DOI QR코드

DOI QR Code

A comprehensive review on the modeling of smart piezoelectric nanostructures

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Hosseini, S.H.S. (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Singhal, Abhinav (Department of mathematics, Madanapalle Institute of technology and sciences)
  • Received : 2019.04.02
  • Accepted : 2019.08.26
  • Published : 2020.06.10

Abstract

In this paper, a comprehensive review of nanostructures that exhibit piezoelectric behavior on all mechanical, buckling, vibrational, thermal and electrical properties is presented. It is firstly explained vast application of materials with their piezoelectric property and also introduction of other properties. Initially, more application of material which have piezoelectric property is introduced. Zinc oxide (ZnO), boron nitride (BN) and gallium nitride (GaN) respectively, are more application of piezoelectric materials. The nonlocal elasticity theory and piezoelectric constitutive relations are demonstrated to evaluate problems and analyses. Three different approaches consisting of atomistic modeling, continuum modeling and nano-scale continuum modeling in the investigation atomistic simulation of piezoelectric nanostructures are explained. Focusing on piezoelectric behavior, investigation of analyses is performed on fields of surface and small scale effects, buckling, vibration and wave propagation. Different investigations are available in literature focusing on the synthesis, applications and mechanical behaviors of piezoelectric nanostructures. In the study of vibration behavior, researches are studied on fields of linear and nonlinear, longitudinal and transverse, free and forced vibrations. This paper is intended to provide an introduction of the development of the piezoelectric nanostructures. The key issue is a very good understanding of mechanical and electrical behaviors and characteristics of piezoelectric structures to employ in electromechanical systems.

Keywords

References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.
  2. Abdollahian, M., Ghorbanpour Arani, A., Mosallaie Barzoki, A. A., Kolahchi, R. and Loghman, A. (2013), "Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM", Physica B: Condensed Matter, 418, 1-15. https://doi.org/10.1016/j.physb.2013.02.037.
  3. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  4. Agrawal, R. and Espinosa, H.D. (2011), "Giant piezoelectric size effects in zinc oxide and gallium nitride nanowires. A first principles investigation", Nano letters, 11(2), 786-790. https://doi.org/10.1021/nl104004d
  5. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct, 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963.
  6. Aissani, K., Bouiadjra, M. B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743.
  7. Akbas, S. D. (2018), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219-242. https://doi.org/10.12989/anr.2018.6.3.219.
  8. Akgoz, B. and Civalek, O. (2011), "Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories", J. Comput. Theroetical Nanosci., 8, 1821-1827. https://doi.org/10.1166/jctn.2011.1888.
  9. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195.
  10. Akgoz, B. and Civalek O. (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024.
  11. Al-Basyouni, K. S., Tounsi, A. and Mahmoud, S. R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct, 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070.
  12. Ansari, R., Norouzzadeh, A., Gholami, R., Faghih Shojaei, M. and Hosseinzadeh, M. (2014), "Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment", Physica E Low Dimensional Syst. Nanostruct., 61, 148-157. https://doi.org/10.1016/j.physe.2014.04.004.
  13. Ansari, R., Rouhi, S., Mirnezhad, M. and Aryayi, M. (2015), "Stability characteristics of single-walled boron nitride nanotubes", Arch. Civil Mech. Eng., 15(1), 162-170. https://doi.org/10.1016/j.acme.2014.01.008.
  14. Ansari, R., Oskouie, M. F., Gholami, R. and Sadeghi, F. (2016), "Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory", Compos. Part B Eng., 89, 316-327. https://doi.org/10.1016/j.compositesb.2015.12.029.
  15. Aphale, S., Fleming, A.J. and Moheimani, S.O.R. (2007), "High speed nano-scale positioning using a piezoelectric tube actuator with active shunt control", Micro Nano Lett., 2(1), 9-12. https://doi.org/10.1049/mnl:20065075.
  16. Araneo, R. and Falconi, C. (2013), "Lateral bending of tapered piezo-semiconductive nanostructures for ultra-sensitive mechanical force to voltage conversion", Nanotechnology, 24(26), 265707. https://doi.org/10.1088/0957-4484/24/26/265707.
  17. Arani, A. G. and Haghparast, E. (2011), "Electro-Mechanical Buckling of a Piezoelectric Annular Plate Reinforced with BNNTs Under Thermal Environment", J. Solid Mech., 3(4), 379-391.
  18. Arani, A. G., Haghparast, E. and Amir, S. (2012a), "Analytical Solution for Electro-mechanical Behavior of Piezoelectric Rotating Shaft Reinforced by BNNTs under Non-axisymmetric Internal Pressure", J. Solid Mech., 4(4), 339-354.
  19. Arani, A. G., Atabakhshian, V., Loghman, A., Shajari, A. R. and Amir, S. (2012b), "Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method", Physica B: Condensed Matter, 407(13), 2549-2555. https://doi.org/10.1016/j.physb.2012.03.065.
  20. Arani, A. G., Vossough, H., Kolahchi, R. and Barzoki, A. M. (2012c), "Electro-thermo nonlocal nonlinear vibration in an embedded polymeric piezoelectric micro plate reinforced by DWBNNTs using DQM", J. Mech. Sci. Technol., 26(10), 3047-3057. https://doi.org/10.1007/s12206-012-0816-6.
  21. Arani, A. G., Shokravi, M., Amir, S. and Mozdianfard, M. R. (2012d), "Nonlocal electro-thermal transverse vibration of embedded fluid-conveying DWBNNTs", J. Mech. Sci. Technol., 26(5), 1455-1462. https://doi.org/10.1007/s12206-012-0307-9.
  22. Arani, A. G., Haghshenas, A., Amir, S., Mozdianfard, M. R. and Latifi, M. (2013a), "Electro-thermo-mechanical response of thick-walled piezoelectric cylinder reinforced by boron-nitride nanotubes", Strength Mater., 45(1), 102-115. https://doi.org/10.1007/s11223-013-9437-2.
  23. Arani, A. G., Bidgoli, A. H., Ravandi, A. K., Roudbari, M. A., Amir, S., & Azizkhani, M. B. (2013b), "Induced nonlocal electric wave propagation of boron nitride nanotubes", J. Mech. Sci. Technol., 27(10), 3063-3071. https://doi.org/10.1007/s12206-013-0705-7.
  24. Arani, A. G., Kolahchi, R. and Mortazavi, S. A. (2014), "Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems", J. Mech. Mater. Design, 10(2), 179-191. https://doi.org/10.1007/s10999-014-9239-0.
  25. Arefi, M. and Zenkour, A. M. (2017), "Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin-Voigt viscoelastic nanoplate and two piezoelectric layers", Acta Mechanica, 228(2), 475-493. https://doi.org/10.1007/s00707-016-1716-0.
  26. Arya, S. K., Saha, S., Ramirez-Vick, J. E., Gupta, V., Bhansali, S. and Singh, S. P. (2012), "Recent advances in ZnO nanostructures and thin films for biosensor applications: Review", Analytica Chimica Acta, 737, 1-21. https://doi.org/10.1016/j.aca.2012.05.048.
  27. Asemi, S. R. and Farajpour, A. (2014), "Thermo-electro-mechanical vibration of coupled piezoelectric-nanoplate systems under non-uniform voltage distribution embedded in Pasternak elastic medium", Current Appl. Phys., 14(5), 814-832. https://doi.org/10.1016/j.cap.2014.03.012.
  28. Attia, A., Bousahla, A. A., Tounsi, A., Mahmoud, S. R. and Alwabli, A. S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  29. Aydin, M. (2013), "Vibrational and electronic properties of single-walled and double-walled boron nitride nanotubes", Vib. Spectroscopy, 66, 30-42. https://doi.org/10.1016/j.vibspec.2013.01.011.
  30. Badr, B. M. and Ali, W. G. (2010), "Nanopositioning fuzzy control for piezoelectric actuators", J. Eng. Technol., 10, 70-74.
  31. Bagheri, M., Bahari, A., Amiri, M. and Dehbandi, B. (2014), "Electronic and structural properties of Au-doped zigzag boron nitride nanotubes: A DFT study", Solid State Communications, 189, 1-4. https://doi.org/10.1016/j.ssc.2014.02.027.
  32. Bailey, T. and Ubbard, J. E. (1985), "Distributed piezoelectric-polymer active vibration control of a cantilever beam", J. Guidance Control Dynam., 8(5), 605-611. https://doi.org/10.2514/3.20029.
  33. Baima, J., Erba, A., Maschio, L., Zicovich-Wilson, C. M., Dovesi, R. and Kirtman, B. (2016), "Direct Piezoelectric Tensor of 3D Periodic Systems through a Coupled Perturbed Hartree- Fock/Kohn-Sham Method", Z. Phys. Chem., 230(5-7), 719-736. https://doi.org/10.1515/zpch-2015-0701.
  34. Bando, Y., Ogawa, K. and Golberg, D. (2001), "Insulating nanocables: Invar Fe-Ni alloy nanorods inside BN nanotubes", Chem. Phys. Lett., 347(4), 349-354. https://doi.org/10.1016/S0009-2614(01)01075-2.
  35. Barati, M.R. (2017), "On non-linear vibrations of flexoelectric nanobeams", J. Eng. Sci., 121, 143-153. https://doi.org/10.1016/j.ijengsci.2017.09.001.
  36. Boughey, F. L., Davies, T., Datta, A., Whiter, R. A., Sahonta, S. L. and Kar-Narayan, S. (2016), "Vertically aligned zinc oxide nanowires electrodeposited within porous polycarbonate templates for vibrational energy harvesting", Nanotechnology, 27(28), 28LT02. https://doi.org/10.1088/0957-4484/27/28/28LT02.
  37. Brush, D. O. and Almroth, B. O. (1975), Buckling of Bars, Plates, And Shells, McGraw-Hill, NY, USA.
  38. Capsal, J.F., Dantras, E., Laffont, L., Dandurand, J. and Lacabanne, C. (2010), "Nanotexture influence of BaTiO3 particles on piezoelectric behaviour of PA 11/BaTiO3 nanocomposites", J. Non Crystalline Solids, 356(11-17), 629-634. https://doi.org/10.1016/j.jnoncrysol.2009.06.050.
  39. Chang, J., Dommer, M., Chang, C. and Lin, L. (2012), "Piezoelectric nanofibers for energy scavenging applications", Nano Energy, 1(3), 356-371. https://doi.org/10.1016/j.nanoen.2012.02.003.
  40. Chen, C. Q., Shi, Y., Zhang, Y. S., Zhu, J. and Yan, Y. J. (2006), "Size dependence of Young's modulus in ZnO nanowires", Physical Rev. Lett., 96(7), 075505. https://doi.org/10.1103/PhysRevLett.96.075505.
  41. Chen, H., Chen, Y., Liu, Y., Fu, L., Huang, C. and Llewellyn, D. (2008), "Over 1.0 mm-long boron nitride nanotubes", Chem. Phys. Lett., 463(1), 130-133. https://doi.org/10.1016/j.cplett.2008.08.007.
  42. Chen, X., Xu, S., Yao, N. and Shi, Y. (2010), "1.6 V nanogenerator for mechanical energy harvesting using PZT nanofibers", Nano Letters, 10(6), 2133-2137. https://doi.org/10.1021/nl100812k.
  43. Chen, J. and Lee, J. D. (2010), "Atomic Formulation of Nano-Piezoelectricity in Barium Titanate", Nanosci. Nanotechnol. Lett., 2(1), 26-29. https://doi.org/10.1166/nnl.2010.1048.
  44. Chen, Y. Q., Zheng, X. J. and Li, W. (2010), "Size effect of mechanical behavior for lead-free (Na0. 82K0. 18) 0.5 Bi0. 5TiO3 nanofibers by nanoindentation", Mater. Sci. Eng. A Struct. Mater., 527(21), 5462. https://doi.org/10.1016/j.msea.2010.05.066
  45. Cheng, G. S., Zhang, L. D., Zhu, Y., Fei, G. T., Li, L., Mo, C. M. and Mao, Y. Q. (1999), "Large-scale synthesis of single crystalline gallium nitride nanowires", Appl. Phys. Lett., 75(16), 2455-2457. https://doi.org/10.1063/1.125046.
  46. Cheng, J., Ding, R., Liu, Y., Ding, Z. and Zhang, L. (2007a), "Computer simulation of hydrogen physisorption in single-walled boron nitride nanotube arrays", Comput. Mater. Sci., 40(3), 341-344. https://doi.org/10.1016/j.commatsci.2007.01.006.
  47. Cheng, J., Zhang, L., Ding, R., Ding, Z., Wang, X. and Wang, Z. (2007b), "Grand canonical Monte Carlo simulation of hydrogen physisorption in single-walled boron nitride nanotubes", J. Hydrogen Energy, 32(15), 3402-3405. https://doi.org/10.1016/j.ijhydene.2007.02.037.
  48. Cherif, R. H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1.
  49. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  50. Choi, M., Murillo, G., Hwang, S., Kim, J. W., Jung, J. H., Chen, C. Y. and Lee, M. (2017), "Mechanical and electrical characterization of PVDF-ZnO hybrid structure for application to nanogenerator", Nano Energy, 33, 462-468. https://doi.org/10.1016/j.nanoen.2017.01.062
  51. Chopra, N. G. and Zettl, A. (1998), "Measurement of the elastic modulus of a multi-wall boron nitride nanotube", Solid State Communications, 105(5), 297-300. https://doi.org/10.1016/S0038-1098(97)10125-9
  52. Chowdhury, R., Adhikari, S. and Scarpa, F. (2010), "Elasticity and piezoelectricity of zinc oxide nanostructure", Physica E Low Dimensional Syst. Nanostruct., 42(8), 2036-2040. https://doi.org/10.1016/j.physe.2010.03.018.
  53. Ciofani, G., Raffa, V., Menciassi, A. and Cuschieri, A. (2009), "Boron nitride nanotubes: An innovative tool for nanomedicine", Nano Today, 4(1), 8-10. https://doi.org/10.1016/j.nantod.2008.09.001.
  54. Civalek, O. and Demir C. (2011), "Buckling and bending analyses of cantilever carbon nanotubes using the Euler-Bernoulli beam theory based on non-local continuum model", Asian J. Civil Eng., 12(5), 651-661.
  55. Croft, D., Stilson, S. and Devasia, S. (1999), "Optimal tracking of piezo-based nanopositioners", Nanotechnology, 10(2), 201. https://doi.org/10.1088/0957-4484/10/2/316.
  56. Curie, J. (1880), "Developpement par compression de l'electricite polaire dans les cristaux hemiedres a faces inclinees", Bull. Soc. Fr. Mineral., 3(90). https://doi.org/10.3406/bulmi.1880.1564.
  57. Dai, S., Gharbi, M., Sharma, P. and Park, H. S. (2011), "Surface piezoelectricity: size effects in nanostructures and the emergence of piezoelectricity in non-piezoelectric materials", J. Appl. Phys., 110(10), 104305. https://doi.org/10.1063/1.3660431.
  58. Dai, S. and Park, H. S. (2013), "Surface effects on the piezoelectricity of ZnO nanowires", J. Mech. Phys. Solids, 61(2), 385-397. https://doi.org/10.1016/j.jmps.2012.10.003.
  59. Dehkordi, S. F. and Beni, Y. T. (2017), "Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory", Int. J. Mech. Sci., 128, 125-139. https://doi.org/10.1016/j.ijmecsci.2017.04.004.
  60. Demir, C., Mercan, K. and Civalek, O. (2016), "Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel", Composites Part B, 94, 1-10. https://doi.org/10.1016/j.compositesb.2016.03.031.
  61. Demir, C. and Civalek, O. (2017), "A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix", Compos Struct, 168, 872-884. https://doi.org/10.1016/j.compstruct.2017.02.091.
  62. Djurisic, A. B., Tam, K. H., Hsu, Y. F., Zhang, S. L., Xie, M. H. and Chan, W. K. (2007), "GaN nanowires-influence of the starting material on nanowire growth", Thin Solid Films, 516(2), 238-242. https://doi.org/10.1016/j.tsf.2007.06.031.
  63. Djurisic, A. B., Ng, A. M. C. and Chen, X. Y. (2010), "ZnO nanostructures for optoelectronics: material properties and device applications", Progress Quantum Electronics, 34(4), 191-259. https://doi.org/10.1016/j.pquantelec.2010.04.001.
  64. Draiche, K., Tounsi, A. and Mahmoud, S. R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671.
  65. Duan, X. and Lieber, C. M. (2000), "Laser-assisted catalytic growth of single crystal GaN nanowires", J. American Chem. Society, 122(1), 188-189. https://doi.org/10.1021/ja993713u.
  66. Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007.
  67. Ebrahimi, F. and Barati, M. R. (2017a), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazilian Soc. Mech. Sci. Eng., 39(3), 937-952. https://doi.org/10.1007/s40430-016-0551-5.
  68. Ebrahimi, F. and Barati, M. R. (2017b), "Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects", Nanomater. Nanotechnol., 7, https://doi.org/10.1177/1847980417713106.
  69. Ebrahimi, F. and Barati, M.R. (2017c), "Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects", Mech. Adv. Mater. Struct., 1-11. https://doi.org/10.1080/15376494.2017.1285464.
  70. Ebrahimi, F. and Dabbagh, A. (2018), "Viscoelastic wave propagation analysis of axially motivated double-layered graphene sheets via nonlocal strain gradient theory", Waves in Random Complex Media, 1-20. https://doi.org/10.1080/17455030.2018.1490505.
  71. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  72. Fakrach, B., Rahmani, A., Chadli, H., Sbai, K. and Sauvajol, J. L. (2009), "Raman spectrum of single-walled boron nitride nanotube", Physica E Low Dimensional Syst. Nanostruct., 41(10), 1800-1805. https://doi.org/10.1016/j.physe.2009.07.002.
  73. Fan, Z. and Lu, J. G. (2005), "Zinc oxide nanostructures: synthesis and properties", J. Nanosci. Nanotechnol., 5(10), 1561-1573. https://doi.org/10.1166/jnn.2005.182.
  74. Fang, X. Q. and Liu, J. X. (2011), "Dynamic stress and electric displacement around a nano-fiber in piezoelectric nanocomposites under electro-elastic waves", Philosophical Magazine Letters, 91(9), 621-631. https://doi.org/10.1080/09500839.2011.600258.
  75. Fang, X. Q. and Zhu, C. S. (2017), "Size-dependent nonlinear vibration of nonhomogeneous shell embedded with a piezoelectric layer based on surface/interface theory", Compos. Struct., 160, 1191-1197. https://doi.org/10.1016/j.compstruct.2016.11.008.
  76. Farajpour, A., Rastgoo, A. and Mohammadi, M. (2017), "Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment", Physica B: Condensed Matter, 509, 100-114. https://doi.org/10.1016/j.physb.2017.01.006.
  77. Fourn, H., Atmane, H. A., Bourada, M., Bousahla, A. A., Tounsi, A. and Mahmoud, S. R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  78. Freitas, A., Azevedo, S. and Kaschny, J. R. (2013), "Effects of a transverse electric field on the electronic properties of single-and multi-wall BN nanotubes", Solid State Communications, 153(1), 40-45. https://doi.org/10.1016/j.ssc.2012.09.024.
  79. Ganji, M. D. and Mohammadi-Nejad, A. (2008), "Simulation of STM technique for electron transport through boron-nitride nanotubes", Physics Letters A, 372(27), 4839-4844. https://doi.org/10.1016/j.physleta.2008.05.038.
  80. Gao, P. X. and Wang, Z. L. (2005), "Nanoarchitectures of semiconducting and piezoelectric zinc oxide", J. Appl. Phys., 97(4), 044304. https://doi.org/10.1063/1.1847701.
  81. Gheshlaghi, B. and Hasheminejad, S. M. (2012), "Vibration analysis of piezoelectric nanowires with surface and small scale effects", Current Appl. Phys., 12(4), 1096-1099. https://doi.org/10.1016/j.cap.2012.01.014.
  82. Ghorbanpour Arani, A., Shams, S., Amir, S. and Khoddami Maraghi, Z. (2012a), "Effects of Electro-Thermal Fields on Buckling of a Piezoelectric Polymeric Shell Reinforced with DWBNNTs", J. Nanostruct., 2(3), 345-355.
  83. Ghorbanpour Arani, A., Amir, S., Shajari, A. R. and Mozdianfard, M.R. (2012b), "Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory", Compos. Part B Eng., 43(2), 195-203. https://doi.org/10.1016/j.compositesb.2011.10.012.
  84. Ghorbanpour Arani, A., Shajari, A. R., Amir, S. and Loghman, A. (2012c), "Electro-thermo-mechanical nonlinear nonlocal vibration and instability of embedded micro-tube reinforced by BNNT, conveying fluid", Physica E Low Dimensional Syst. Nanostruct., 45, 109-121. https://doi.org/10.1016/j.compositesb.2011.10.012.
  85. Ghorbanpour Arani, A., Roudbari, M. A. and Amir, S. (2012d), "Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle", Physica B Condensed Matter, 407(17), 3646-3653. https://doi.org/10.1016/j.physb.2012.05.043.
  86. Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012e), "Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory", Physica B: Condensed Matter, 407(21), 4281-4286. https://doi.org/10.1016/j.physb.2012.07.018.
  87. Ghorbanpour Arani, A., Abdollahian, M., Kolahchi, R. and Rahmati, A. H. (2013a), "Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model", Compos. Part B Eng., 51, 291-299. https://doi.org/10.1016/j.compositesb.2013.03.017.
  88. Ghorbanpour Arani, A., Shajari, A. R., Atabakhshian, V., Amir, S. and Loghman, A. (2013a), "Nonlinear dynamical response of embedded fluid-conveyed micro-tube reinforced by BNNTs", Compos. Part B Eng., 44(1), 424-432. https://doi.org/10.1016/j.compositesb.2012.04.025.
  89. Ghorbanpour Arani, A., Hashemian, M. and Kolahchi, R. (2013b), "Time discretization effect on the nonlinear vibration of embedded SWBNNT conveying viscous fluid", Compos. Part B Eng., 54, 298-306. https://doi.org/10.1016/j.compositesb.2013.05.031.
  90. Ghorbanpour Arani, A. and Roudbari, M. A. (2013), "Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle", Thin Solid Films, 542, 232-241. https://doi.org/10.1016/j.tsf.2013.06.025.
  91. Ghorbanpour Arani, A. and Amir, S. (2013), "Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory", Physica B: Condensed Matter, 419, 1-6. https://doi.org/10.1016/j.physb.2013.03.010.
  92. Guo, L. and Singh, R. N. (2009), "Catalytic growth of boron nitride nanotubes using gas precursors", Physica E Low Dimensional Syst. Nanostruct., 41(3), 448-453. https://doi.org/10.1016/j.physe.2008.09.009.
  93. Gupta, M. K., Sinha, N., Singh, B. K., Singh, N., Kumar, K. and Kumar, B. (2009), "Piezoelectric, dielectric, optical and electrical characterization of solution grown flower-like ZnO nanocrystal", Materials Lett., 63(22), 1910-1913. https://doi.org/10.1016/j.matlet.2009.06.003.
  94. Haghpanahi, M., Oveisi, A. and Gudarzi, M. (2013), "Vibration analysis of piezoelectric nanowires using the finite element method", Int. Res. J. Appl. Basic Sci., 4(1), 205-212.
  95. Hai-Bo, L., Mao-Sheng, C., Jie, Y., Da-Wei, W., Quan-Liang, Z. and Fu-Chi, W. (2008), "Enhanced mechanical behaviour of lead zirconate titanate piezoelectric composites incorporating zinc oxide nanowhiskers", Chinese Physics B, 17(11), 4323. https://doi.org/10.1088/1674-1056/17/11/060.
  96. Han, W., Fan, S., Li, Q. and Hu, Y. (1997), "Synthesis of gallium nitride nanorods through a carbon nanotube-confined reaction", Science, 277(5330), 1287-1289. https://doi.org/10.1126/science.277.5330.1287.
  97. Han, W., Redlich, P., Ernst, F. and Ruhle, M. (2000), "Synthesis of GaN-carbon composite nanotubes and GaN nanorods by arc discharge in nitrogen atmosphere", Appl. Phys. Lett., 76(5), 652-654. https://doi.org/10.1063/1.125848.
  98. He, J. and Lilley, C. M. (2008a), "Surface effect on the elastic behavior of static bending nanowires", Nano Letters, 8(7), 1798-1802. https://doi.org/10.1021/nl0733233.
  99. He, J. and Lilley, C. M. (2008b), "Surface stress effect on bending resonance of nanowires with different boundary conditions", Appl. Phys. Lett., 93(26), 263108. https://doi.org/10.1063/1.3050108.
  100. Hebali, H., Tounsi, A., Houari, M. S. A., Bessaim, A. and Bedia, E. A. A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.
  101. Hiralal, P., Unalan, H. E. and Amaratunga, G. A. (2012), "Nanowires for energy generation", Nanotechnology, 23(19), 194002. https://doi.org/10.1088/0957-4484/23/19/194002.
  102. Hocevar, M., Songmuang, R., Den Hertog, M., Besombes, L., Bleuse, J., Niquet, Y. M. and Pelekanos, N. T. (2013), "Residual strain and piezoelectric effects in passivated GaAs/AlGaAs core-shell nanowires", Appl. Phys. Lett., 102(19), 191103. https://doi.org/10.1063/1.4803685.
  103. Hosseini, M., Maryam, A. Z. B. and Bahaadini, R. (2017), "Forced vibrations of fluid-conveyed double piezoelectric functionally graded micropipes subjected to moving load", Microfluidics Nanofluidics, 21(8), 134. https://doi.org/10.1007/s10404-017-1963-y.
  104. Hosseini-Hashemi, S., Nazemnezhad, R. and Bedroud, M. (2014), "Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity", Appl. Math. Modelling, 38(14), 3538-3553. https://doi.org/10.1016/j.apm.2013.11.068.
  105. Houari, M. S. 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., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257.
  106. Huang, G. Y. and Yu, S. W. (2006), "Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring", Physica Status Solidi (b), 243(4), 22-24. https://doi.org/10.1002/pssb.200541521.
  107. Hughes, W. L. and Wang, Z. L. (2004), "Formation of piezoelectric single-crystal nanorings and nanobows", J. American Chem. Soc., 126(21), 6703-6709. https://doi.org/10.1021/ja049266m.
  108. Hughes, W. L. and Wang, Z. L. (2005), "Controlled synthesis and manipulation of ZnO nanorings and nanobows", Appl. Phys. Lett., 86(4), 043106. https://doi.org/10.1063/1.1853514.
  109. Hwang, H. J., Choi, W. Y. and Kang, J. W. (2005), "Molecular dynamics simulations of nanomemory element based on boron-nitride nanotube-to-peapod transition", Comput. Mater. Sci., 33(1), 317-324. https://doi.org/10.1016/j.commatsci.2004.12.068.
  110. Hanifi Hachemi Amar, L., Kaci, A., Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/sem.2017.64.5.527.
  111. Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y., (2016c), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. http://dx.doi.org/10.12989/sem.2016.57.2.315.
  112. Ishii, T., Sato, T., Sekikawa, Y. and Iwata, M. (1981), "Growth of whiskers of hexagonal boron nitride", J. Crystal Growth, 52, 285-289. https://doi.org/10.1016/0022-0248(81)90206-2.
  113. Jafari, A., Khatibi, A. A. and Mashhadi, M. M. (2012), "Evaluation of Mechanical and Piezoelectric Properties of Boron Nitride Nanotube: A Novel Electrostructural Analogy Approach", J. Comput. Theroetical Nanosci., 9(3), 461-468. https://doi.org/10.1166/jctn.2012.2047.
  114. Jiang, L. and Guo, W. (2011), "A molecular mechanics study on size-dependent elastic properties of single-walled boron nitride nanotubes", J. Mech. Phys. Solids, 59(6), 1204-1213. https://doi.org/10.1016/j.jmps.2011.03.008.
  115. Jing, Y. H., Yu, K. P., Qin, X. and Shen, J. (2012), "Composition-dependent mechanical and thermal transport properties of carbon/silicon core/shell nanowires", J. Shanghai Jiaotong University (Science), 17, 743-747. https://doi.org/10.1007/s12204-012-1357-y.
  116. Karimi, M., Shahidi, A. R. and Ziaei-Rad, S. (2017), "Surface layer and nonlocal parameter effects on the in-phase and out-of-phase natural frequencies of a double-layer piezoelectric nanoplate under thermo-electro-mechanical loadings", Microsyst. Technol., 23(10), 4903-4915. https://doi.org/10.1007/s00542-017-3395-8.
  117. 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.
  118. 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.
  119. Kheibari, F. and Beni, Y. T. (2017), "Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model", Mater. Design, 114, 572-583. https://doi.org/10.1016/j.matdes.2016.10.041.
  120. Khodami Maraghi, Z., Ghorbanpour Arani, A., Kolahchi, R., Amir, S. and Bagheri, M. R. (2013), "Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid", Compos. Part B Eng., 45(1), 423-432. https://doi.org/10.1016/j.compositesb.2012.04.066.
  121. Kim, J. W., Nunez, J. C., Siochi, E. J., Wise, K. E., Lin, Y., Connell, J. W. and Smith, M. W. (2012), "In situ mechanical property measurements of amorphous carbon-boron nitride nanotube nanostructures", Nanotechnology, 23(3), 035701. https://doi.org/10.1088/0957-4484/23/3/035701
  122. Kolahchi, R. and Ghorbanpour, A. A. (2012), "Nonlinear Vibration and Instability Analysis of a PVDF Cylindrical Shell Reinforced with BNNTs Conveying Viscose Fluid Using HDQ Method", J. Solid Mech., 4(3), 267-276.
  123. Kolodyazhnaya, M. P., Zvyagina, G. A., Gudim, I. A., Bilych, I. V., Burma, N. G., Zhekov, K. R. and Fil, V. D. (2017), "Piezoelectric response in SmFe3 (BO3) 4, a non-piezoactive configuration. The surface piezoelectric effect", Low Temperature Physics, 43(8), 924-929. https://doi.org/10.1063/1.5001291.
  124. Kong, X. Y. and Wang, Z. L. (2003), "Spontaneous polarization-induced nanohelixes, nanosprings, and nanorings of piezoelectric nanobelts", Nano Letters, 3(12), 1625-1631. https://doi.org/10.1021/nl034463p.
  125. Kumar, B., Lee, K. Y., Park, H. K., Chae, S. J., Lee, Y. H. and Kim, S. W. (2011), "Controlled growth of semiconducting nanowire, nanowall, and hybrid nanostructures on graphene for piezoelectric nanogenerators", Acs Nano, 5(5), 4197-4204. https://doi.org/10.1021/nn200942s.
  126. Kumar, B. and Kim, S. W. (2012), "Energy harvesting based on semiconducting piezoelectric ZnO nanostructures", Nano Energy, 1(3), 342-355. https://doi.org/10.1016/j.nanoen.2012.02.001.
  127. Lahiri, D., Singh, V., Benaduce, A. P., Seal, S., Kos, L. and Agarwal, A. (2011), "Boron nitride nanotube reinforced hydroxyapatite composite: Mechanical and tribological performance and in-vitro biocompatibility to osteoblasts", J. Mech. Behavior Biomedical Mater., 4(1), 44-56. https://doi.org/10.1016/j.jmbbm.2010.09.005.
  128. Larbi Chaht, F., Kaci, A., Houari, M. S. A., Tounsi, A., Anwar Beg, O. 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, 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  129. Lee, Y. B., Han, J. K., Noothongkaew, S., Kim, S. K., Song, W., Myung, S. and An, K. S. (2017), "Toward Arbitrary-Direction Energy Harvesting through Flexible Piezoelectric Nanogenerators Using Perovskite PbTiO3 Nanotube Arrays", Adv. Mater., 29(6). https://doi.org/10.1002/adma.201604500.
  130. Li, F. M., Hsieh, G. W., Dalal, S., Newton, M. C., Stott, J. E., Hiralal, P. and Milne, W. I. (2008), "Zinc oxide nanostructures and high electron mobility nanocomposite thin film transistors", Electron Devices, IEEE Transactions on, 55(11), 3001-3011. https://doi.org/10.1109/TED.2008.2005180.
  131. Li, C., Liu, J. J., Cheng, M. and Fan, X.L. (2017), "Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces", Compos. Part B Eng., 116, 153-169. https://doi.org/10.1016/j.compositesb.2017.01.071.
  132. Li, X. B., Li, L., Hu, Y. J., Ding, Z. and Deng, W. M. (2017), "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory", Compos. Struct., 165, 250-265. https://doi.org/10.1016/j.compstruct.2017.01.032.
  133. Liang, X., Yang, W., Hu, S. and Shen, S. (2016), "Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads", J. Phys D Appl. Phys., 49(11), 115307. https://doi.org/10.1088/0022-3727/49/11/115307.
  134. Lin, H. B., Cao, M. S., Zhao, Q. L., Shi, X. L., Wang, D. W. and Wang, F. C. (2008), "Mechanical reinforcement and piezoelectric properties of nanocomposites embedded with ZnO nanowhiskers", Scripta Materialia, 59(7), 780-783. https://doi.org/10.1016/j.scriptamat.2008.06.016.
  135. Lippmann, G. (1881), "Principe de la conservation de l'electricite, ou second principe de la theorie des phenomenes electriques", Journal de Physique Theorique et Appliquee, 10(1), 381-394. https://doi.org/10.1051/jphystap:0188100100038100.
  136. Liu, W., Lee, M., Ding, L., Liu, J. and Wang, Z. L. (2010), "Piezopotential Gated Nanowire- Nanotube Hybrid Field-Effect Transistor", Nano Letters, 10(8), 3084-3089. https://doi.org/10.1021/nl1017145.
  137. Liu, C., Hu, S. and Shen, S. (2012), "Effect of flexoelectricity on electrostatic potential in a bent piezoelectric nanowire", Smart Mater. Struct., 21(11), 115024. https://doi.org/10.1088/0964-1726/21/11/115024.
  138. Liu, C., Ke, L. L., Wang, Y. S., Yang, J. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031
  139. Liu, C. and Wang, J. (2017), "Size-dependent electromechanical properties in piezoelectric superlattices due to flexoelectric effect", Theoretical Appl. Mech. Lett., 7(2), 88-92. https://doi.org/10.1016/j.taml.2017.02.007.
  140. Loh, K. P., Lin, M., Yeadon, M., Boothroyd, C. and Hu, Z. (2004), "Growth of boron nitride nanotubes and iron nanowires from the liquid flow of FeB nanoparticles", Chem. Phys. Lett., 387(1), 40-46. https://doi.org/10.1016/j.cplett.2004.01.093.
  141. Lu, Y. H., Shen, Y. G., Li, K. Y. and Chen, H. (2006), "Effects of nitrogen content on nanostructure evolution, mechanical behaviors and thermal stability in Ti-B-N thin films", Surface Coatings Technol., 201(3), 1228-1235. https://doi.org/10.1016/j.surfcoat.2006.01.045.
  142. Ma, L.H., Ke, L.L., Wang, Y.Z. and Wang, Y.S. (2017), "Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models", Physica E Low Dimensional Syst. Nanostruct., 86, 253-261. https://doi.org/10.1016/j.physe.2016.10.036.
  143. Maity, K., Mahanty, B., Sinha, T.K., Garain, S., Biswas, A., Ghosh, S.K. and Mandal, D. (2017), "Two-Dimensional Piezoelectric MoS2-Modulated Nanogenerator and Nanosensor Made of Poly (vinlydine Fluoride) Nanofiber Webs for Self-Powered Electronics and Robotics", Energy Technol., 5(2), 234-243. https://doi.org/10.1002/ente.201600419.
  144. Majidi, C., Haataja, M. and Srolovitz, D.J. (2010), "Analysis and design principles for shear-mode piezoelectric energy harvesting with ZnO nanoribbons", Smart Mater. Struct., 19(5), 055027. https://doi.org/10.1088/0964-1726/19/5/055027.
  145. Malikan, M. (2017), "Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory", Appl. Math. Model., 48, 196-207. https://doi.org/10.1016/j.apm.2017.03.065.
  146. Meitzler, A.W., A.H., Tiersten, H.F., Warner, A.W., Berlincourt, D., Couqin, G. A. and Welsh III, F. S. (1988), IEEE Standard on Piezoelectricity, IEEE, USA.
  147. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E. A. and Mahmoud, S. R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandwich Struct. Mater., 21(2), 727-757. https://doi.org/10.1177%2F1099636217698443. https://doi.org/10.1177/1099636217698443
  148. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  149. Meng, Y., Xiu, P., Huang, B., Wang, Z., Zhang, R.Q. and Zhou, R. (2014), "A unique feature of chiral transition of a difluorobenzo [c] phenanthrene molecule confined in a boron-nitride nanotube based on molecular dynamics simulations", Chem. Phys. Lett., 591, 265-267. https://doi.org/10.1016/j.cplett.2013.11.052.
  150. Mercan, K. and Civalek, O. (2016), "DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Compos. Struct. 143, 300-309. https://doi.org/10.1016/j.compstruct.2016.02.040.
  151. Mercan K and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocalelasticity using the method of HDQ", Compos. Part B, 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067.
  152. Meziane, M. A. A., Abdelaziz, H. H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandwich Struct. Mater., 16(3), 293-318. https://doi.org/10.1177%2F1099636214526852. https://doi.org/10.1177/1099636214526852
  153. Minary-Jolandan, M., Bernal, R.A. and Espinosa, H.D. (2011), "Strong piezoelectricity in individual GaN nanowires", MRS Communications, 1(01), 45-48. https://doi.org/10.1557/mrc.2011.14
  154. Minary-Jolandan, M., Bernal, R.A., Kuljanishvili, I., Parpoil, V. and Espinosa, H.D. (2012), "Individual GaN nanowires exhibit strong piezoelectricity in 3D", Nano Letters, 12(2), 970-976. https://doi.org/10.1021/nl204043y.
  155. Mirnezhad, M., Ansari, R. and Rouhi, H. (2013), "Mechanical properties of multilayer boron nitride with different stacking orders", Superlattices Microstructures, 53, 223-231. https://doi.org/10.1016/j.spmi.2012.10.016.
  156. Mohai, I., Mohai, M., Bertoti, I., Sebestyen, Z., Nemeth, P., Babievskaya, I.Z. and Szepvolgyi, J. (2011), "Formation of thin boron nitride coating on multiwall carbon nanotube surfaces" Diamond Related Mater., 20(2), 227-231. https://doi.org/10.1016/j.diamond.2010.12.001.
  157. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1).
  158. Moheimani, S.R. and Fleming, A.J. (2006), Piezoelectric Transducers For Vibration Control And Damping, Springer Science & Business Media, Germany.
  159. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018a), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  160. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  161. Momeni, K., Odegard, G.M. and Yassar, R.S. (2012), "Finite size effect on the piezoelectric properties of ZnO nanobelts: a molecular dynamics approach", Acta materialia, 60(13), 5117-5124. https://doi.org/10.1016/j.actamat.2012.06.041.
  162. Moon, W.H. and Hwang, H.J. (2004), "Molecular mechanics of structural properties of boron nitride nanotubes", Physica E Low Dimensional Syst. Nanostruct., 23(1), 26-30. https://doi.org/10.1016/j.physe.2003.11.273
  163. Mortazavi, B. and Remond, Y. (2012), "Investigation of tensile response and thermal conductivity of boron-nitride nanosheets using molecular dynamics simulations", Physica E Low Dimensional Syst. Nanostruct., 44(9), 1846-1852. https://doi.org/10.1016/j.physe.2012.05.007.
  164. Mosallaie Barzoki, A.A., Ghorbanpour Arani, A., Kolahchi, R. and Mozdianfard, M.R. (2012), "Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core", Appl. Math. Modelling, 36(7), 2983-2995. https://doi.org/10.1016/j.apm.2011.09.093.
  165. Mosallaie Barzoki, A.A., Ghorbanpour Arani, A., Kolahchi, R., Mozdianfard, M.R. and Loghman, A. (2013), "Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro-thermo-mechanical loadings using HDQM", Compos. Part B Eng., 44(1), 722-727. https://doi.org/10.1016/j.compositesb.2012.01.052.
  166. Mouffoki, A., Adda Bedia, E. A., Houari, M. S. A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369.
  167. Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006.
  168. Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001.
  169. Oku, T., Koi, N. and Suganuma, K. (2008), "Synthesis and nanostructure of boron nitride nanotubes grown from iron-evaporated boron", Diamond Related Mater., 17(7), 1805-1807. https://doi.org/10.1016/j.diamond.2008.01.009.
  170. Panchal, M.B. and Upadhyay, S.H. (2013), "Cantilevered single walled boron nitride nanotube based nanomechanical resonators of zigzag and armchair forms", Physica E Low Dimensional Syst. Nanostruct., 50, 73-82. https://doi.org/10.1016/j.physe.2013.02.018
  171. Panchal, M.B., Upadhyay, S.H. and Harsha, S.P. (2013), "Vibrational characteristics of defective single walled BN nanotube based nanomechanical mass sensors: single atom vacancies and divacancies", Sensors Actuators A Physical, 197, 111-121. https://doi.org/10.1016/j.sna.2013.04.011.
  172. Pandya, H.J. and Chandra, S. (2011), "Zinc oxide nanostructures by oxidation of zinc films deposited on oxidized silicon substrate", J. Nano-Electron. Phys., 3(1), 409-413.
  173. Patil, S.R. and Melnik, R.V. (2009), "Coupled electromechanical effects in II-VI group finite length semiconductor nanowires", J. Physics D Appl. Phys., 42(14), 145113. https://doi.org/10.1088/0022-3727/42/14/145113.
  174. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061.
  175. Qi, J., Qian, X., Qi, L., Feng, J., Shi, D. and Li, J. (2012), "Strain-engineering of band gaps in piezoelectric boron nitride nanoribbons", Nano Letters, 12(3), 1224-1228. https://doi.org/10.1021/nl2035749.
  176. Rafiee, R. and Moghadam, R.M. (2014), "On the modeling of carbon nanotubes: A critical review", Compos. Part B Eng., 56, 435-449. https://doi.org/10.1016/j.compositesb.2013.08.037
  177. Rahmati, A.H. and Mohammadimehr, M. (2014), "Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM", Physica B: Condensed Matter, 440, 88-98. https://doi.org/10.1016/j.physb.2014.01.036.
  178. Razavi, H., Babadi, A.F. and Beni, Y.T. (2017), "Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309. https://doi.org/10.1016/j.compstruct.2016.10.056.
  179. Refaeinejad, V., Rahmani, O. and Hosseini, S.A.H. (2017), "Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures", Mech. Adv. Mater. Struct., 24(13), 1116-1123. https://doi.org/10.1080/15376494.2016.1227496.
  180. Rezania, H. (2014), "The effect of local electronic interaction on the optical properties of boron-nitride nanotubes", Physica E Low Dimensional Syst. Nanostruct., 61, 48-52. https://doi.org/10.1016/j.physe.2014.03.014.
  181. Sadek, A.S., Karabalin, R.B., Du, J., Roukes, M.L., Koch, C. and Masmanidis, S. C. (2010), "Wiring nanoscale biosensors with piezoelectric nanomechanical resonators", Nano letters, 10(5), 1769-1773. https://doi.org/10.1021/nl100245z.
  182. Sahmani, S., Aghdam, M.M. and Akbarzadeh, A.H. (2016), "Size-dependent buckling and postbuckling behavior of piezoelectric cylindrical nanoshells subjected to compression and electrical load", Mater. Design, 105, 341-351. https://doi.org/10.1016/j.matdes.2016.05.065
  183. Sahmani, S. and Fattahi, A.M. (2017), "Thermo-electro-mechanical size-dependent postbuckling response of axially loaded piezoelectric shear deformable nanoshells via nonlocal elasticity theory", Microsyst. Technol., 23(10), 5105-5119. https://doi.org/10.1007/s00542-017-3316-x.
  184. Salehi-Khojin, A. and Jalili, N. (2008), "Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings", Compos. Sci. Technol., 68(6), 1489-1501. https://doi.org/10.1016/j.compscitech.2007.10.024.
  185. Scrymgeour, D.A. and Hsu, J.W. (2008), "Correlated piezoelectric and electrical properties in individual ZnO nanorods", Nano Letters, 8(8), 2204-2209. https://doi.org/10.1021/nl080704n.
  186. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by nonlocal FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  187. Seo, M., Jung, Y., Lim, D., Cho, D. and Jeong, Y. (2013), "Piezoelectric and field emitted properties of controlled ZnO nanorods on CNT yarns", Mater. Letters, 92, 177-180. https://doi.org/10.1016/j.matlet.2012.10.076.
  188. Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates". J. Eng. Sci., 120, 82-99. https://doi.org/10.1016/j.ijengsci.2017.06.008.
  189. Sharma, N.D., Maranganti, R. and Sharma, P. (2007), "On the possibility of piezoelectric nanocomposites without using piezoelectric materials", J. Mech. Phys. Solids, 55(11), 2328-2350. https://doi.org/10.1016/j.jmps.2007.03.016.
  190. Shokuhfar, A. and Ebrahimi-Nejad, S. (2013)' "Effects of structural defects on the compressive buckling of boron nitride nanotubes", Physica E Low Dimensional Syst. Nanostruct., 48, 53-60. https://doi.org/10.1016/j.physe.2012.11.024.
  191. Sinha, N., Wabiszewski, G.E., Mahameed, R., Felmetsger, V.V., Tanner, S. M., Carpick, R. W. and Piazza, G. (2009), "Ultra-thin AlN piezoelectric nano-actuators", Solid-State Sensors, Actuators and Microsystems Conference, 2009, TRANSDUCERS 2009. International, Denver, Colorado, USA. 469-472. https://doi.org/10.1109/SENSOR.2009.5285460.
  192. Soltani, A., Moradi, A.V., Bahari, M., Masoodi, A. and Shojaee, S. (2013), "Computational investigation of the electronic and structural properties of CN radical on the pristine and Al-doped (6, 0) BN nanotubes", Physica B: Condensed Matter, 430, 20-26. https://doi.org/10.1016/j.physb.2013.07.032.
  193. Song, F., Huang, G.L., Park, H.S. and Liu, X.N. (2011), "A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses", J. Solids Struct., 48(14), 2154-2163. https://doi.org/10.1016/j.ijsolstr.2011.03.021.
  194. Sun, C., Shi, J. and Wang, X. (2010), "Fundamental study of mechanical energy harvesting using piezoelectric nanostructures", J. Appl. Phys., 108(3), 034309. https://doi.org/10.1063/1.3462468.
  195. Taghizadeh, M., Ovesy, H.R. and Ghannadpour, S.A.M. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., 54(4), 755-769. https://doi.org/10.12989/sem.2015.54.4.755.
  196. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.
  197. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547.
  198. Ulus, H., Ustun, T., Eskizeybek, V., Sahin, O.S., Avci, A. and Ekrem, M. (2013), "Boron nitride-MWCNT/epoxy hybrid nanocomposites: Preparation and mechanical properties", Appl. Surface Sci., 37-42. https://doi.org/10.1016/j.apsusc.2013.12.070.
  199. Vahedi Fakhrabad, D. and Shahtahmassebi, N. (2013), "First-principles calculations of the Young's modulus of double wall boron-nitride nanotubes", Mater. Chem. Phys., 138(2), 963-966. https://doi.org/10.1016/j.matchemphys.2013.01.004.
  200. Wang, Z.L. (2004), "Nanostructures of zinc oxide", Mater. Today, 7(6), 26-33. https://doi.org/10.1016/S1369-7021(04)00286-X.
  201. Wang, Z.L. (2004), "Zinc oxide nanostructures: growth, properties and applications", J. Phys. Condensed Matter, 16(25), R829. https://doi.org/10.1088/0953-8984/16/25/R01.
  202. Wang, Z.L. (2004), "Zinc oxide nanostructures: growth, properties and applications", J. Phys. Condensed Matter, 16(25), R829. https://doi.org/10.1088/0953-8984/16/25/R01.
  203. Wang, Z., Suryavanshi, A.P. and Yu, M.F. (2006), "Ferroelectric and piezoelectric behaviors of individual single crystalline BaTiO3 nanowire under direct axial electric biasing", Appl. Phys. Lett., 89(8), 082903. https://doi.org/10.1063/1.2338015.
  204. Wang, Z. L. (2007), "Novel nanostructures of ZnO for nanoscale photonics, optoelectronics, piezoelectricity, and sensing", Appl. Phys. A, 88(1), 7-15. https://doi.org/10.1007/s00339-007-3942-8.
  205. Wang, Z., Zu, X., Yang, L., Gao, F. and Weber, W. J. (2008), "Molecular dynamics simulation on the buckling behavior of GaN nanowires under uniaxial compression", Physica E Low Dimensional Syst. Nanostruct., 40(3), 561-566. https://doi.org/10.1016/j.physe.2007.08.040.
  206. Wang, X. and Lee, J.D. (2010), "Nano-Piezoelectricity in BaTiO3: An Atomistic/Continuum Simulation", Adv. Sci. Lett.,, 3(4), 422-427. https://doi.org/10.1166/asl.2010.1164.
  207. Wang, G.F. and Feng, X.Q. (2010), "Effect of surface stresses on the vibration and buckling of piezoelectric nanowires", Europhys. Lett., 91(5), 56007. https://doi.org/10.1209/0295-5075/91/56007
  208. Wang, C.Y., Li, L.J. and Chew, Z.J. (2011), "Vibrating ZnO-CNT nanotubes as pressure/stress sensors", Physica E Low Dimensional Syst. Nanostruct., 43(6), 1288-1293. https://doi.org/10.1016/j.physe.2011.03.003.
  209. Wang, J., Li, H., Li, Y., Yu, H., He, Y. and Song, X. (2011), "Deformation of copper-filled single-walled boron-nitride nanotubes under axial compression", Physica E Low Dimensional Syst. Nanostruct., 44(1), 286-289. https://doi.org/10.1016/j.physe.2011.08.024.
  210. Wang, X. and Shi, J. (2012), "Piezoelectric nanogenerators for self-powered nanodevices", Piezoelectric Nanomaterials for Biomedical Applications, Springer Berlin Heidelberg, Berlin, Germany. 135-172. https://doi.org/10.1007/978-3-642-28044-3_5.
  211. Wang, K.F. and Wang, B.L. (2012), "The electromechanical coupling behavior of piezoelectric nanowires: Surface and small-scale effects", EPL (Europhysics Letters), 97(6), 66005. https://doi.org/10.1209/0295-5075/97/66005.
  212. Wang, W., Li, P., Jin, F. and Wang, J. (2016), "Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects", Compos. Struct., 140, 758-775. https://doi.org/10.1016/j.compstruct.2016.01.035.
  213. Wu, W. (2016), "High-performance piezoelectric nanogenerators for self-powered nanosystems: Quantitative standards and figures of merit", Nanotechnology, 27(11), 112503. http://dx.doi.org/10.1088/0957-4484/27/11/112503.
  214. Xi, Y., Song, J., Xu, S., Yang, R., Gao, Z., Hu, C. and Wang, Z.L. (2009), "Growth of ZnO nanotube arrays and nanotube based piezoelectric nanogenerators", J. Mater. Chem., 19(48), 9260-9264. https://doi.org/10.1039/B917525C.
  215. Xu, Z., Golberg, D. and Bando, Y. (2009), "Electrical field-assisted thermal decomposition of boron nitride nanotube: experiments and first principle calculations", Chem. Phys. Lett., 480(1), 110-112. https://doi.org/10.1016/j.cplett.2009.08.072.
  216. Xu, S. and Wang, Z.L. (2011), "One-dimensional ZnO nanostructures: solution growth and functional properties", Nano Res., 4(11), 1013-1098. https://doi.org/10.1007/s12274-011-0160-7.
  217. Xu, S., Poirier, G. and Yao, N. (2012), "Fabrication and piezoelectric property of PMN-PT nanofibers", Nano Energy, 1(4), 602-607. https://doi.org/10.1016/j.nanoen.2012.03.011.
  218. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech, 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  219. Yan, Z. and Jiang, L. (2011a), "Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects", J. Phys. D Appl. Phys., 44(36), 365301. https://doi.org/10.1088/0022-3727/44/36/365301.
  220. Yan, Z. and Jiang, L. (2011b), "Surface effects on the electromechanical coupling and bending behaviors of piezoelectric nanowires", J. Phys. D Appl. Phys., 44(7), 75404. https://doi.org/10.1088/0022-3727/44/7/075404
  221. Yan, Z. and Jiang, L.Y. (2011c), "The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects", Nanotechnology, 22(24), 245703. https://doi.org/10.1088/0957-4484/22/24/245703.
  222. Yan, Z. and Jiang, L.Y. (2012a), "Surface effects on the vibration and buckling of piezoelectric nanoplates", EPL (Europhysics Letters), 99(2), 27007. https://doi.org/10.1209/0295-5075/99/27007.
  223. Yan, Z. and Jiang, L.Y. (2012b), "Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints", Proceedings of the Royal Society A: Mathematical, Phys. Eng. Sci., https://doi.org/10.1098/rspa.2012.0214.
  224. Yan, Z. (2013), "Continuum modeling on size-dependent properties of piezoelectric nanostructures", https://ir.lib.uwo.ca/etd/1322.
  225. Yan, Z. and Jiang, L. (2013), "Size-dependent bending and vibration behaviour of piezoelectric nanobeams due to flexoelectricity", J. Phys. D Appl. Phys., 46(35), 355502. https://doi.org/10.1088/0022-3727/46/35/355502
  226. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A. A. and Houari, M. S. A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst.., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015.
  227. Ye, L., Lu, G. and Ong, L. S. (2011), "Buckling of a thin-walled cylindrical shell with foam core under axial compression", Thin-walled struct., 49(1), 106-111. https://doi.org/10.1016/j.tws.2010.08.011.
  228. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A. A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065.
  229. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A. A. and Mahmoud, S. R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519.
  230. Yun, S. and Kim, J. (2011), "Mechanical, electrical, piezoelectric and electro-active behavior of aligned multi-walled carbon nanotube/cellulose composites", Carbon, 49(2), 518-527. https://doi.org/10.1016/j.carbon.2010.09.051.
  231. Zaoui, F. Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  232. Zemri, A., Houari, M. S. A., Bousahla, A. A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693.
  233. Zenkour, A. M. and Sobhy, M. (2017), "Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin-Voigt viscoelastic nanoplate embedded in a viscoelastic medium", Acta Mechanica, 1-17. https://doi.org/10.1007/s00707-017-1920-6.
  234. Zenkour, A. M. and Arefi, M. (2017), "Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation", J. Thermal Stresses, 40(2), 167-184. https://doi.org/10.1080/01495739.2016.1229146.
  235. Zhang, L. and Huang, H. (2006), "Young's moduli of ZnO nanoplates: Ab initio determinations", Appl. Phys. Lett., 89(18), 183111. https://doi.org/10.1063/1.2374856.
  236. Zhang, S., Liu, Y., Xia, M., Zhang, L., Zhang, E., Liang, R. and Zhao, S. (2008), "Long-wavelength optical phonons in single-walled boron nitride nanotubes", Physica B Condensed Matter, 403(23), 4196-4201. https://doi.org/10.1016/j.physb.2008.09.010.
  237. Zhang, Y., Hong, J., Liu, B. and Fang, D. (2010), "Strain effect on ferroelectric behaviors of BaTiO3 nanowires: A molecular dynamics study", Nanotechnology, 21(1), 015701. https://doi.org/10.1088/0957-4484/21/1/015701.
  238. Zhang, J., Wang, R. and Wang, C. (2012), "Piezoelectric ZnO-CNT nanotubes under axial strain and electrical voltage", Physica E Low Dimensional Syst. Nanostruct., 46, 105-112. https://doi.org/10.1016/j.physe.2012.09.001.
  239. Zhang, J. and Wang, C. (2012), "Vibrating piezoelectric nanofilms as sandwich nanoplates", J. Appl. Phys., 111(9), 094303. https://doi.org/10.1063/1.4709754.
  240. Zhang, L. L., Liu, J. X., Fang, X. Q. and Nie, G. Q. (2014)' "Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates", Europ. J. Mech. A/Solids, 46, 22-29. https://doi.org/10.1016/j.euromechsol.2014.01.005.
  241. Zheng, X. P., Cao, Y. P., Li, B., Feng, X. Q. and Wang, G. F. (2010), "Surface effects in various bending-based test methods for measuring the elastic property of nanowires", Nanotechnology, 21(20), 205702. https://doi.org/10.1088/0957-4484/21/20/205702.
  242. Zhi, C., Bando, Y., Tang, C. and Golberg, D. (2010), "Boron nitride nanotubes", Mater. Sci. Eng. R: Reports, 70(3), 92-111. https://doi.org/10.1126/science.269.5226.966.
  243. Zhou, J., Xu, N. S. and Wang, Z. L. (2006), "Dissolving behavior and stability of ZnO wires in biofluids: a study on biodegradability and biocompatibility of ZnO nanostructures", Adv. Mater., 18(18), 2432-2435. https://doi.org/10.1002/adma.200600200.
  244. Zhou, J., Wang, Z., Grots, A. and He, X. (2007), "Electric field drives the nonlinear resonance of a piezoelectric nanowire", Solid State Communications, 144(3), 118-123. https://doi.org/10.1016/j.ssc.2007.08.011.
  245. Zhukovskii, Y. F., Piskunov, S., Pugno, N., Berzina, B., Trinkler, L. and Bellucci, S. (2009), "Ab initio simulations on the atomic and electronic structure of single-walled BN nanotubes and nanoarches", J. Phys. Chem. Solids, 70(5), 796-803. https://doi.org/10.1016/j.jpcs.2009.03.016.
  246. Zidi, M., Houari, M. S. A., Tounsi, A., Bessaim, A. and Mahmoud, S. R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145.

Cited by

  1. Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation vol.2021, 2021, https://doi.org/10.1155/2021/1301044