Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method

Dehghan, Mehdi; Baradaran, Gholam Hossein

doi:10.1016/j.amc.2011.08.020

Cited by 41 publications

(17 citation statements)

References 16 publications

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“…The plate thickness ratios are taken to be 0.001 and 0.1. It is evident that the IMLS-Ritz solutions compare favorably with the reported results for all cases (Leissa, 1973;Zhou et al, 2004;Dehghan and Baradaran, 2011).…”

Section: Comparison and Convergence Studiessupporting

confidence: 70%

“…The nondimensional frequency parameters (Kwa4/D) of thin and moderately thick SSSS plates resting on an elastic foundation are presented in Table 3, together with the vibration solutions reported by Leissa (1973), Zhou et al. (2004), and Dehghan and Baradaran (2011). For direct comparison, the frequency parameters expressed in λm,n(m,n=1,2,3,…,) are adopted to denote the plate flexural modes, where subscripts m and n refer to the wave numbers in the x and y directions, respectively.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

Zhang

Lei

Liew

2016

Journal of Vibration and Control

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The vibration behavior was investigated of thin-to-moderately thick functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates resting on elastic foundations. In the study, transverse shear and rotatory inertia were incorporated through first-order shear deformation theory. The improved moving least-squares-Ritz method was employed to derive the eigenvalue equation of the plate vibration. The study examined the effects of the elastic Winkler medium, CNT ratios, distributions of CNTs, boundary conditions, side angles, thickness-to-width ratios, and the relative plate aspect ratios on the vibration response of the FG-CNT reinforced composite plates. A set of vibration frequencies and mode shapes for the FG-CNT reinforced composite quadrilateral plates is presented. Additionally, a comprehensive parametric study and vivid mode shape plots demonstrate details of the vibration spectrum of the FG-CNT reinforced composite plates.

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Section: Comparison and Convergence Studiessupporting

confidence: 70%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

Zhang

Lei

Liew

2016

Journal of Vibration and Control

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“…There is a good agreement between the present results and the literatures. ) and various method including finite element (FE) and differential quadrature (DQ) methods [55], mesh free method [44], Ritz method [54] and classical method [56] are compared with the obtained results by the present work based on meshless method in Table 2. The best agreement is observed between the obtained results by the meshless method (present work) and the other methods.…”

Section: -Numerical Results and Discussionmentioning

confidence: 94%

Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method

Mohammadimehr

Navi

Arani

2015

Composite Structures

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“…2, x P an y P represent the applied stresses along the x and y-axis, respectively. In this expression the terms in the bracket represent the in-plane and the out-of-plane destabilizing influence of the applied stresses (Dehghan & Baradaran, 2011), (Ventsel, 2001). Substituting Eqs.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Recently, The Differential Quadrature Method (DQM) has been used for free vibration analysis of nonhomogeneous orthotropic rectangular plate resting on elastic foundation (Gupta et al, 2016). Previously, the FE-DQ method has been used to analyze the free vibration and buckling of thick plates (Dehghan and Baradaran, 2011).…”

Section: Introductionmentioning

confidence: 99%

An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation

Dehghan¹,

Nejad²,

Moosaie³

2016

10.5267/j.esm

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This paper is concerned with the vibration and stability analysis of thick rectangular plates resting on elastic foundation, which is distributed over the particular area of the plate. A twoparameter (Pasternak) model is considered to describe the elastic foundation. The eigenvalue problem in 3-D domain is numerically solved by a combination of the finite element and differential quadrature method (DQM). The energy principle is employed to derive the governing equations in the framework of three-dimensional, linear and small strain theory of elasticity. The in-plane domain of the problem is discretized using two-dimensional finite elements and spatial derivatives of equations in the thickness direction are discretized in strongform using DQM. As a first endeavor, the mixed FE-DQ method has been employed for 3-D buckling and free vibration analysis of rectangular thick plates partially supported by an elastic foundation. The accuracy of obtained results is validated by comparing to the few analytical solutions in the literature.

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Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method

Cited by 41 publications

References 16 publications

Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method

An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation

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