6(1), 121-135. https://doi.org/10.3390/mi6010121
  91. 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
  92. Popoola, P., Farotade, G., Fatoba, O. and Popoola, O. (2016), "Laser engineering net shaping method in the area of development of functionally graded materials (FGMs) for aero engine applications-a review", Chapter 17 - Fiber Laser, pp. 383-399. http://dx.doi.org/10.5772/61711
  93. 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. Mathe. Applicat., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041
  94. Ramadi, K.B., Bashyam, A., Frangieh, C.J., Rousseau, E.B., Cotler, M.J., Langer, R., Graybiel, A.M. and Cima, M.J. (2020), "Computationally guided intracerebral drug delivery via chronically implanted microdevices", Cell Reports, 31(10), 107734. https://doi.org/10.1016/j.celrep.2020.107734
  95. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019a), "A size-dependent 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
  96. Safarpour, H., Pourghader, J. and Habibi, M. (2019b), "Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator", J. Vib. Control, 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465
  97. 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
  98. 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
  99. 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
  100. 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-dimens. Syst. Nanostruct., 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011
  101. 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), 1-18. https://doi.org/10.1007/s00339-016-0245-y
  102. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016c), "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
  103. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016d), "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
  104. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016e), "On size-dependent vibration of rotary axially functionally graded microbeam", Int. J. Eng. Sci., 101, 29-44. https://doi.org/10.1016/j.ijengsci.2015.12.008
  105. Shafiei, N., Kazemi, M., Safi, M. and Ghadiri, M. (2016f), "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
  106. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016g), "On size-dependent 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
  107. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016h), "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
  108. 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. Mathe. Modell., 43, 191-206. https://doi.org/10.1016/j.apm.2016.10.061
  109. 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
  110. 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
  111. 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
  112. 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
  113. 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
  114. Sharabiani, P.A. and Yazdi, M.R.H. (2013), "Nonlinear free vibrations of functionally graded nanobeams with surface effects", Compos. Part B: Eng., 45(1), 581-586. https://doi.org/10.1016/j.compositesb.2012.04.064
  115. 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
  116. Shu, C. (2012), Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
  117. Si, Z., Yang, M., Yu, Y. and Ding, T. (2021), "Photovoltaic power forecast based on satellite images considering effects of solar position", Appl. Energy, 302, 117514. https://doi.org/10.1016/j.apenergy.2021.117514
  118. Sola, A., Bellucci, D. and Cannillo, V. (2016), "Functionally graded materials for orthopedic applications-an update on design and manufacturing", Biotechnol. Adv., 34(5), 504-531. https://doi.org/10.1016/j.biotechadv.2015.12.013
  119. Stieglitz, T. (2001), "Flexible biomedical microdevices with double-sided electrode arrangements for neural applications", Sensors Actuat. A: Physi., 90(3), 203-211. https://doi.org/10.1016/S0924-4247(01)00520-9
  120. Stieglitz, T. and Meyer, J.-U. (2006), Biomedical Microdevices for Neural Implants, Springer.
  121. Timoshenko, S.P. (1922), "X. On the transverse vibrations of bars of uniform cross-section", London, Edinburgh, and Dublin Philosoph. Magaz. J. Sci., 43(253), 125-131. https://doi.org/10.1080/14786442208633855
  122. Truckenmuller, R., Giselbrecht, S., Rivron, N., Gottwald, E., Saile, V., Van den Berg, A., Wessling, M. and Van Blitterswijk, C. (2011), "Thermoforming of film-based biomedical microdevices", Adv. Mater., 23(11), 1311-1329. https://doi.org/10.1002/adma.201003538
  123. Wang, P., Huo, J., Dehini, R. and Forsat, M. (2021), "Buckling of functionally graded nonuniform and imperfect nanotube using higher order theory", Waves Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1892864
  124. Wang, M., Yang, M., Fang, Z., Wang, M. and Wu, Q. (2022a), "A Practical Feeder Planning Model for Urban Distribution System", IEEE Transact. Power Syst., 1-1. https://doi.org/10.1109/TPWRS.2022.3170933
  125. Wang, P., Gao, Z., Pan, F., Moradi, Z., Mahmoudi, T. and Khadimallah, M.A. (2022b), "A couple of GDQM and iteration techniques for the linear and nonlinear buckling of bidirectional functionally graded nanotubes based on the nonlocal strain gradient theory and high-order beam theory", Eng. Anal. Bound. Elements, 143, 124-136. https://doi.org/10.1016/j.enganabound.2022.06.007
  126. Willis, A.J., Pernal, S.P., Gaertner, Z.A., Lakka, S.S., Sabo, M.E., Creighton, F.M. and Engelhard, H.H. (2020), "Rotating magnetic nanoparticle clusters as microdevices for drug delivery", Int. J. Nanomed., 15, 4105.
  127. Xie, L., Zhu, Y., Yin, M., Wang, Z., Ou, D., Zheng, H., Liu, H. and Yin, G. (2022), "Self-feature-based point cloud registration method with a novel convolutional Siamese point net for optical measurement of blade profile", Mech. Syst. Signal Process., 178, 109243. https://doi.org/10.1016/j.ymssp.2022.109243
  128. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021a), "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
  129. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021b), "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
  130. Yang, C., Zhang, J. and Huang, Z. (2022), "Numerical study on cavitation-vortex-noise correlation mechanism and dynamic mode decomposition of a hydrofoil", Phys. Fluids, 34(12), 125105. https://doi.org/10.1063/5.0128169
  131. Yuan, Y., Zhao, X., Zhao, Y., Sahmani, S. and Safaei, B. (2021), "Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation", Thin-Wall. Struct., 159, 107249. https://doi.org/10.1016/j.tws.2020.107249
  132. Zarga, D., Tounsi, A., Bousahla Abdelmoumen, A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  133. Zhang, H., Zhao, X., Wang, H., Zong, G. and Xu, N. (2022), "Hierarchical Sliding-Mode Surface-Based Adaptive Actor-Critic Optimal Control for Switched Nonlinear Systems With Unknown Perturbation", IEEE Transact. Neural Networks Learn. Syst., 1-13. https://doi.org/10.1109/TNNLS.2022.3183991
  134. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. (2021), "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
  135. Zhao, Y., Tang, F., Zong, G., Zhao, X. and Xu, N. (2022), "Event-Based Adaptive Containment Control for Nonlinear Multiagent Systems With Periodic Disturbances", IEEE Transact. Circuits Syst. II: Express Briefs, 69(12), 5049-5053. https://doi.org/10.1109/TCSII.2022.3200053