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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

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2191-0294
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Volume 19, Issue 3-4

Issues

Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness

Feng Wang / Yu-fang Zheng / Chang-ping Chen
Published Online: 2018-04-21 | DOI: https://doi.org/10.1515/ijnsns-2015-0105

Abstract

With employing the von Karman plate theory, and considering the linearly thickness variation in one direction, the bending problem of a rectangular magnetoelectroelastic plates with linear variable thickness is investigated. According to the Maxwell’s equations, when applying the magnetoelectric load on the plate’s surfaces and neglecting the in-plane electric and magnetic fields in thin plates, the electric and magnetic potentials varying along the thickness direction for the magnetoelectroelastic plates are determined. The nonlinear differential equations for magnetoelectroelastic plates with linear variable thickness are established based on the Hamilton’s principle. The Galerkin procedure is taken to translate a set of differential equations into algebraic equations. The numerical examples are presented to discuss the influences of the aspect ratio and span–thickness ratio on the nonlinear load–deflection curves for magnetoelectroelastic plates with linear variable thickness. In addition, the induced electric and magnetic potentials are also presented with the various values of the taper constants.

Keywords: linearly varying thickness; magnetoelectroelastic plates; nonlinear bending; Galerkin truncation

PACS: 46.25Hf; 46.70.De

MSC 2010: 74F15; 74B20

References

  • [1]

    E. Pan and P.R. Heyliger, Free vibrations of simply supported and multilayered magneto-electro-elastic plates, J. Sound Vib. 252 (2002), 429–442.CrossrefGoogle Scholar

  • [2]

    A.R. Annigeri, N. Ganesan and S. Swarnamani, Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells, Smart Mater. Struct. 15 (2006), 459–467.CrossrefGoogle Scholar

  • [3]

    Y.S. Li, Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation, Mech. Res. Commun. 56 (2014), 104–114.Web of ScienceCrossrefGoogle Scholar

  • [4]

    L. Xin and Z. Hu, Free vibration of simply supported and multilayered magneto-electro-elastic plates, Compos. Struct. 121 (2015), 344–350.CrossrefWeb of ScienceGoogle Scholar

  • [5]

    M.F. Liu, An exact deformation analysis for the magneto-electro-elastic fiber-reinforced thin plate, Appl. Math. Model. 35 (2011), 2443–2461.Web of ScienceCrossrefGoogle Scholar

  • [6]

    B. Zakaria, M.S.A. Houari, A. Tounsi, S.R. Mahmoud and O.A. Beg, An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates, Compos.: Part B. 60 (2014), 274–283.CrossrefWeb of ScienceGoogle Scholar

  • [7]

    A. Mahi, E.A.A. Bedia and A. Tounsi, A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates, Appl. Math. Model. 39 (2015), 2489–2508.Web of ScienceCrossrefGoogle Scholar

  • [8]

    C.X. Xue, E. Pan, S.Y. Zhang and H.J. Chu, Large deflection of a rectangular magnetoelectroelastic thin plate, Mech. Res. Commun. 38 (2011), 518–523.Web of ScienceCrossrefGoogle Scholar

  • [9]

    A. Alaimo, I. Benedetti and A. Milazzo, A finite element formulation for large deflection of multilayered magneto-electro-elastic plates, Compos. Struct. 107 (2014), 643–653.CrossrefWeb of ScienceGoogle Scholar

  • [10]

    J. Sladek, V. Sladek, S. Krahulec and E. Pan, The MLPG analyses of large deflections of magnetoelectroelastic plates, Eng. Anal. Bound. Elem. 37 (2013), 673–682.CrossrefWeb of ScienceGoogle Scholar

  • [11]

    A. Milazzo, Large deflection of magneto-electro-elastic laminated plates, Appl. Math. Model. 38 (2014), 1737–1752.Web of ScienceCrossrefGoogle Scholar

  • [12]

    T.H.L. Nguyen, I. Elishakoff and T.V. Nguyen, Buckling under the external pressure of cylindrical shells with variable thickness, Int. J. Solids Struct. 46 (2009), 4163–4168.Web of ScienceCrossrefGoogle Scholar

  • [13]

    P. Malekzadeh and S.A. Shahpari, Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM, Thin Wall. Struct. 43 (2005), 1037–1050.CrossrefGoogle Scholar

  • [14]

    Y. Kumar and R. Lal, Buckling and vibration of orthotropic nonhomogeneous rectangular plates with bilinear thickness variation, J. Appl. Mech. 78 (2001), 061012–1-11.Web of ScienceGoogle Scholar

  • [15]

    A.K. Gupta and A. Khanna, Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, J. Sound Vib. 301 (2007), 450–457.CrossrefWeb of ScienceGoogle Scholar

  • [16]

    C.Y. Chia, Nonlinear analysis of plates, McGraw-Hill, New York, 1980.Google Scholar

  • [17]

    G.R. Buchanan, Layered versus multiphase magneto-electro-elastic composites, Compos.: Part B. 35 (2004), 413–420.CrossrefGoogle Scholar

About the article

Received: 2015-07-24

Accepted: 2018-02-04

Published Online: 2018-04-21

Published in Print: 2018-06-26


The project was supported by the National Natural Science Foundation of China (Grant No. 51778551), the Natural Science Foundation of Fujian Province (Grant No. 2012J01009), and the Education Department of Fujian Province (Grant No. JA14050).


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 351–356, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2015-0105.

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