Exact vibration analysis of variable thickness thick annular isotropic and FGM plates

Efraim, Elia; Eisenberger, Moshe

doi:10.1016/j.jsv.2006.06.068

Cited by 300 publications

(71 citation statements)

References 29 publications

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“…The FGM annular plate defined in the work by Efraim and Eisenberger [90] is considered in the current section to validate the proposed approach. The plate middle surface is described by the following position vector r(x, ϑ) = (R i + x) cos ϑ e 1 − (R i + x) sin ϑ e 2 (91) where x, ϑ are the principal coordinate of the surface, assuming x ∈ [0, L] and ϑ ∈ [0, 2π].…”

Section: Comparison With the Literaturementioning

confidence: 99%

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A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

et al. 2017

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Abstract:The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

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Section: Comparison With the Literaturementioning

confidence: 99%

“…At this point, some works concerning FGM structures with variable thickness can be cited. Firstly, the exact element method was used by Efraim and Eisenberger [90] to provide some benchmark solutions to the free vibration problem of FGM annular plates. Several thickness profiles, as well as volume fraction distributions, were considered.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

et al. 2017

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“…For isotropic materials, the transverse shear correction coefficient K is taken to be 5/6, and is suggested to be =5/ [6 − ( 1 1 + 2 2 )] for functionally graded materials by Efraim and Eisenberger [34].…”

Section: Modeling Of Cnt-reinforced Functionally Graded Composite Platesmentioning

confidence: 99%

Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

Zhang

2017

Journal of Modeling in Mechanics and Materials

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Abstract:The geometrical nonlinear analysis of internally supported nanocomposite plates subjected to a uniformly distributed load is carried out. This study investigates the effects of internal point/column supports on the large deformation bending of nanocomposite plates reinforced by carbon nanotubes (CNTs) with different types of distributions, namely, uniform and two kinds of functionally graded distributions through the thickness of the plates. Two-dimensional displacement field of the plate is approximated by a set of Improved Moving Least Squares (IMLS) functions. The arc-length iterative algorithm with the modified Newton method is employed to obtain the nonlinear response of nanocomposite plates. Convergence studies indicate the validity and effectiveness of the element-free IMLS-Ritz method. The effects of plate thickness-to-width ratio, volume fraction ratio, and plate aspect ratio on the large deformation behavior of nanocomposite plates under various boundary conditions are examined. To the best of the authors' knowledge, the problem has not been attempted in the open literature.

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“…The classical plate theory (CPT) (Feldman and Aboudi 1997, Javaheri and Eslami 2002, Mahdavian 2009, Mohammadi et al 2010, Chen et al 2006, Baferani et al 2011) yields acceptable results only for the thin plates, whereas accuracy of the first-order shear deformation theory (FSDT) (Mohammadi et al 2010, Croce and Venini 2004, Efraim and Eisenberger 2007, Zhao et al 2009a, b, Lee et al 2009, Hosseini-Hashemi et al 2011, Naderi and Saidi 2010, Nguyen-Xuan et al 2012, Thai and Choi 2013a) depends on the shear correction factor. Higherorder shear deformation theories with five unknown functions, which are included third-order shear deformation plate theory (TSDT), sinusoidal shear deformation plate theory (SSDT), hyperbolic shear deformable plate theory (HSDT), exponential shear deformation plate theory (ESDT), predict more accurate the response of moderate and thick FG plates (Reddy 2000, Zenkour 2006, Matsunaga 2008, Chen et al 2009, Pradyumna and Bandyopadhyay 2008, Gilhooley et al 2007, Talha and Singh 2010, Mantari and Soares 2012, 2013, Neves et al 2012a, b, Jha et al 2013, Thai and Kim 2013, Thai and Choi 2013b, Zenkour 2013.…”

Section: Introductionmentioning

confidence: 99%

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates

Nguyen¹,

Thai²,

Vo³

2015

Steel Compos. Struct.

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Thuc (2015) A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates. Steel and Composite Structures, 18 (1 Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates Abstract. A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

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Exact vibration analysis of variable thickness thick annular isotropic and FGM plates

Cited by 300 publications

References 29 publications

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates

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