290
Views
18
CrossRef citations to date
0
Altmetric
Original Articles

Longitudinal varying elastic foundation effects on vibration behavior of axially graded nanobeams via nonlocal strain gradient elasticity theory

&
Pages 953-963 | Received 18 Dec 2016, Accepted 27 Mar 2017, Published online: 26 Sep 2017

References

  • F. Ebrahimi and A. Rastgoo, Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers, Smart Mater. Struct., vol. 17, p. 015044, 2008a.
  • F. Ebrahimi and A. Rastgoo, An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory, Thin-Walled Struct., vol. 46, pp. 1402–1408, 2008b.
  • F. Ebrahimi and A. Rastgoo, Free vibration analysis of smart FGM plates, Int. J. Mech. Syst. Sci. Eng., vol. 2, no. 2, pp. 94–99, 2008c.
  • F. Ebrahimi, A. Rastgoo, and A.A. Atai, Theoretical analysis of smart moderately thick shear deformable annular functionally graded plate, Eur. J. Mech. A: Solids, vol. 28, pp. 962–997, 2009.
  • F. Ebrahimi and M. Zia, Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities, Acta Astronaut., vol. 116, pp. 117–125, 2015.
  • F. Ebrahimi, F. Ghasemi, and E. Salari, Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica, vol. 51, no. 1, pp. 223–249, 2016.
  • F. Ebrahimi and M. Mokhtari (2015). Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. J. Braz. Soc. Mech. Sci. Eng., vol. 37, no. 4, pp. 1435–1444.
  • F. Ebrahimi, M.H. Naei, and A. Rastgoo, Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation, J. Mech. Sci. Technol., vol. 23, no. 8, pp. 2107–2124, 2009.
  • F. Ebrahimi, A. Rastgoo, and M.H. Kargarnovin, Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers, J. Mech. Sci. Technol., vol. 22, no. 6, pp. 1058–1072, 2008.
  • M. Rahaeifard, M.H. Kahrobaiyan, M.T. Ahmadian, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, DETC2009-86254, 3rd International Conference on Micro- and Nanosystems (MNS3), San Diego, CA, USA, 2009.
  • A.C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci., vol. 10, no. 1, pp. 1–16, 1972.
  • A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983.
  • F. Ebrahimi and M.R. Barati, Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams, Eur. Phys. J. Plus, vol. 131, no. 9, p. 346, 2016.
  • 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, p. 105014, 2016.
  • 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, 2016.
  • F. Ebrahimi and E. Salari, Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams, Smart Mater. Struct., vol. 24, no. 12, p. 125007, 2015
  • 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, 2016.
  • F. Ebrahimi and M.R. Barati, Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams, J. Mech., vol. 33, no. 1, pp. 23–33, 2017.
  • F. Ebrahimi and S.H.S. Hosseini, Double nanoplate-based NEMS under hydrostatic and electrostatic actuations, Eur. Phys. J. Plus, vol. 131, no. 5, pp. 1–19, 2016.
  • F. Ebrahimi and S.H.S. Hosseini, Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates, Appl. Phys. A, vol. 122, no. 10, p. 922, 2016.
  • F. Ebrahimi and S.H.S. Hosseini, Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates, J. Therm. Stresses, vol. 39, no. 5, pp. 606–625, 2016.
  • F. Ebrahimi and M.R. Barati, A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams, Arab. J. Sci. Eng., vol. 41, no. 5, pp. 1679–1690, 2016a.
  • F. Ebrahimi and P. Nasirzadeh, A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method, J. Theor. Appl. Mech., vol. 53, no. 4, pp. 1041–1052, 2015.
  • R. Barretta, L. Feo, R. Luciano, F.M. de Sciarra, and R. Penna, Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation, Compos. Part B: Eng., vol. 100, pp. 208–219, 2016.
  • M.A. Eltaher, S.A. Emam, and F.F. Mahmoud, Free vibration analysis of functionally graded size-dependent nanobeams, Appl. Math. Comput., vol. 218, no. 14, pp. 7406–7420, 2012.
  • M.A. Eltaher, S.A. Emam, and F.F. Mahmoud, Static and stability analysis of nonlocal functionally graded nanobeams, Compos. Struct., vol. 96, 82–88, 2013.
  • A. Zemri, M.S.A. Houari, A.A. Bousahla, and A. Tounsi, A mechanical response of functionally graded nanoscale beam: An assessment of a refined nonlocal shear deformation theory beam theory, Struct. Eng. Mech., vol. 54, no. 4, pp. 693–710, 2015.
  • 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, 2016.
  • F. Ebrahimi and M.R. Barati, Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, J. Braz. Soc. Mech. Sci. Eng., vol. 39, no. 3, pp. 937–952, 2017.
  • F. Ebrahimi and M.R. Barati, Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams, Mech. Adv. Mater. Struct., vol. 24, no. 11, pp. 924–936, 2017.
  • 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, 2016.
  • F. Ebrahimi, Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment, Mech. Adv. Mater. Struct., vol. 20, no. 10, pp. 854–870, 2013.
  • F. Ebrahimi and E. Salari, Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams, Mech. Adv. Mater. Struct., vol. 23, no. 12, pp. 1379–1397, 2016.
  • 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.
  • F. Ebrahimi, E. Salari, and S.A.H. Hosseini, Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions, J. Therm. Stresses, vol. 38, no. 12, pp. 1360–1386, 2015.
  • 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, 2016.
  • F. Ebrahimi and M.R. Barati, Vibration analysis of nonlocal beams made of functionally graded material in thermal environment, Eur. Phys. J. Plus, vol. 131, no. 8, p. 279, 2016.
  • 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, 2016.
  • 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, 2016.
  • 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, p. 792, 2016.
  • 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., vol. 7, no. 2, pp. 69–90, 2016.
  • F. Ebrahimi and M.R. Barati, Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory, Appl. Phys. A, vol. 122, no. 9, p. 843, 2016.
  • F. Ebrahimi and M.R. Barati, Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory, Arab. J. Sci. Eng., vol. 42, no. 5, pp. 1715–1726, 2017.
  • F. Ebrahimi and M.R. Barati, On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions, Appl. Phys. A, vol. 122, no. 10, p. 880, 2016.
  • F. Ebrahimi and M.R. Barati, Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field, J. Intell. Mater. Syst. Struct., 1045389X16672569, Vol. 28, no. 11, pp. 1472–1490, 2017.
  • 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, p. 910, 2016.
  • F. Ebrahimi and M.R. Barati, Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates, J. Braz. Soc. Mech. Sci. Eng., vol. 39, no. 6, pp. 2203–2223, 2017.
  • F. Ebrahimi and M.R. Barati, Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Compos. Struct., vol. 159, pp. 433–444, 2017.
  • 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.
  • F. Ebrahimi, M.R. Barati, and P. Haghi, Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams, J. Therm. Stresses, vol. 40, no. 5, pp. 535–547, 2017.
  • N.T. Nguyen, N.I. Kim, and J. Lee, Analytical solutions for bending of transversely or axially FG nonlocal beams, Steel Compos. Struct., vol. 17, no. 5, pp. 641–665, 2014.
  • N. Shafiei, M. Kazemi, M. Safi, and M. Ghadiri, Nonlinear vibration of axially functionally graded non-uniform nanobeams, Int. J. Eng. Sci., vol. 106, pp. 77–94, 2016.
  • D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, and P. Tong, Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids, vol. 51, no. 8, pp. 1477–1508, 2003.
  • C.W. Lim, G. Zhang, and J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, vol. 78, pp. 298–313, 2015.
  • L. Li, Y. Hu, and L. Ling, Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory, Phys. E: Low-Dimensional Syst. Nanostructures, vol. 75, pp. 118–124, 2016.
  • M. Şimşek, Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, Int. J. Eng. Sci., vol. 105, pp. 12–27, 2016.
  • 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, 2016.
  • F. Ebrahimi, M.R. Barati, and A. Dabbagh, Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams, Appl. Phys. A, vol. 122, no. 11, p. 949, 2016.
  • F. Ebrahimi, M. Ghadiri, E. Salari, S. Amir, 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, p. 1207, 2015.
  • S. Ziaee, Postbuckling and nonlinear free vibration of size-dependent prestressed FG nanobeams resting on elastic foundation based on nonlocal Euler-Bernoulli beam theory, J. Mech. Behav.. Mater., vol. 24, no. 3-4, pp. 91–103, 2015.
  • S.C. Pradhan and T. Murmu, Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method, J. Sound Vib., vol. 321, no. 1, pp. 342–362, 2009.
  • J. Murin, M. Aminbaghai, V. Kutis, and J. Hrabovsky, Modal analysis of the FGM beams with effect of axial force under longitudinal variable elastic Winkler foundation, Eng. Struct., vol. 49, pp. 234–247, 2013.

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.