486
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams

ORCID Icon &
Pages 943-952 | Received 06 Jan 2017, Accepted 25 Mar 2017, Published online: 03 Jan 2018

References

  • Y. Z. Wang, F. M. Li, and K. Kishimoto, “Effects of axial load and elastic matrix on flexural wave propagation in nanotube with nonlocal timoshenko beam model,” J. Vib. Acoustics, vol. 134, no. 3, pp. 031011, 2016a. DOI: 10.1115/1.4005832.
  • F. Ebrahimi and A. Dabbagh, “On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory,” Compos. Struct., 2016.
  • F. Ebrahimi and S. H. S. Hosseini, “Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates,” J. Thermal Stresses, vol. 39, no. 5, pp. 606–625, 2016a. DOI: 10.1080/01495739.2016.1160684.
  • F. Ebrahimi and S. H. S. Hosseini, “Double nanoplate-based NEMS under hydrostatic and electrostatic actuations,” The Eur. Phys. J. Plus, vol. 131, no. 5, pp. 1–19, 2016b. DOI: 10.1140/epjp/i2016-16160-1.
  • C. S. Lao, Q. Kuang, Z. L. Wang, M. C. Park, and Y. Deng, “Polymer functionalized piezoelectric-FET as humidity/chemical nanosensors,” Appl. Phys. Lett., vol. 90, no. 26, pp. 262107, 2007. DOI: 10.1063/1.2748097.
  • F. Ebrahimi and M. R. Barati, “Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment,” J. Vib. Control, 1077546316646239, 2016a. DOI: 10.1177/1077546316646239.
  • F. Ebrahimi and M. R. Barati, “Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments,” Appl. Phys. A, vol. 122, no. 10, pp. 910, 2016b. DOI: 10.1007/s00339-016-0441-9.
  • F. Ebrahimi and M. R. Barati, “Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory,” Smart Mater. Struct., vol. 25, no. 10, pp. 105014, 2016c. DOI: 10.1088/0964-1726/25/10/105014.
  • F. Ebrahimi and M. R. Barati, “Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field,” J. Intell. Mater. Syst. Struct., 1045389X16672569, 2016d.
  • F. Ebrahimi and M. R. Barati, “Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field,” Appl. Phys. A, vol. 122, no. 4, pp. 1–18, 2016e. DOI: 10.1007/s00339-016-0001-3.
  • F. Ebrahimi and M. R. Barati, “A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures,” Int. J. Eng. Sci., vol. 107, pp. 183–196, 2016f. DOI: 10.1016/j.ijengsci.2016.08.001.
  • F. Ebrahimi and M. R. Barati, “Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium,” J. Brazilian Soc. Mech. Sci. Eng., pp. 1–16, 2016g.
  • F. Ebrahimi and M. R. Barati, “Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams,” Eur. Phys. J. Plus, vol. 131, no. 7, pp. 1–14, 2016h. DOI: 10.1140/epjp/i2016-16238-8.
  • F. Ebrahimi and M. R. Barati, “Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams,” J. Mech., pp. 1–11, 2016i.
  • F. Ebrahimi and M. R. Barati, “An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams,” Adv. Nano Res, vol. 4, no. 2, pp. 65–84, 2016j. DOI: 10.12989/anr.2016.4.2.065.
  • F. Ebrahimi and M. R. Barati, “Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment,” Int. J. Smart Nano Mater., pp. 1–22, 2016k.
  • A. C. Eringen, “Mechanics of micromorphic continua,” Mech. Generalized Continua, pp. 18–35, 1968.‏ DOI: 10.1007/978-3-662-30257-6_2.
  • A. C. Eringen, “Linear theory of nonlocal elasticity and dispersion of plane waves,” Int. J. Eng. Sci., vol. 10, no. 5, pp. 425–435, 1972.‏ DOI: 10.1016/0020-7225(72)90050-X.
  • M. Xu, “Free transverse vibrations of nano-to-micron scale beams,” Proc. Royal Soc. A: Math. Phys. Eng. Sci., vol. 462, no. 2074, pp. 2977–2995, 2006.
  • H. L. Lee and W. J. Chang, “Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory,” J. Appl. Phys., vol. 108, no. 9, pp. 093503, 2010. DOI: 10.1063/1.3503853.
  • I. Elishakoff and C. Soret, “A consistent set of nonlocal Bresse–Timoshenko equations for nanobeams with surface effects,” J. Appl. Mech., vol. 80, no. 6, pp. 061001, 2013.‏ DOI: 10.1115/1.4023630.
  • P. Malekzadeh and M. Shojaee, “Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams,” Compos. Part B: Eng., vol. 52, pp. 84–92, 2013. DOI: 10.1016/j.compositesb.2013.03.046.
  • B. Gheshlaghi and S. M. Hasheminejad, “Vibration analysis of piezoelectric nanowires with surface and small scale effects,” Curr. Appl. Phys., vol. 12, no. 4, pp. 1096–1099, 2012.‏ DOI: 10.1016/j.cap.2012.01.014.
  • A. T. Samaei, B. Gheshlaghi, and G. F. Wang, “Frequency analysis of piezoelectric nanowires with surface effects,” Curr. Appl. Phys., vol. 13, no. 9, pp. 2098–2102, 2013. DOI: 10.1016/j.cap.2013.08.018.
  • T. Murmu and S. C. Pradhan, “Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory,” Phys. E: Low-Dimensional Syst. Nanostructures, vol. 41, no. 8, pp. 1451–1456, 2009.‏ DOI: 10.1016/j.physe.2009.04.015.
  • M. E. Gurtin and A. Ian Murdoch, “A continuum theory of elastic material surfaces,” Arch. Ration. Mech. Anal., vol. 57, no. 4, pp. 291–323, 1975.‏ DOI: 10.1007/BF00261375.
  • K. F. Wang and B. L. Wang, “Vibration of nanoscale plates with surface energy via nonlocal elasticity,” Phys. E: Low-Dimensional Syst. Nanostructures, vol. 44, no. 2, pp. 448–453, 2011a.‏ DOI: 10.1016/j.physe.2011.09.019.
  • F. Ebrahimi, M. R. Barati, and A. Dabbagh, “A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates,” Int. J. Eng. Sci., vol. 107, pp. 169–182, 2016r. DOI: 10.1016/j.ijengsci.2016.07.008.
  • F. Ebrahimi, G. R. Shaghaghi, and M. Boreiry, “A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions,” Int. J. Struct. Stab. Dynam., 1550023, 2015a.
  • F. Ebrahimi and M. Boreiry, “Investigating various surface effects on nonlocal vibrational behavior of nanobeams,” Appl. Phys. A, vol. 121, no. 3, pp. 1305–1316, 2015b. DOI: 10.1007/s00339-015-9512-6.
  • F. Ebrahimi, M. Ghadiri, E. Salari, S. A. H. Hoseini, and G. R. Shaghaghi, “Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams,” J. Mech. Sci. Technol., vol. 29, no. 3, pp. 1207–1215, 2015. DOI: 10.1007/s12206-015-0234-7.
  • T. D. Nguyen, S. Mao, Y. W. Yeh, P. K. Purohit, and M. C. McAlpine, “Nanoscale flexoelectricity,” Adv. Mater., vol. 25, no. 7, pp. 946–974, 2013.‏ DOI: 10.1002/adma.201203852.
  • W. Ma, and L. E. Cross, “Flexoelectric polarization of barium strontium titanate in the paraelectric state,” Appl. Phys. Lett., vol. 81, no. 18, pp. 3440–3442, 2002. DOI: 10.1063/1.1518559.
  • R. Toupin, “The elastic dielectric,” J. Ration. Mech. Anal., vol. 5, no. 6, pp. 849–915, 1956.‏
  • M. S. Majdoub, pp. Sharma, and T. Cagin, “Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect,” Phys. Rev. B, vol. 77, no. 12, pp. 125424, 2008.‏ DOI: 10.1103/PhysRevB.77.125424.
  • W. Yang, X. Liang, and S. Shen, “Electromechanical responses of piezoelectric nanoplates with flexoelectricity,” Acta Mech., vol. 226, no. 9, pp. 3097–3110, 2015.‏ DOI: 10.1007/s00707-015-1373-8.
  • L. Wang, “Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale,” Computat. Mater. Sci., vol. 45, no. 2, pp. 584–588, 2009.‏ DOI: 10.1016/j.commatsci.2008.12.006.
  • F. Ebrahimi, G. R. Shaghaghi, and M. Boreiry, “An investigation into the influence of thermal loading and surface effects on mechanical characteristics of nanotubes,” Struct. Eng. Mech., vol. 57, no. 1, pp. 179–200, 2016r. DOI: 10.12989/sem.2016.57.1.179.
  • F. Ebrahimi, E. Salari, and S. A. H. Hosseini, “In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams,” Meccanica, vol. 51, no. 4, pp. 951–977, 2016s. DOI: 10.1007/s11012-015-0248-3.
  • F. Ebrahimi and M. R. Barati, “Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams,” Mech. Adv. Mater. Struct., pp. 1–13, 2016t.‏
  • F. Ebrahimi and M. R. Barati, “Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory,” Int. J. Smart Nano Mater., pp. 1–25, 2016l.
  • F. Ebrahimi and M. R. Barati, “A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams,” Arabian J. Sci. Eng., vol. 41, no. 5, pp. 1679–1690, 2016m. DOI: 10.1007/s13369-015-1930-4.
  • F. Ebrahimi and M. R. Barati, “Vibration analysis of nonlocal beams made of functionally graded material in thermal environment,” The Eur. Phys. J. Plus, vol. 131, no. 8, pp. 279, 2016n. DOI: 10.1140/epjp/i2016-16279-y.
  • F. Ebrahimi and M. R. Barati, “A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment,” Appl. Phys. A, vol. 122, no. 9, pp. 792, 2016o. DOI: 10.1007/s00339-016-0322-2.
  • F. Ebrahimi and M. R. Barati, “Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory,” Compos. Struct., 2016p.
  • F. Ebrahimi and M. R. Barati, “Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams,” Mech. Adv. Mater. Struct., (just-accepted), 00-00, 2016q.
  • F. Ebrahimi and E. Salari, “Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments,” Compos. Struct., vol. 128, pp. 363–380, 2015c. DOI: 10.1016/j.compstruct.2015.03.023.
  • F. Ebrahimi and E. Salari, “Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method,” Compos. Part B: Eng., vol. 79, pp. 156–169, 2015d. DOI: 10.1016/j.compositesb.2015.04.010.
  • F. Ebrahimi and E. Salari, “Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment,” Acta Astronaut., vol. 113, pp. 29–50, 2015, 2015e. DOI: 10.1016/j.actaastro.2015.03.031.
  • F. Ebrahimi and M. R. Barati, “A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams,” Compos. Struct., vol. 159, pp. 174–182, 2017. DOI: 10.1016/j.compstruct.2016.09.058.
  • R. Ansari, M. F. Oskouie, R. Gholami, and F. Sadeghi, “Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory,” Compos. Part B: Eng., vol. 89, pp. 316–327, 2016.‏ DOI: 10.1016/j.compositesb.2015.12.029.
  • W. Wang, pp. Li, F. Jin, and J. Wang, “Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects,” Compos. Struct., vol. 140, pp. 758–775, 2016b. DOI: 10.1016/j.compstruct.2016.01.035.
  • A. Jamalpoor, A. Ahmadi-Savadkoohi, M. Hossein, and S. Hosseini-Hashemi, “Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco-Pasternak medium via nonlocal elasticity theory,” Eur. J. Mech.-A/Solids, 2016.‏
  • S. P. Timoshenko and J. M. Gere, Theory of elastic stability. New York: McGraw-Hill, 1961.‏
  • D.-H. Wang and G.-F. Wang, “Surface effects on the vibration and buckling of double-nanobeam-systems,” Hindawi Publishing Corporation J. Nanomaterials, vol. 7, no. 2, pp. 7–14, 2011b.
  • Z. Yan and L. Y. Jiang, “Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints,” In Proc. R. Soc. A (p. rspa20120214), The Royal Society, 2012.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.