Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates

Structures ◽  
2021 ◽  
Vol 29 ◽  
pp. 1435-1444
Author(s):  
Pham Van Vinh ◽  
Nguyen Thai Dung ◽  
Nguyen Chi Tho ◽  
Do Van Thom ◽  
Le Kha Hoa
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Single Variable ◽  
Variable Shear ◽  
Shear Deformation Plate Theory

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.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

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