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

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.

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

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.

OUT-OF-PLANE FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR CURVED BEAMS SUPPORTED ON ELASTIC FOUNDATION

2010 ◽  
Vol 02 (03) ◽  
pp. 635-652 ◽  
Author(s):  
P. MALEKZADEH ◽  
M. R. GOLBAHAR HAGHIGHI ◽  
M. M. ATASHI
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Curved Beams ◽  
Out Of Plane ◽  
Benchmark Solutions

As a first endeavor, the out-of-plane free vibration analysis of thin-to-moderately thick functionally graded (FG) circular curved beams supported on two-parameter elastic foundation is presented. The formulation is derived based on the first-order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be graded in the direction normal to the plane of the beam curvature. The differential quadrature method (DQM), as an efficient and accurate method, is employed to discretize the equations of motion and the related boundary conditions. In order to assure the accuracy of the formulation and the method of solution, convergence behavior of the nondimensional natural frequencies is examined for FG circular curved beams and comparison studies with those of isotropic curved beams, available in the literature, are performed. The effects of the elastic foundation coefficients, boundary conditions, the material graded index and different geometrical parameters on the natural frequency parameters of the FG circular curved beams are investigated. The new results can be used as benchmark solutions for future research works.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

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