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Analyzing exact nonlinear forced vibrations of two-phase magneto-electro-elastic nanobeams under an elliptic-type force

  • Mirjavadi, Seyed Sajad (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Nikookar, Mohammad (Department of Civil Engineering, Faculty of Engineering, University of Guilan) ;
  • Mollaee, Saeed (Auckland Bioengineering Institute, University of Auckland) ;
  • Forsat, Masoud (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Barati, Mohammad Reza (Fidar project Qaem Company) ;
  • Hamouda, A.M.S. (Department of Mechanical and Industrial Engineering, Qatar University)
  • Received : 2020.01.31
  • Accepted : 2020.05.20
  • Published : 2020.07.25
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Abstract

The present paper deals with analyzing nonlinear forced vibrational behaviors of nonlocal multi-phase piezo-magnetic beam rested on elastic substrate and subjected to an excitation of elliptic type. The applied elliptic force may be presented as a Fourier series expansion of Jacobi elliptic functions. The considered multi-phase smart material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. Additionally, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton's principle and von-Kármán geometric nonlinearity. Then, an exact solution based on Jacobi elliptic functions has been provided to obtain nonlinear vibrational frequencies. It is found that nonlinear vibrational behaviors of the nanobeam are dependent on the magnitudes of induced electrical voltages, magnetic field intensity, elliptic modulus, force magnitude and elastic substrate parameters.

Keywords

Acknowledgement

The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.

References

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, Int. J., 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489
  2. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, Int. J., 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347
  3. 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., Int. J., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175
  4. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  5. Alasadi, A.A., Ahmed, R.A. and Faleh, N.M. (2019), "Analyzing nonlinear vibrations of metal foam nanobeams with symmetric and non-symmetric porosities", Adv. Aircr. Spacecr. Sci., Int. J., 6(4), 273-282. https://doi.org/10.12989/aas.2019.6.4.273
  6. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magnetoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  7. Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., Int. J., 6(2), 147-159. https:// doi.org/10.12989/smm.2019.6.2.147
  8. Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electroelastic beam", J. Sound Vib., 299(1-2), 44-63. https://doi.org/10.1016/j.jsv.2006.06.044
  9. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., Int. J., 6(3), 257-278. https://doi.org/10.12989/anr.2018.6.3.257
  10. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2017), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123(1), 104. https://doi.org/10.1007/s00339-016-0712-5
  11. Azimi, M., Mirjavadi, S.S., Shafiei, N., Hamouda, A.M.S. and Davari, E. (2018), "Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution", Mech. Adv. Mater. Struct., 25(6), 467-480. https://doi.org/10.1080/15376494.2017.1285455
  12. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, Int. J., 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579
  13. Barati, M.R. (2017), "Coupled effects of electrical polarizationstrain gradient on vibration behavior of double-layered flexoelectric nanoplates", Smart Struct. Syst., Int. J., 20(5), 573-581. https://doi.org/10.12989/sss.2017.20.5.573
  14. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019). "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., Int. J., 3(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
  15. Bedia, A., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic twounknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
  16. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., Int. J., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081
  17. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S. and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., Int. J., 7(6), 443-457. https://doi.org/10.12989/anr.2019.7.6.443
  18. Berghouti, H., Bedia, A.E.A., Benkhedda, A. and Tounsi, A. (2019). "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  19. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  20. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  21. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  22. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  23. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  24. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191
  25. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F. Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  26. Chaudhary, S., Sahu, S.A. and Singhal, A. (2017), "Analytic model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum", Acta Mechanica, 228(2), 495-529. https://doi.org/10.1007/s00707-016-1708-0
  27. Dehghan, M. and Ebrahimi, F. (2018), "On wave dispersion characteristics of magneto-electro-elastic nanotubes considering the shell model based on the nonlocal strain gradient elasticity theory. Eur. Phys. J. Plus, 133(11), 466. https://doi.org/10.1140/epjp/i2018-12304-7
  28. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  29. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
  30. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  31. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  32. Eshraghi, I., Jalali, S.K. and Pugno, N.M. (2016), "Imperfection sensitivity of nonlinear vibration of curved single-walled carbon nanotubes based on nonlocal timoshenko beam theory", Materials, 9(9), 786. https://doi.org/10.3390/ma9090786
  33. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  34. 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
  35. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and nonuniform porosities", Coupl. Syst. Mech., Int. J., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247
  36. Guo, J., Chen, J. and Pan, E. (2016), "Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory", Compos. Part B Eng., 107, 84-96. https://doi.org/10.1016/j.compositesb.2016.09.044
  37. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater. [In press] https://doi.org/10.1177/1099636219845841
  38. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, Int. J., 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037
  39. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart Mater. Struct., 23(12), 125036. https://doi.org/10.1088/0964-1726/23/12/125036
  40. Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscip. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401
  41. Li, Y. and Shi, Z. (2009), "Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature", Compos. Struct., 87(3), 257-264. https://doi.org/10.1016/j.compstruct.2008.01.012
  42. Li, L., Tang, H. and Hu, Y. (2018), "Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature", Compos. Struct., 184, 1177-1188. https://doi.org/10.1016/j.compstruct.2017.10.052
  43. Liu, S., Fu, Z., Liu, S. and Zhao, Q. (2001), "Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations", Phys. Lett. A, 289(1-2), 69-74. https://doi.org/10.1016/S0375-9601(01)00580-1
  44. Liu, H., Liu, H. and Yang, J. (2018), "Vibration of FG magnetoelectro-viscoelastic porous nanobeams on visco-Pasternak foundation", Compos. Part B Eng., 155, 244-256. https://doi.org/10.1016/j.compositesb.2018.08.042
  45. Mahesh, V. and Kattimani, S. (2019), "Finite element simulation of controlled frequency response of skew multiphase magnetoelectro-elastic plates", J. Intell. Mater. Syst. Struct., 30(12), 1757-1771. https://doi.org/10.1177%2F1045389X19843674 https://doi.org/10.1177/1045389X19843674
  46. Mahesh, V., Sagar, P.J. and Kattimani, S. (2018), "Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate", J. Intell. Mater. Syst. Struct., 29(7), 1430-1455. https://doi.org/10.1177%2F1045389X17740739 https://doi.org/10.1177/1045389X17740739
  47. Mahesh, V., Kattimani, S., Harursampath, D. and Trung, N.T. (2019), "Coupled evaluation of the free vibration characteristics of magneto-electro-elastic skew plates in hygrothermal environment", Smart Struct. Syst., Int. J., 24(2), 267-292. https://doi.org/10.12989/sss.2019.24.2.267
  48. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Bedia, A.E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177%2F1099636217727577 https://doi.org/10.1177/1099636217727577
  49. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A, 123(5), 315. https://doi.org/10.1007/s00339-017-0918-1
  50. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M. S. (2018a), "Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load", Mater. Res. Express, 6(3), 035029. https://doi.org/10.1088/2053-1591/aaf5a2
  51. Mirjavadi, S.S., Afshari, B.M., Khezel, M., Shafiei, N., Rabby, S. and Kordnejad, M. (2018b), "Nonlinear vibration and buckling of functionally graded porous nanoscaled beams", J. Brazil. Soc. Mech. Sci. Eng., 40(7), 352. https://doi.org/10.1007/s40430-018-1272-8
  52. Mirjavadi, S.S., Forsat, M., Hamouda, A.M.S. and Barati, M.R. (2019a), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552
  53. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", Eur. J. Mech. A Solids, 74, 210-220. https://doi.org/10.1016/j.euromechsol.2018.11.004
  54. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019c), "Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection", Microsyst. Technol., 25, 3137-3150. https://doi.org/10.1007/s00542-018-4277-4
  55. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2019d), "Postbuckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technol., 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3
  56. Mohammadi, H., Mahzoon, M., Mohammadi, M. and Mohammadi, M. (2014), "Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation", Nonlinear Dyn., 76(4), 2005-2016. https://doi.org/10.1007/s11071-014-1264-x
  57. 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. http://dx.doi.org/10.12989/sem.2016.59.3.431
  58. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397
  59. Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383. https://doi.org/10.12989/sss.2017.19.2.115
  60. Mutasim, S., Al-Qaisia, A.A. and Shatarat, N.K. (2017), "Nonlinear vibrations of a SWCNT with geometrical imperfection using nonlocal elasticity theory", Modern Appl. Sci., 11(10), 91. https://doi.org/10.5539/mas.v11n10p91
  61. Nan, C.W. (1994), "Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases", Phys. Rev. B, 50(9), 6082. https://doi.org/10.1103/PhysRevB.50.6082
  62. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  63. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A (2019), "Free vibration analysis of angle-ply laminated composite and softcore sandwich plates", Steel Compos. Struct., Int. J., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663
  64. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  65. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063
  66. Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
  67. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637
  68. Vinyas, M. (2020a), "Computational analysis of smart magnetoelectro-elastic materials and structures: review and classification", Arch. Comput. Methods Eng., 1-44. https://doi.org/10.1007/s11831-020-09406-4
  69. Vinyas, M. (2020b), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044
  70. Vinyas, M. (2020c), "Interphase effect on the controlled frequency response of three-phase smart magneto-electro-elastic plates embedded with active constrained layer damping: FE study", Mater. Res. Express, 6(12), 125707. https://doi.org/10.1088/2053-1591/ab6649
  71. Vinyas, M. and Kattimani, S.C. (2017a), "A finite element based assessment of static behavior of multiphase magneto-electroelastic beams under different thermal loading", Struct. Eng. Mech., Int. J., 62(5), 519-535. https://doi.org/10.12989/sem.2017.62.5.519
  72. Vinyas, M. and Kattimani, S.C. (2017b), "Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: a finite element study", Compos. Struct., 178, 63-86. https://doi.org/10.1016/j.compstruct.2017.06.068
  73. Vinyas, M. and Kattimani, S.C. (2017c), "Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis", Compos. Struct., 180, 617-637. https://doi.org/10.1016/j.compstruct.2017.08.015
  74. Vinyas, M. and Kattimani, S.C. (2017d), "A 3D finite element static and free vibration analysis of magneto-electro-elastic beam", Coupl. Syst. Mech., Int. J., 6(4), 465-485. https://doi.org/10.12989/csm.2017.6.4.465
  75. Vinyas, M. and Kattimani, S.C. (2018), "Investigation of the effect of $BaTiO_3/CoFe_2O_4$ particle arrangement on the static response of magneto-electro-thermo-elastic plates", Compos. Struct., 185, 51-64. https://doi.org/10.1016/j.compstruct.2017.10.073
  76. Vinyas, M., Sandeep, A.S., Nguyen-Thoi, T., Ebrahimi, F. and Duc, D.N. (2019a), "A finite element-based assessment of free vibration behaviour of circular and annular magneto-electroelastic plates using higher order shear deformation theory", J Intell. Mater. Syst. Struct., 30(16), 2478-2501. https://doi.org/10.1177%2F1045389X19862386 https://doi.org/10.1177/1045389X19862386
  77. Vinyas, M., Nischith, G., Loja, M.A.R., Ebrahimi, F. and Duc, N.D. (2019b), "Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory", Compos. Struct., 214, 132-142. https://doi.org/10.1016/j.compstruct.2019.02.010
  78. Vinyas, M., Harursampath, D. and Thoi, T.N. (2020), "A higher order coupled frequency characteristics study of smart magnetoelectro-elastic composite plates with cut-outs using finite element methods", Def. Technol. [In press] https://doi.org/10.1016/j.dt.2020.02.009
  79. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015
  80. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  81. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  82. 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., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693

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