Free vibrations of plate using two variable refined plate theory

2006 ◽  
Vol 296 (4-5) ◽  
pp. 979-999 ◽  
Author(s):  
R.P. Shimpi ◽  
H.G. Patel
Keyword(s):  
Plate Theory ◽  
Free Vibrations ◽  
Refined Plate Theory

Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

2019 ◽  
Vol 19 (11) ◽  
pp. 1950136
Author(s):  
Mounia Khetib ◽  
Hichem Abbad ◽  
Nourredine Elmeiche ◽  
Ismail Mechab
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Refined Plate Theory ◽  
Various Boundary Conditions ◽  
Graded Material ◽  
Principle Of Virtual Displacements ◽  
Good Agreement

This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.

A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient

2011 ◽  
Vol 42 (6) ◽  
pp. 1386-1394 ◽  
Author(s):  
Abdelkader Benachour ◽  
Hassaine Daouadji Tahar ◽  
Hassen Ait Atmane ◽  
Abdelouahed Tounsi ◽  
Meftah Sid Ahmed
Keyword(s):  
Plate Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Refined Plate Theory

Refined plate theory and its variants

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 137-146 ◽  
Author(s):  
R. P. Shimpi
Keyword(s):  
Plate Theory ◽  
Refined Plate Theory

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory

2014 ◽  
Vol 34 ◽  
pp. 24-34 ◽  
Author(s):  
Mohamed Zidi ◽  
Abdelouahed Tounsi ◽  
Mohammed Sid Ahmed Houari ◽  
El Abbas Adda Bedia ◽  
O. Anwar Bég
Keyword(s):  
Mechanical Loading ◽  
Plate Theory ◽  
Refined Plate Theory ◽  
Bending Analysis
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