Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

In this paper free vibration analysis of skew plates with fully clamped boundary condition made of functionally graded materials is investigated. The study is based on the second order shear deformation plate theory (SSDT) using Generalized Differential Quadrature (GDQ) method. With a proper transformation, partial differential equations of a rectangular plate in Cartesian coordinates into skew coordinates are obtained; the governing differential equations are seven second order partial differential equations. The comparison of simulation results with those presented previously in the literature shows the accuracy of the proposed method. Also, fast rate of convergence is achieved by this method. Finally, the effects of angle of skew plate, power law index and plate geometrical parameters on the natural frequencies of the plate are also obtained and the related results are presented in this paper.

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Static bending and free vibration analysis of functionally graded porous plates laid on elastic foundation using the meshless method

Journal of Science and Technology in Civil Engineering (STCE) - NUCE ◽

10.31814/stce.nuce2021-15(2)-12 ◽

2021 ◽

Vol 15 (2) ◽

pp. 141-159

Author(s):

Vu Tan Van ◽

Nguyen Huynh Tan Tai ◽

Nguyen Ngoc Hung

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Elastic Foundation ◽

Meshless Method ◽

Vibration Analysis ◽

Plate Theory ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Kriging Interpolation ◽

Moving Kriging Interpolation

This paper presents a numerical approach for static bending and free vibration analysis of the functionally graded porous plates (FGPP) resting on the elastic foundation using the refined quasi-3D sinusoidal shear deformation theory (RQSSDT) combined with the Moving Kriging–interpolation meshfree method. The plate theory considers both shear deformation and thickness-stretching effects by the sinusoidal distribution of the in-plane displacements, satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without shear correction coefficient. The advantage of the plate theory is that the displacement field of plate is approximated by only four variables leading to reduce computational efforts. Comparison studies are performed for the square FGPP with simply supported all edges to verify the accuracy of the present approach. The effect of the aspect ratio, volume fraction exponent, and elastic foundation parameters on the static deflections and natural frequency of FGPP are also investigated and discussed. Keywords: meshless method; Moving Kriging interpolation; refined quasi-3D theory; porous functionally\break graded plate; Pasternak foundation.

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Free Vibration Analysis of Functionally Graded FG Nano-Plates with Porosities

Journal of Nano Research ◽

10.4028/www.scientific.net/jnanor.64.61 ◽

2020 ◽

Vol 64 ◽

pp. 61-74

Author(s):

Merdaci Slimane ◽

Adda Hadj Mostefa ◽

Sabrina Boutaleb ◽

Hadjira Hellal

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Analytical Solutions ◽

Vibration Analysis ◽

Natural Frequencies ◽

Plate Theory ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Correction Factors ◽

Simply Supported

This study presents the analytical solutions of free vibration analysis of simply supported nanoplate FG porous using nonlocal high order shear deformation plate theory. This theory contains four unknowns without the use of shear correction factors unlike the others. The objective of this article is to develop a model to use the function f (z) on vibration and the natural frequencies of functionally graded nanoplates nonlocal to study the effect of the various parameters. The validity of the theory is shown by comparing the present results with obtained with those reported in the literature. The effects of various parameters are all discussed.

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