Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis of porous micro sandwich plate: Free and forced vibration under magneto-electro-elastic loadings

  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Meskini, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.04.14
  • Accepted : 2019.10.26
  • Published : 2020.01.25
⟨ Previous Next ⟩

Abstract

In this study, the free and forced vibration analysis of micro sandwich plate with porous core layer and magneto-electric face sheets based on modified couple stress theory and first order shear deformation theory under simply supported boundary conditions is illustrated. It is noted that the core layer is composed from balsa wood and also piezo magneto-electric facesheets are made of BiTiO3-CoFe2O4. Using Hamilton's principle, the equations of motion for micro sandwich plate are obtained. Also, the Navier's method for simply support boundary condition is used to solve these equations. The effects of applied voltage, magnetic field, length to width ratio, thickness of porous to micro plate thickness ratio, type of porous, coefficient of porous on the frequency ratio are investigated. The numerical results indicate that with increasing of the porous coefficient, the non-dimensional frequency increases. Also, with an increase in the electric potential, the non-dimensional frequency decreases, while and with increasing of the magnetic potential is vice versa.

Keywords

Acknowledgement

Supported by : University of Kashan

The authors would like to thank the referees for their valuable comments. Also, they are thankful to the Iranian Nanotechnology Development Committee for their financial support, and the University of Kashan for supporting this work by Grant No. 682561/20.

References

  1. Abazid, M.A. and Sobhy, M. (2018), "Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory", Microsyst. Technol., 24(2), 1227-1245. https://doi.org/10.1007/s00542-017-3492-8
  2. Arefi, M. and Zenkour, A.M. (2016), "Free vibration wave propagation and tension analyses of a sandwich micro nano rod subjected to electric potential using strain gradient theory", Mater. Res. Exp., 3(11), 115704. https://doi.org/10.1088/2053-1591/3/11/115704
  3. Arefi, M. and Zenkour, A.M. (2017a), "Effect of thermos magneto- electromechanical fields on the bending behaviors of a three-layered nano plate based on sinusoidal shear deformation plate theory", J. Sand. Struct. Mater., 21(2), 639-669. https://doi.org/10.1177/1099636217697497
  4. Arefi, M. and Zenkour, A.M. (2017b), "Electro-magneto-elastic analysis of a three-layer curved beam", Smart. Struct. Syst., Int. J., 19(6), 695-703. https://doi.org/10.12989/sss.2017.19.6.695
  5. Arefi, M. and Zenkour, A.M. (2017c), "Nonlocal electro-thermomechanical analysis of a sandwich nanoplate containing a Kelvin-Voigt viscoelastic nanoplate and two piezoelectric layers", Acta. Mech., 228(2), 475-493. https://doi.org/10.1007/s00707-016-1716-0
  6. Barati, M.R. and Zenkour, A.M. (2017), "Investigating postbuckling of geometrically imperfect metal foam nano beams with symmetric and asymmetric porosity distributions", Compos. Struct., 182, 91-98. https://doi.org/10.1016/j.compstruct.2017.09.008
  7. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025
  8. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aero. Sci. Tech., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020
  9. Dong, Y.H., He, L.W., Wang, L., Li, Y.H. and Yang, J. (2018), "Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: An analytical study", Aero. Sci. Tech., 82-83, 466-478. https://doi.org/10.1016/j.ast.2018.09.037
  10. Ebrahimi, F. and Barati, M.R. (2019), "On static stability of electro-magnetically affected smart magneto-electro-elastic nanoplates", Adv. Nano Res., Int. J., 7(1), 63-75. https://doi.org/10.12989/anr.2019.7.1.063
  11. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109-123. https://doi.org/10.12989/anr.2019.7.2.109
  12. Fakhari, V., Ohadi, A. and Yousefian, P. (2011), "Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layer in thermal environment", Compos. Struct., 93, 2310-2321. https://doi.org/10.1016/j.compstruct.2011.03.019
  13. Farajpour, A., Yazdi, M.R.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
  14. Farokhi, H. and Ghayesh, M.H. (2018), "Modified couple stress theory in orthogonal curvilinear coordinates", Acta. Mech., 230(3), 851-869. https://doi.org/10.1007/s00707-018-2331-z
  15. Gao, K., Gao, W., Chen, D. and Yang, J. (2018a), "Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation", Comp. Struct., 204, 831-846. https://doi.org/10.1016/j.compstruct.2018.08.013
  16. Gao, K., Gao, W., Wu, B., Wu, D. and Song, C. (2018b), "Chongmin Song; Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales", Thin-wall. Struct. 125, 281-293. https://doi.org/10.1016/j.tws.2017.12.039
  17. Gao, K., Huang, Q., Kitipornchai, S. and Yang, J. (2019), "Nonlinear dynamic buckling of functionally graded porous beams", Mech. Adv. Mater. Struct., 1-12. https://doi.org/10.1080/15376494.2019.1567888
  18. Ghasemi, A.R. and Meskini, M. (2019), "Free vibration analysis of porous laminated rotating circular cylindrical shells", J. Vib. Control, 25(18), 2494-2508. https://doi.org/10.1177/1077546319858227
  19. Ghayesh, M.H., Farokhi, H., Hussain, S., Gholipour, A. and Arjomandi, M. (2017), "A size-dependent nonlinear third-order shear-deformable dynamic model for a microplate on an elastic medium", Microsyst. Technol., 23(8), 3281-3299. https://doi.org/10.1007/s00542-016-3096-8
  20. Ghorbanpour Arani, A. and Zamani, M.H. (2018), "Nonlocal free vibration analysis of FG-porous shear and normal deformable sandwich nanoplate with piezoelectric face sheets resting on silica aerogel foundation", Arab. J. Sci. Eng., 43(9), 4675-4688. https://doi.org/10.1007/s13369-017-3035-8
  21. Ghorbanpour Arani, A., Rousta Navi, B., Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189
  22. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory", J. Sound. Vib., 331, 94-106. https://doi.org/10.1016/j.jsv.2011.08.020
  23. Kim, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023
  24. Li, Y.S. and Pan, E. (2015), "Static bending and free vibration of a functionally graded piezo electric micro plate based on the modified couple-stress theory", Int. J. Eng. Sci., 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009
  25. 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
  26. Mao, J.J. and Zhang, W. (2018), "Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation", Compos. Struct., 203, 551-565. https://doi.org/10.1016/j.compstruct.2018.06.076
  27. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431
  28. Mohammadimehr, M. and Rostami, R. (2017), "Bending buckling and forced vibration analysis of nonlocal nano compsite microplate using TSDT considering MEE properties dependent to various volume fractions of $CoFe_{2}O_{4}-BaTiO_{3}$", J. Theo. Appl. Mech., 55(3), 853-868. https://doi.org/10.15632/jtam-pl.55.3.853
  29. Mohammadimehr, M., Mohandes, M. and Moradi, M. (2014), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J. Vib. Control, 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513
  30. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Surface stress effect on the nonlocal biaxial buckling and bending analysis of polymeric piezoelectric nanoplate reinforced by CNT using eshelby-mori-tanaka approach", J. Solid Mech., 7(2), 173-190.
  31. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic microplate based on surface stress and modified couple stress theories using differential quadrature method", Appl. Mathe. Mech., 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9
  32. Mohammadimehr, M., BabaAkbar, H.Z., Parakandeh, A. and Ghorbanpour Arani, A. (2017a), "Vibration analysis of doublebonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., Int. J., 64(3), 361-379. https://doi.org/10.12989/sem.2017.64.3.361
  33. Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2017b), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622
  34. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2017c), "Dynamic stability of modified strain gradient theory sinusoidal viscoelastic piezoelectric polymeric functionally graded singlewalled carbon nanotubes reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Structu., 24(16), 1325-1342. https://doi.org/10.1080/15376494.2016.1227507
  35. Mohammadimehr, M., Okhravi, S.V., Akhavan Alavi, S.M., (2018), "Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT", J. Vib. Control, 24(8), 1551-1569. https://doi.org/10.1177/1077546316664022
  36. Mohandes, M. and Ghasemi, A.R. (2016), "Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro nano laminated composite Euler-Bernoulli beam under thermal loading", Part C. J. Mech. Eng. Sci., 231(21), 4044-4056. https://doi.org/10.1177/0954406216656884
  37. Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008
  38. Newaz, G., Mayeed, M. and Rasul, A. (2016), "Characterization of balsa wood mechanical properties required for continuum damage mechanics analysis", J. Mater. Design. Appl., 230(1), 206-218. https://doi.org/10.1177/1464420714564711
  39. Razavi, S. and Shooshtari, A. (2015), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384. https://doi.org/10.1016/j.compstruct.2014.08.034
  40. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, New Jersey, USA.
  41. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125
  42. Sasmal, S., Ravivarman, N., Sindu, B.S. and Vignesh, K. (2017), "Electrical conductivity and piezo-resistive characteristics of CNT and CNF incorporated cementitious nanocomposites under static and dynamic loading", Compos. Part A. Appl. Sci. Manufact., 100, 227-243. https://doi.org/10.1016/j.compositesa.2017.05.018
  43. Sek, M.S., Aydin, M., Yurtcu, H.H. and Reddy, J.N. (2015), "Sizedependent vibration of a microplate under the action of a moving load based on the modified couple stress theory", Acta. Mech., 226(11), 3807-3822. https://doi.org/10.1007/s00707-015-1437-9
  44. Selim, B.A., Yin, B.B. and Liew, K.M. (2108), "Impact analysis of CNT-reinforced composite plates integrated with piezoelectric layers based on Reddy's higher-order shear deformation theory", Compos. Part B. Eng., 136, 10-19. https://doi.org/10.1016/j.compositesb.2017.09.074
  45. Shojaeefard, M.H., Googarchin, H.S., Ghadiri, M. and Mahinzare, M. (2017), "Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT", Appl. Math. Model., 50, 633-655. https://doi.org/10.1016/j.apm.2017.06.022
  46. Thai, H.T. and Vo, T.P. (2013), "A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory", Compos. Struct., 96, 376-383. https://doi.org/10.1016/j.compstruct.2012.09.025
  47. Wang, Y., Feng, C., Santiuste, C., Zhao, Z. and Yang, J. (2019), "Buckling and postbuckling of dielectric composite beam reinforced with Graphene Platelets (GPLs)", Aero. Sci. Tech, 91, 208-218. https://doi.org/10.1016/j.ast.2019.05.008
  48. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  49. Zhang, Y.F., Zhang, W. and Yao, Z.G. (2018), "Analysis on nonlinear vibrations near internal resonances of a composite laminated piezoelectric rectangular plate", Eng. Struct., 173, 89-106. https://doi.org/10.1016/j.engstruct.2018.04.100
  50. Zhao, J., Choe, K., Xie, F., Wang, A., Shuai, C. and Wang, Q. (2018), "Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions", Compos. Part B. Eng., 155, 369-381. https://doi.org/10.1016/j.compositesb.2018.09.001

Cited by

  1. Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.115
  2. Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.151
  3. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2020, https://doi.org/10.12989/amr.2021.10.3.169