DOI QR코드

DOI QR Code

Vibration control, energy harvesting and forced vibration of the piezoelectric NEMS via paradox-free local/nonlocal theory

  • Zohre Moradi (Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University) ;
  • Farzad Ebrahimi (Faculty of Engineering, Department of Mechanics, Imam Khomeini International University) ;
  • Mohsen Davoudi (Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University)
  • 투고 : 2021.01.24
  • 심사 : 2022.06.14
  • 발행 : 2023.04.25

초록

The possibility of energy harvesting as well as controlled vibration of a three-layered beam consisting of two piezoelectric layer and one core layer made of nonpiezoelectric material is investigated using paradox-free local/nonlocal theory. The three-layered nanobeam is resting on an elastic foundation and subjected to a blast load. Also, the core layer is made of Nano-composites reinforced by CNTs and carbon fibers (MHCD). Governing equations as well as boundary conditions are obtained using Hamilton,s principle. The equations discretized by Generalized Differential Quadrature Method (GDQM) and solved by Newmark beta method. In addition, two differential and integral gains are employed for controlling the forced vibration. The size-dependency of the elastic foundation is considered using two-phase elasticity. The effect of elastic foundation, control gains, nonlocal factor, as well as parameters affecting the core material on the forced vibration and energy harvesting is investigated in detail. The equations as well as solution procedure is validated utilizing some compassion studies. This work can be a basis for future studies on energy harvesting and controlled vibration in small scales.

키워드

참고문헌

  1. Adamian, A., Safari, K.H., Sheikholeslami, M., Habibi, M., AlFurjan, 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. Adhikari, S., Gilchrist, D., Murmu, T. and McCarthy, M. (2015), "Nonlocal normal modes in nanoscale dynamical systems", Mech. Syst. Signal Pr., 60, 583-603. https://doi.org/10.1016/j.ymssp.2014.12.004 
  3. Akbas, S.D. (2018a), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219. http://doi.org/10.12989/anr.2018.6.3.219 
  4. Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39. http://doi.org/10.12989/anr.2018.6.1.039 
  5. 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 
  6. 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 
  7. 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 
  8. 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 
  9. 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 
  10. 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 
  11. 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 
  12. Allahkarami, F., Nikkhah-Bahrami, M. and Saryazdi, M.G. (2017), "Damping and vibration analysis of viscoelastic curved microbeam reinforced with FG-CNTs resting on viscoelastic medium using strain gradient theory and DQM", Steel. Compos. Struct., 25(2), 141-155. https://doi.org/10.12989/scs.2017.25.2.141 
  13. Apuzzo, A., Barretta, R., Luciano, R., de Sciarra, F.M. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model", Compos. Part B Eng., 123, 105-111. https://doi.org/10.1016/j.compositesb.2017.03.057 
  14. Arefi, M. and Zenkour, A.M. (2018), "Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory", Steel. Compos. Struct., 26(4), 421-437. https://doi.org/10.12989/scs.2018.26.4.421 
  15. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257. http://doi.org/10.12989/anr.2018.6.3.257 
  16. Bai, B., Jiang, S., Liu, L., Li, X. and Wu, H. (2021), "The transport of silica powders and lead ions under unsteady flow and variable injection concentrations", Powder Technol., 387, 22-30. https://doi.org/10.1016/j.powtec.2021.04.014 
  17. 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 
  18. Behdad, S., Fakher, M. and Hosseini-Hashemi, S. (2021), "Dynamic stability and vibration of two-phase local/nonlocal VFGP nanobeams incorporating surface effects and different boundary conditions", Mech. Mater., 153, 103633. https://doi.org/10.1016/j.mechmat.2020.103633 
  19. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279. http://doi.org/10.12989/anr.2018.6.3.279 
  20. Challamel, N. and Wang, C. (2008), "The small length scale effect for a non-local cantilever beam: A paradox solved", Nanotechnology, 19(34), 345703. https://doi.org/10.1088/0957-4484/19/34/345703 
  21. Challamel, N., Zhang, Z., Wang, C., Reddy, J., Wang, Q., Michelitsch, T. and Collet, B. (2014), "On nonconservativeness of Eringen,s nonlocal elasticity in beam mechanics: correction from a discrete-based approach", Arch. Appl. Mech., 84(9), 1275-1292. https://doi.org/10.1007/s00419-014-0862-x 
  22. Chen, C., Shi, L., Shariati, M., Toghroli, A., Mohamad, E.T., Bui, D.T. and Khorami, M. (2019), "Behavior of steel storage pallet racking connection-A review", Steel. Compos. Struct., 30(5), 457. https://doi.org/10.12989/scs.2019.30.5.457 
  23. 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 
  24. 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 
  25. 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. https://doi.org/10.12989/anr.2021.10.2.175 
  26. 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 
  27. Dong, Y., Gao, Y., Zhu, Q., Moradi, Z. and Safa, M. (2022), "TEGDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring", Eng. Anal. Bound. Elem., 138, 95-107. https://doi.org/10.1016/j.enganabound.2022.01.017 
  28. Ebrahimi, F. and Barati, M.R. (2017), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 39(3), 937-952. https://doi.org/10.1007/s40430-016-0551-5 
  29. Ebrahimi, F., Barati, M.R. and Haghi, P. (2018), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, 24(17), 3809-3818. https://doi.org/10.1177/1077546317711537 
  30. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019a), "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 
  31. Ebrahimi, F., Hajilak, Z.E., Habibi, M. and Safarpour, H. (2019b), "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 
  32. 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 
  33. Ebrahimi, F., Kokaba, M., Shaghaghi, G. and Selvamani, R. (2020b), "Dynamic characteristics of hygro-magneto-thermoelectrical nanobeam with non-ideal boundary conditions", Adv. Nano Res., 8(2), 169-182. https://doi.org/10.12989/anr.2020.8.2.169 
  34. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2019c), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Waves Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1694729 
  35. Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020c), "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 
  36. 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. http://doi.org/10.12989/anr.2017.5.2.141 
  37. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5 
  38. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803 
  39. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0 
  40. 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/10.1080/15397734.2019.1566743 
  41. 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 
  42. Fakher, M. and Hosseini-Hashemi, S. (2020a), "Nonlinear vibration analysis of two-phase local/nonlocal nanobeams with size-dependent nonlinearity by using Galerkin method", J. Vib. Control, 1077546320927619. https://doi.org/10.1177/1077546320927619 
  43. Fakher, M. and Hosseini-Hashemi, S. (2020b), "Vibration of twophase local/nonlocal Timoshenko nanobeams with an efficient shear-locking-free finite-element model and exact solution", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-020-01058-z 
  44. Fan, L., Huang, Y., Ji, D., Moradi, Z., Safa, M. and Amine Khadimallah, M. (2022), "Interaction of angular velocity and temperature rise in the thermo-inertia bifurcation buckling of FG laminated nanocomposite annular plates", Eng. Struct., 265, 114518. https://doi.org/10.1016/j.engstruct.2022.114518 
  45. Fernandez-Saez, J. and Zaera, R. (2017), "Vibrations of BernoulliEuler beams using the two-phase nonlocal elasticity theory", Int. J. Eng. Sci., 119, 232-248. https://doi.org/10.1016/j.ijengsci.2017.06.021 
  46. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037 
  47. Gao, N., Zhang, Z., Deng, J., Guo, X., Cheng, B. and Hou, H. (2022), "Acoustic metamaterials for noise reduction: A review", Adv. Mater. Technol., 2100698. https://doi.org/10.1002/admt.202100698 
  48. 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 
  49. 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 
  50. 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 
  51. 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 
  52. 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 
  53. 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 
  54. 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: Journal of Materials: Design and Applications, 232(8), 625-636.  https://doi.org/10.1177/1464420716642258
  55. 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
  56. 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. Pr., 31, 310-323.  https://doi.org/10.1016/j.jmapro.2017.11.009
  57. 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 
  58. 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/10.12989/ANR.2021.10.1.001
  59. 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 
  60. 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 
  61. 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 
  62. Hamidi, A., Houari, M.S.A., Mahmoud, S. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel. Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235 
  63. Hamidian, M., Shariati, M., Arabnejad, M. and Sinaei, H. (2011), "Assessment of high strength and light weight aggregate concrete properties using ultrasonic pulse velocity technique", Int. J. Phys. Sci., 6(22), 5261-5266. https://doi.org/10.5897/IJPS11.1081 
  64. 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", Waves Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1662968 
  65. 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 
  66. Hosseini, S.A. and Toghroli, A. (2021), "Effect of mixing Nanosilica and Perlite with pervious concrete for nitrate removal from the contaminated water", Adv. Concr. Constr., 11(6), 531-544. https://doi.org/10.12989/acc.2021.11.6.531 
  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., 
  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., 1-13. https://doi.org/10.1007/s00366-021-01320-y 
  71. Jiang, L., Wang, Y., Wang, X., Ning, F., Wen, S., Zhou, Y., Chen, S., Betts, A., Jerrams, S. and Zhou, F.L. (2021), "Electrohydrodynamic printing of a dielectric elastomer actuator and its application in tunable lenses", Compos. Part A, 147, 106461. https://doi.org/10.1016/j.compositesa.2021.106461 
  72. 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., 1-15. https://doi.org/10.1007/s00366-021-01391-x 
  73. Ke, L.L., Liu, C. and Wang, Y.S. (2015), "Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions", Physica E, 66, 93-106. https://doi.org/10.1016/j.physe.2014.10.002 
  74. Ke, L.L. and Wang, Y.S. (2012), "Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21(2), 025018. https://doi.org/10.1088/0964-1726/21/2/025018 
  75. Ke, L.L., Wang, Y.S. and Wang, Z.D. (2012), "Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory", Compos. Struct., 94(6), 2038-2047.  https://doi.org/10.1016/j.compstruct.2012.01.023
  76. Khanouki, M.M.A., Ramli Sulong, N.H., Shariati, M. and Tahir, M.M. (2016), "Investigation of through beam connection to concrete filled circular steel tube (CFCST) column", J. Constr. Steel Res., 121, 144-162. https://doi.org/10.1016/j.jcsr.2016.01.002 
  77. Kroner, E. (1967), "Elasticity theory of materials with long range cohesive forces", Int. J. Solids Struct., 3(5), 731-742. https://doi.org/10.1016/0020-7683(67)90049-2 
  78. Krumhansl, J. (1968), Some Considerations of the Relation Between Solid State Physics and Generalized Continuum Mechanics, Springer. 
  79. Kunin, I. (1968), The Theory of Elastic Media with Microstructure and the Theory of Dislocations, Springer 
  80. Li, D.Y., Toghroli, A., Shariati, M., Sajedi, F., Bui, D.T., Kianmehr, P., Mohamad, E.T. and Khorami, M. (2019), "Application of polymer, silica-fume and crushed rubber in the production of Pervious concrete", Smart Struct. Syst., 23(2), 207-214. https://doi.org/10.12989/sss.2019.23.2.207 
  81. Li, G., Yuan, H., Mou, J., Dai, E., Zhang, H., Li, Z., Zhao, Y., Dai, Y. and Zhang, X. (2022a), "Electrochemical detection of nitrate with carbon nanofibers and copper co-modified carbon fiber electrodes", Compos. Commun., 29, 101043. https://doi.org/10.1016/j.coco.2021.101043 
  82. Li, H., Hou, K., Xu, X., Jia, H., Zhu, L. and Mu, Y. (2022b), "Probabilistic energy flow calculation for regional integrated energy system considering cross-system failures", Appl. Energy, 308, 118326. https://doi.org/10.1016/j.apenergy.2021.118326 
  83. Li, J., Tang, F. and Habibi, M. (2020a), "Bi-directional thermal buckling and resonance frequency characteristics of a GNPreinforced composite nanostructure", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01110-y 
  84. 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., 1-22. https://doi.org/10.1007/s00366-020-01166-w 
  85. Li, Z., Peng, X., Hu, G., Zhang, D., Xu, Z., Peng, Y. and Xie, S. (2022c), "Towards real-time self-powered sensing with ample redundant charges by a piezostack-based frequency-converted generator from human motions", Energy Convers. Manag., 258, 115466. https://doi.org/10.1016/j.enconman.2022.115466 
  86. 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 
  87. 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 
  88. 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., 
  89. 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 
  90. 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 
  91. 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 
  92. Lu, C., Zhu, R., Yu, F., Jiang, X., Liu, Z., Dong, L., Hua, Q. and Ou, Z. (2021), "Gear rotational speed sensor based on FeCoSiB/Pb (Zr, Ti) O3 magnetoelectric composite", Measurement, 168, 108409. https://doi.org/10.1016/j.measurement.2020.108409 
  93. Luo, J., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Effect of simultaneous compressive and inertia loads on the bifurcation stability of shear deformable functionally graded annular fabrications reinforced with graphenes", Eur. J. Mech. A Solids, 104581. https://doi.org/10.1016/j.euromechsol.2022.104581 
  94. Ma, L., Liu, X. and Moradi, Z. "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 
  95. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E., Tounsi, A., Mahmoud, S., Tounsi, A. and Benrahou, K. (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 
  96. Mehrabi, P., Shariati, M., Kabirifar, K., Jarrah, M., Rasekh, H., Trung, N.T., Shariati, A. and Jahandari, S. (2021), "Effect of pumice powder and nano-clay on the strength and permeability of fiber-reinforced pervious concrete incorporating recycled concrete aggregate", Constr. Build. Mater., 287, 122652. https://doi.org/10.1016/j.conbuildmat.2021.122652 
  97. Michael, M., Meyyazhagan, A., Velayudhannair, K., Pappuswamy, M., Maria, A., Xavier, V., Balasubramanian, B., Baskaran, R., Kamyab, H. and Vasseghian, Y. (2022), "The content of heavy metals in cigarettes and the impact of their leachates on the aquatic ecosystem", Sustainability, 14(8), 4752. https://doi.org/10.3390/su14084752 
  98. 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 
  99. 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 
  100. 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 
  101. 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 
  102. 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 
  103. 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 Med., 1-24. https://doi.org/10.1080/17455030.2021.1926572 
  104. 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 
  105. 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 
  106. Naghipour, M., Yousofizinsaz, G. and Shariati, M. (2020), "Experimental study on axial compressive behavior of welded built-up CFT stub columns made by cold-formed sections with different welding lines", Steel. Compos. Struct., 34(3), 347-359. https://doi.org/10.12989/scs.2020.34.3.347 
  107. 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 
  108. Navi, B.R., Mohammadimehr, M. and Arani, A.G. (2019), "Active control of three-phase CNT/resin/fiber piezoelectric polymeric nanocomposite porous sandwich microbeam based on sinusoidal shear deformation theory", Steel. Compos. Struct., 32(6), 753-767. https://doi.org/10.12989/scs.2019.32.6.753 
  109. Nguyen, D.D., Tran, Q.Q. and Nguyen, D.K. (2017), "New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature", Aerosp. Sci. Technol., 71, 360-372. https://doi.org/10.1016/j.ast.2017.09.031 
  110. 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 
  111. Peng, Y., Xu, Z., Wang, M., Li, Z., Peng, J., Luo, J., Xie, S., Pu, H. and Yang, Z. (2021), "Investigation of frequency-up conversion effect on the performance improvement of stack-based piezoelectric generators", Renewable Energy, 172, 551-563. https://doi.org/10.1016/j.renene.2021.03.064 
  112. Polyanin, A.D. and Manzhirov, A.V. (2008), Handbook of Integral Equations, CRC press. 
  113. 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
  114. Razavian, L., Naghipour, M., Shariati, M. and Safa, M. (2020), "Experimental study of the behavior of composite timber columns confined with hollow rectangular steel sections under compression", Struct. Eng. Mech., 74(1), 145-156. https://doi.org/10.12989/sem.2020.74.1.145 
  115. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004 
  116. Romano, G. and Barretta, R. (2017), "Nonlocal elasticity in nanobeams: The stress-driven integral model", Int. J. Eng. Sci., 115, 14-27. https://doi.org/10.1016/j.ijengsci.2017.03.002 
  117. Romano, G., Barretta, R., Diaco, M. and de Sciarra, F.M. (2017), "Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams", Int. J. Mech. Sci., 121, 151-156. https://doi.org/10.1016/j.ijmecsci.2016.10.036 
  118. 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. 
  119. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019a), "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
  120. 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 threedimensional shell coupled with piezoelectric actuator", J. Vib. Control, 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465 
  121. 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 
  122. Shah, S.N.R., Sulong, N.H.R., Jumaat, M.Z. and Shariati, M. (2016a), "State-of-the-art review on the design and performance of steel pallet rack connections", Eng. Fail. Anal., 66, 240-258. https://doi.org/10.1016/j.engfailanal.2016.04.017 
  123. Shah, S.N.R., Sulong, N.H.R., Khan, R., Jumaat, M.Z. and Shariati, M. (2016b), "Behavior of industrial steel rack connections", Mech. Syst. Signal Pr., 70-71, 725-740. https://doi.org/10.1016/j.ymssp.2015.08.026 
  124. Shah, S.N.R., Sulong, N.H.R., Shariati, M. and Jumaat, M.Z. (2015), "Steel rack connections: Identification of most influential factors and a comparison of stiffness design methods", Plos One, 10(10), e0139422. https://doi.org/10.1371/journal.pone.0139422 
  125. 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 
  126. 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 
  127. 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 
  128. 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 
  129. Shariati, M. (2008), Assessment Building Using None-destructive Test Techniques (ultra Sonic Pulse Velocity and Schmidt Rebound Hammer), Universiti Putra Malaysia 
  130. Shariati, M., Ghorbani, M., Naghipour, M., Alinejad, N. and Toghroli, A. (2020d), "The effect of RBS connection on energy absorption in tall buildings with braced tube frame system", Steel. Compos. Struct., 34(3), 393. https://doi.org/10.12989/scs.2020.34.3.393 
  131. Shariati, M., Heyrati, A., Zandi, Y., Laka, H., Toghroli, A., Kianmehr, P., Safa, M., Salih, M.N.A. and Poi-Ngian, S. (2019), "Application of waste tire rubber aggregate in porous concrete", Smart Struct. Syst., 24(4), 553-566. https://doi.org/10.12989/sss.2019.24.4.553 
  132. Shariati, M., Ramli Sulong, N.H., Sinaei, H., Arabnejad Khanouki, M.M. and Shafigh, P. (2011), "Behavior of channel shear connectors in normal and light weight aggregate concrete (experimental and analytical study)", Adv. Mater. Res., 168, 2303-2307. https://doi.org/10.4028/www.scientific.net/AMR.168-170.2303 
  133. Shariati, M., Tahir, M.M., Wee, T.C., Shah, S.N.R., Jalali, A., Abdullahi, M.M. and Khorami, M. (2018), "Experimental investigations on monotonic and cyclic behavior of steel pallet rack connections", Eng. Fail. Anal., 85, 149-166. https://doi.org/10.1016/j.engfailanal.2017.08.014 
  134. Shen, Z., Zhang, J., Wu, S., Luo, X., Jenkins, B.M., Moody, M.P., Lozano-Perez, S. and Zeng, X. (2022), "Microstructure understanding of high Cr-Ni austenitic steel corrosion in hightemperature steam", Acta Materialia, 117634. https://doi.org/10.1016/j.actamat.2022.117634 
  135. Shi, D., Chen, Y., Li, Z., Dong, S., Li, L., Hou, M., Liu, H., Zhao, S., Chen, X. and Wong, C.P. (2022), "Anisotropic charge transport enabling high-throughput and high-aspect-ratio wet etching of silicon carbide", Small Methods, 2200329. https://doi.org/10.1002/smtd.202200329 
  136. 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 
  137. Toghroli, A., Mehrabi, P., Shariati, M., Trung, N.T., Jahandari, S. and Rasekh, H. (2020), "Evaluating the use of recycled concrete aggregate and pozzolanic additives in fiber-reinforced pervious concrete with industrial and recycled fibers", Constr. Build. Mater., 252, 118997. https://doi.org/10.1016/j.conbuildmat.2020.118997 
  138. Toghroli, A., Shariati, M., Karim, M.R. and Ibrahim, Z. (2017). "Investigation on composite polymer and silica fume-rubber aggregate pervious concrete", Fifth International Conference on Advances in Civil, Structural and Mechanical Engineering - CSM 2017, Zurich, Switzerland, September. 
  139. Toghroli, A., Shariati, M., Sajedi, F., Ibrahim, Z., Koting, S., Mohamad, E.T. and Khorami, M. (2018), "A review on pavement porous concrete using recycled waste materials", Smart Struct. Syst., 22(4), 433-440. https://doi.org/10.12989/sss.2018.22.4.433 
  140. Wan, Q., Li, Q., Chen, Y., Wang, T.H., He, X., Li, J. and Lin, C. (2004), "Fabrication and ethanol sensing characteristics of ZnO nanowire gas sensors", Appl. Phys. Lett., 84(18), 3654-3656. https://doi.org/10.1063/1.1738932 
  141. Wang, H., Habibi, M., Marzouki, R., Majdi, A., Shariati, M., Denic, N., Zakic, A., Khorami, M., Khadimallah, M.A. and Ebid, A.A.K. (2022a), "Improving the self-healing of cementitious materials with a hydrogel system", Gels, 8(5), 278. https://doi.org/10.3390/gels8050278 
  142. Wang, H., Wu, X., Zheng, X. and Yuan, X. (2021), "Virtual voltage vector based model predictive control for a nine-phase open-end winding pmsm with a common DC Bus", IEEE T. Industr. Electr., https://doi.org/10.1109/TIE.2021.3088372 
  143. 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 
  144. Wang, Q. (2002), "On buckling of column structures with a pair of piezoelectric layers", Eng. Struct., 24(2), 199-205. https://doi.org/10.1016/S0141-0296(01)00088-8 
  145. Wang, Y., Yang, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022b), "Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation", Eur. J. Mech. A Solids, 95, 104638. https://doi.org/10.1016/j.euromechsol.2022.104638 
  146. Wang, Y., Zhu, X. and Dai, H. (2016), "Exact solutions for the static bending of Euler-Bernoulli beams using Eringen,s twophase local/nonlocal model", Aip Adv., 6(8), 085114. https://doi.org/10.1063/1.4961695 
  147. 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 
  148. Wang, Z.L. and Song, J. (2006), "Piezoelectric nanogenerators based on zinc oxide nanowire arrays", Science, 312(5771), 242-246. https://doi.org/10.1126/science.1124005 
  149. Wu, H., Hu, X., Li, X., Sheng, M., Sheng, X., Lu, X. and Qu, J. (2022), "Large-scale fabrication of flexible EPDM/MXene/PW phase change composites with excellent light-to-thermal conversion efficiency via water-assisted melt blending", Compos. Part A, 152, 106713. https://doi.org/10.1016/j.compositesa.2021.106713 
  150. 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 
  151. Wu, T. and Liu, G. (2000), "Application of generalized differential quadrature rule to sixth-order differential equations", Commun. Numer. Methods Eng., 16(11), 777-784. https://doi.org/10.1002/1099-0887(200011)16:11<777::AIDCNM375>3.0.CO,2-6 
  152. Xia, W., Du, J., Habibi, M., Shariati, M. and Khadimallah, M.A. (2022), "Application of Chebyshev-based GDQ and Newmark methods to viscothermoelasticity responses of FG composite annular systems", Eng. Anal. Bound. Elem., 143, 28-42. https://doi.org/10.1016/j.enganabound.2022.06.003 
  153. Xie, X. and Chen, D. (2022), "Data-driven dynamic harmonic model for modern household appliances", Appl. Energy, 312, 118759. https://doi.org/10.1016/j.apenergy.2022.118759 
  154. Xiong, Q.M., Chen, Z., Huang, J.T., Zhang, M., Song, H., Hou, X.F., Li, X.B. and Feng, Z.J. (2020), "Preparation, structure and mechanical properties of Sialon ceramics by transition metalcatalyzed nitriding reaction", Rare Metals, 39(5), 589-596.  https://doi.org/10.1007/s12598-020-01385-6
  155. 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 
  156. Yan, W., Feng, G., Luo, X., Hu, Y.-Q., Guo, J., Yu, Z., Zhao, Z. and Ding, S. (2022), "Singlet oxygen-promoted one-pot synthesis of highly ordered mesoporous silica materials via the radical route", Green Chem., 24(12), 4778-4782. https://doi.org/10.1039/D2GC00869F 
  157. Yang, N., Moradi, Z., Khadimallah, M.A. and Arvin, H. (2022), "Application of the Chebyshev-Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment", Eng. Anal. Bound. Elem., 139, 169-179. https://doi.org/10.1016/j.enganabound.2022.03.013 
  158. Yu, D., Ma, Z. and Wang, R. (2022a), "Efficient smart grid load balancing via fog and cloud computing", Math. Probl. Eng., 2022. https://doi.org/10.1155/2022/3151249 
  159. Yu, D., Wu, J., Wang, W. and Gu, B. (2022b), "Optimal performance of hybrid energy system in the presence of electrical and heat storage systems under uncertainties using stochastic p-robust optimization technique", Sust. Cities Soc., 83, 103935. https://doi.org/10.1016/j.scs.2022.103935 
  160. Yu, X., Maalla, A. and Moradi, Z. (2022c), "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. 
  161. 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 
  162. Zhang, L., Zhang, H. and Cai, G. (2022), "The multi-class fault diagnosis of wind turbine bearing based on multi-source signal fusion and deep learning generative model", IEEE T Instr. Measur., 71, 1-12. https://doi.org/10.1109/TIM.2022.3178483 
  163. Zhang, X., Tang, Y., Zhang, F. and Lee, C.S. (2016), "A novel aluminum-graphite dual-ion battery", Adv. Energy Mater., 6(11), 1502588. 
  164. 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", Waves Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1948627 
  165. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. "Bending and stress responses of the hybrid axisymmetric system via statespace method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1 
  166. 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 
  167. Zhou, H., Xu, C., Lu, C., Jiang, X., Zhang, Z., Wang, J., Xiao, X., Xin, M. and Wang, L. (2021), "Investigation of transient magnetoelectric response of magnetostrictive/piezoelectric composite applicable for lightning current sensing", Sensors Actuat. A Phys., 329, 112789. https://doi.org/10.1016/j.sna.2021.112789 
  168. Zhou, J., Bai, J. and Liu, Y. (2022), "Fabrication and modeling of matching system for air-coupled transducer", Micromachines, 13(5), 781. 
  169. Zhou, Z.G., Du, S.Y. and Wu, L.Z. (2007), "Investigation of antiplane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the nonlocal theory", Compos. Struct., 78(4), 575-583. https://doi.org/10.1016/j.compstruct.2005.11.020 
  170. Zhou, Z.-G. and Wang, B. (2002), "The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory", Int. J. Eng. Sci., 40(3), 303-317. https://doi.org/10.1016/S0020-7225(01)00069-6 
  171. Zhou, Z.G., Wu, L.Z. and Du, S.Y. (2006), "Non-local theory solution for a Mode I crack in piezoelectric materials", Eur. J. Mech. A Solids, 25(5), 793-807. https://doi.org/10.1016/j.euromechsol.2005.10.003 
  172. Zhu, X. and Li, L. (2017), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", Int. J. Mech. Sci., 133, 639-650. https://doi.org/10.1016/j.ijmecsci.2017.09.030 
  173. Zhu, X., Wang, Y. and Dai, H.H. (2017), "Buckling analysis of Euler-Bernoulli beams using Eringen,s two-phase nonlocal model", Int. J. Eng. Sci., 116, 130-140. https://doi.org/10.1016/j.ijengsci.2017.03.008