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A numerical and computer simulation for dynamic stability analysis of 3-unknown graded porous nanoplates using a Chebyshev-Ritz-Bolotin method

  • Wei, Dong (Engineering Research Center Heavy Machinery Ministry of Education, Taiyuan University of Science and Technology)
  • Received : 2018.12.18
  • Accepted : 2021.02.19
  • Published : 2021.05.25

Abstract

A numerical and computer simulation for dynamic stability analysis of graded porous nanoplates has been provided using a Chebyshev-Ritz-Bolotin approach. The nanoplate has been formulated according to the nonlocal elasticity and a 3-unkown plate model capturing neutral surface location. All of material properties are assumed to be dependent of porosity factor which determines the amount or volume of pores. The nano-size plate has also been assumed to be under temperature and moisture variation. It will be shown that stability boundaries of the nanoplate are dependent on static and dynamical load factors, porosity factor, temperature variation and nonlocal parameter.

Keywords

References

  1. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. http://doi.org/10.12989/gae.2019.17.2.175.
  2. Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. https://doi.org/10.12989/sem.2020.76.3.413.
  3. Ahouel, M., Houari, M.S.A., 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.
  4. Atmane, H.A., Tounsi, A and Bernard, F. (2015a), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13, 71-84. https://doi.org/10.1007/s10999-015-9318-x.
  5. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015b), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. http://doi.org/10.12989/scs.2015.19.2.369.
  6. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. http://doi.org/10.12989/eas.2018.14.2.103.
  7. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. http://dx.doi.org/10.12989/scs.2015.18.4.1063.
  8. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. http://doi.org/10.12989/sem.2017.62.6.695.
  9. 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.
  10. Faleh, N.M., Abboud, I.K. and Nori, A.F. (2020), "Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects", Smart Struct. Syst., 25(6), 707-717. https://doi.org/10.12989/sss.2020.25.6.707.
  11. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  12. Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020a), "Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams", Eur. Phys. J. Plus, 135(5), 439. https://doi.org/10.1140/epjp/s13360-020-00399-4.
  13. Fenjan, R.M., Ahmed, R.A., Faleh, N.M. and Hani, F.M. (2020e), "Static stability analysis of smart nonlocal thermo-piezo-magnetic plates via a quasi-3D formulation", Smart Struct. Syst., 26(1), 77-87. https://doi.org/10.12989/sss.2020.26.1.077.
  14. Fenjan, R.M., Ahmed, R.A., Hamad, L.B. and Faleh, N.M. (2020b), "A review of numerical approach for dynamic response of strain gradient metal foam shells under constant velocity moving loads", Adv. Comput. Des., 5(4), 349-362. https://doi.org/10.12989/acd.2020.5.4.349.
  15. Fenjan, R.M., Faleh, N.M. and Ahmed, R.A. (2020c), "Geometrical imperfection and thermal effects on nonlinear stability of microbeams made of graphene-reinforced nanocomposites", Adv. Nano Res., 9(3), 147-156. https://doi.org/10.12989/anr.2020.9.3.147.
  16. Fenjan, R.M., Faleh, N.M. and Ridha, A.A. (2020d), "Strain gradient based static stability analysis of composite crystalline shell structures having porosities", Steel Compos. Struct., 36(6), 631-642. https://doi.org/10.12989/scs.2020.36.6.631.
  17. Han, S.C., Park, W.T. and Jung, W.Y. (2015), "A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface", Compos. Struct., 131, 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025.
  18. Hosseini, M. and Jamalpoor, A. (2015), "Analytical solution for thermomechanical vibration of double-viscoelastic nanoplate-systems made of functionally graded materials", J. Therm. Stress., 38(12), 1428-1456. https://doi.org/10.1080/01495739.2015.1073986.
  19. 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. http://doi.org/10.12989/scs.2016.22.2.257.
  20. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631. http://doi.org/10.12989/sem.2018.65.5.621.
  21. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. http://doi.org/10.12989/sem.2017.64.4.391.
  22. Kunbar, L.A.H., Hamad, L.B., Ahmed, R.A. and Faleh, N.M. (2020), "Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects", Smart Struct. Syst., 25(5), 619-630. https://doi.org/10.12989/sss.2020.25.5.619.
  23. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A. and Bedia, E.A.A. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Earthq. Struct., 14(2), 117-128. https://doi.org/10.12989/eas.2018.14.2.117.
  24. Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B. (2016), "Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations", Appl. Math. Model., 40(2), 738-749. https://doi.org/10.1016/j.apm.2015.09.093.
  25. Mehala, T., Belabed, Z., Tounsi, A. and Beg, O.A. (2018), "Investigation of influence of homogenization models on stability and dynamics of FGM plates on elastic foundations", Geomech. Eng., 16(3), 257-271. http://doi.org/10.12989/gae.2018.16.3.257.
  26. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.
  27. Reddy, J.N. (1990), "A general non-linear third-order theory of plates with moderate thickness", Int. J. Nonlin. Mech., 25(6), 677-686. https://doi.org/10.1016/0020-7462(90)90006-U.
  28. Sadoun, M., Houari, M.S.A., Bakora, A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory", Geomech. Eng., 16(2), 141-150. http://doi.org/10.12989/gae.2018.16.2.141.
  29. Taj, M.G., Chakrabarti, A. and Sheikh, A.H. (2013), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 37(18), 8484-8494. https://doi.org/10.1016/j.apm.2013.03.058.
  30. Thai, H.T., Vo, T., Bui, T. and Nguyen, T.K. (2014), "A quasi-3D hyperbolic shear deformation theory for functionally graded plates", Acta Mechanica, 225(3), 951-964. https://doi.org/10.1007/s00707-013-0994-z.
  31. 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.
  32. 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.
  33. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026.
  34. Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E: Low Dimens. Syst. Nanostruct., 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003.
  35. 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. http://doi.org/10.12989/sem.2017.64.2.145.