Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanics of nonlocal advanced magneto-electro-viscoelastic plates

  • Ebrahimi, Farzad (Mechanical Engineering department, faculty of engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Mechanical Engineering department, faculty of engineering, Imam Khomeini International University) ;
  • Tornabene, Francesco (Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna)
  • Received : 2018.05.25
  • Accepted : 2019.04.02
  • Published : 2019.08.10
⟨ Previous Next ⟩

Abstract

This paper develops a nonlocal strain gradient plate model for damping vibration analysis of smart magneto-electro-viscoelastic nanoplates resting on visco-Pasternak medium. For more accurate analysis of nanoplate, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Viscoelastic effect which is neglected in all previous papers on magneto-electro-viscoelastic nanoplates is considered based on Kelvin-Voigt model. Governing equations of a nonlocal strain gradient smart nanoplate on viscoelastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations. Effects of different factors such as viscoelasticity, nonlocal parameter, length scale parameter, applied voltage and magnetic potential on damping vibration characteristics of a nanoplate are studied.

Keywords

References

  1. Aksencer, T. and Aydogdu, M. (2011), "Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory", Physica E, 43(4), 954-959. https://doi.org/10.1016/j.physe.2010.11.024.
  2. Ansari, R. and Gholami, R. (2016), "Nonlocal free vibration in the pre-and post-buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions", Smart Mater. Struct., 25(9). https://doi.org/10.1088/0964-1726/25/9/095033.
  3. Ansari, R. and Sahmani, S. (2013), "Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations", Appl. Math. Model., 37(12), 7338-7351. https://doi.org/10.1016/j.apm.2013.03.004.
  4. Ansari, R., Arash, B. and Rouhi, H. (2011), "Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity", Compos. Struct., 93(9), 2419-2429. https://doi.org/10.1016/j.compstruct.2011.04.006.
  5. Arani, A.G., Haghparast, E. and Zarei, H.B. (2016), "Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field", Physica B, 495, 35-49. https://doi.org/10.1016/j.physb.2016.04.039.
  6. Bessaim, A., Houari, M.S.A., Bernard, F. and Tounsi, A. (2015), "A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates", Struct. Eng. Mech., 56(2), 223-240. https://doi.org/10.12989/sem.2015.56.2.223.
  7. Ebrahimi, F. and Barati, M.R. (2016a), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Europ. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y.
  8. Ebrahimi, F. and Barati, M.R. (2016b), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A., 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2.
  9. Ebrahimi, F. and Barati, M.R. (2016c), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001.
  10. Ebrahimi, F. and Barati, M.R. (2016d), "Hygrothermal buckling analysis of magnetically actuated embedded higher order functionally graded nanoscale beams considering the neutral surface position", J. Therm. Stress, 39(10), 1210-1229. https://doi.org/10.1080/01495739.2016.1215726.
  11. Ebrahimi, F. and Barati, M.R. (2016e), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177/1077546316646239.
  12. Ebrahimi, F. and Barati, M.R. (2016f), "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., 25(10), https://doi.org/10.1088/0964-1726/25/10/105014
  13. Ebrahimi, F. and Barati, M.R. (2016g), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A., 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1.
  14. Ebrahimi, F. and Barati, M.R. (2016h), "Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(23), 4457-4469. https://doi.org/10.1177/0954406216668912.
  15. Ebrahimi, F. and Barati, M.R. (2017i), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092.
  16. Ebrahimi, F. and Barati, M.R. (2017j), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058.
  17. Ebrahimi, F. and Salari, E. (2015), "Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory", J. Mech. Sci. Technol., 29(9), 3797-3803. https://doi.org/10.1007/s12206-015-0826-2.
  18. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008.
  19. 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.
  20. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  21. Farajpour, A., Shahidi, A.R., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Compos. Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032.
  22. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039.
  23. Hashemi, S.H., Mehrabani, H. and Ahmadi-Savadkoohi, A. (2015), "Exact solution for free vibration of coupled double viscoelastic graphene sheets by visco Pasternak medium", Compos. Part B, 78, 377-383. https://doi.org/10.1016/j.compositesb.2015.04.008.
  24. 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.
  25. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solid, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  26. Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mater. Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044.
  27. Li, L., Hu, Y. and Li, X. (2016), "Longitudinal vibration of sizedependent rods via nonlocal strain gradient theory", J. Mech. Sci., 115, 135-144. https://doi.org/10.1016/j.ijmecsci.2016.06.011.
  28. Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033.
  29. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  30. Mohammadi, M., Farajpour, A., Moradi, A. and Ghayour, M. (2014), "Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment", Compos. Part B, 56, 629-637. https://doi.org/10.1016/j.compositesb.2013.08.060.
  31. Mohammadi, M., Goodarzi, M., Ghayour, M. and Farajpour, A. (2013), "Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory", Compos. Part B, 51, 121-129. https://doi.org/10.1016/j.compositesb.2013.02.044.
  32. Murmu, T., McCarthy, M.A. and Adhikari, S. (2013), "In-plane magnetic field affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach", Compos. Struct., 96, 57-63. https://doi.org/10.1016/j.compstruct.2012.09.005.
  33. Pradhan, S. C. and Murmu, T. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Comput. Mater. Sci., 47(1), 268-274. https://doi.org/10.1016/j.commatsci.2009.08.001.
  34. Pradhan, S.C. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93(2), 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004.
  35. Shen, Z.B., Tang, H.L., Li, D.K. and Tang, G.J. (2012), "Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory", Comput. Mater. Sci., 61, 200-205. https://doi.org/10.1016/j.commatsci.2012.04.003.
  36. Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E, 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003.

Cited by

  1. Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method vol.28, pp.3, 2021, https://doi.org/10.12989/cac.2021.28.3.233
  2. Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment vol.40, pp.6, 2021, https://doi.org/10.12989/scs.2021.40.6.893