Abstract
This paper studies nonlinear dynamic characteristics of a nonlocal two-phase piezo-magnetic beam based on a refined higher-order beam formulation and piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. Nonlinear governing equations of a smart nanobeam are derived based on refined beam theory, and a numerical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behavior of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and shear deformation.
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C.N. Anumol, M. Chithra, M.G. Shalini, S.C. Sahoo, Effect of annealing on structural and magnetic properties of NiFe2O4/ZnFe2O4 nanocomposites. J. Magn. Magn. Mater. 469, 81–88 (2019)
S.A. Sahu, A. Singhal, S. Chaudhary, Surface wave propagation in functionally graded piezoelectric material: an analytical solution. J. Intell. Mater. Syst. Struct. 29(3), 423–437 (2018)
A. Singhal, S.A. Sahu, S. Chaudhary, Liouville–Green approximation: an analytical approach to study the elastic waves vibrations in composite structure of piezo material. Compos. Struct. 184, 714–727 (2018)
S. Chaudhary, S.A. Sahu, A. Singhal, Analytic model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum. Acta Mech. 228(2), 495–529 (2017)
E. Pan, F. Han, Exact solution for functionally graded and layered magneto-electro-elastic plates. Int. J. Eng. Sci. 43(3–4), 321–339 (2005)
L. Li, Y. Hu, Critical flow velocity of fluid-conveying magneto-electro-elastic pipe resting on an elastic foundation. Int. J. Mech. Sci. 119, 273–282 (2016)
A.C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10(5), 425–435 (1972)
M. Azimi, S.S. Mirjavadi, N. Shafiei, A.M.S. Hamouda, Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam. Appl. Phys. A 123(1), 104 (2017)
Y. Tlidji, M. Zidour, K. Draiche, A. Safa, M. Bourada, A. Tounsi et al., Vibration analysis of different material distributions of functionally graded microbeam. Struct. Eng. Mech. 69(6), 637–649 (2019)
A. Semmah, H. Heireche, A.A. Bousahla, A. Tounsi, Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT. Adv. Nano Res. 7(2), 89 (2019)
G.L. She, Y.R. Ren, F.G. Yuan, W.S. Xiao, On vibrations of porous nanotubes. Int. J. Eng. Sci. 125, 23–35 (2018)
S.S. Mirjavadi, B.M. Afshari, M. Khezel, N. Shafiei, S. Rabby, M. Kordnejad, Nonlinear vibration and buckling of functionally graded porous nanoscaled beams. J. Braz. Soc. Mech. Sci. Eng. 40(7), 352 (2018)
S.S. Mirjavadi, S. Rabby, N. Shafiei, B.M. Afshari, M. Kazemi, On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment. Appl. Phys. A 123(5), 315 (2017)
M. Rahmanian, M.A. Torkaman-Asadi, R.D. Firouz-Abadi, M.A. Kouchakzadeh, Free vibrations analysis of carbon nanotubes resting on Winkler foundations based on nonlocal models. Physica B 484, 83–94 (2016)
S.S. Mirjavadi, B.M. Afshari, M.R. Barati, A.M.S. Hamouda, Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity. Int. J. Mech. Mater. Des. 1–12 (2019)
G.L. She, K.M. Yan, Y.L. Zhang, H.B. Liu, Y.R. Ren, Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Eur. Phys. J. Plus 133(9), 368 (2018)
L.L. Ke, Y.S. Wang, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E 63, 52–61 (2014)
A.A. Jandaghian, O. Rahmani, Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation. Smart Mater. Struct. 25(3), 035023 (2016)
F. Ebrahimi, M.R. Barati, Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory. Eur. Phys. J. Plus 132(1), 19 (2017)
F. Ebrahimi, M.R. Barati, A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. Int. J. Eng. Sci. 107, 183–196 (2016)
S.S. Mirjavadi, M. Forsat, M. Nikookar, M.R. Barati, A.M.S. Hamouda, Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets. Eur. Phys. J. Plus 134(10), 508 (2019)
R.A. Ahmed, R.M. Fenjan, N.M. Faleh, Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections. Geomech. Eng. 17(2), 175–180 (2019)
L. Li, H. Tang, Y. Hu, Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature. Compos. Struct. 184, 1177–1188 (2018)
A. Kumaravel, N. Ganesan, R. Sethuraman, Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment. Multidiscip. Model. Mater. Struct. 3(4), 461–476 (2007)
A.R. Annigeri, N. Ganesan, S. Swarnamani, Free vibration behaviour of multiphase and layered magneto-electro-elastic beam. J. Sound Vib. 299(1–2), 44–63 (2007)
R.M. Fenjan, R.A. Ahmed, A.A. Alasadi, N.M. Faleh, Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities. Coupled Syst. Mech. 8(3), 247–257 (2019)
D. Zarga, A. Tounsi, A.A. Bousahla, F. Bourada, S.R. Mahmoud, Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory. Steel Compos. Struct. 32(3), 389–410 (2019)
A.F. Al-Maliki, N.M. Faleh, A.A. Alasadi, Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities. Struct. Monit. Maint. 6(2), 147–159 (2019)
L.A. Chaabane, F. Bourada, M. Sekkal, S. Zerouati, F.Z. Zaoui, A. Tounsi et al., Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Struct. Eng. Mech. 71(2), 185–196 (2019)
A. Mahmoudi, S. Benyoucef, A. Tounsi, A. Benachour, E.A. Adda Bedia, S.R. Mahmoud, 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), 1906–1929 (2019)
M. Medani, A. Benahmed, M. Zidour, H. Heireche, A. Tounsi, A.A. Bousahla et al., Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle. Steel Compos. Struct. 32(5), 595–610 (2019)
A. Besseghier, H. Heireche, A.A. Bousahla, A. Tounsi, A. Benzair, Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix. Adv. Nano Res. 3(1), 029 (2015)
S.S. Mirjavadi, M. Forsat, M.R. Barati, G.M. Abdella, A.M.S. Hamouda, B.M. Afshari, S. Rabby, Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents. Microsyst. Technol. 25(9), 3477–3488 (2019)
M. Forsat, S. Badnava, S.S. Mirjavadi, M.R. Barati, A.M.S. Hamouda, Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory. Eur. Phys. J. Plus 135(1), 81 (2020)
S.S. Mirjavadi, Y.Z. Yahya, M. Forsat, I. Khan, A.M.S. Hamouda, M.R. Barati, Magneto-electric effects on nonlocal nonlinear dynamic characteristics of imperfect multi-phase magneto-electro-elastic beams. J. Magn. Magn. Mater. 503, 166649 (2020)
Acknowledgement
The authors would like to thank Mustansiriyah university (http://www.uomustansiriyah.edu.iq) Baghdad-Iraq, for their support in the present work.
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Fenjan, R.M., Ahmed, R.A. & Faleh, N.M. Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams. Eur. Phys. J. Plus 135, 439 (2020). https://doi.org/10.1140/epjp/s13360-020-00399-4
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DOI: https://doi.org/10.1140/epjp/s13360-020-00399-4