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.

scholarly journals Free vibration and buckling of bidirectional functionally graded sandwich plates using an efficient Q9 element

2021 ◽  
Author(s):  
Le Cong Ich ◽  
Tran Quang Dung ◽  
Pham Vu Nam ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Sandwich Plates ◽  
Various Boundary Conditions ◽  
Fundamental Frequencies ◽  
Numerical Result ◽  
Three Phase ◽  
Graded Material

Free vibration and buckling of three-phase bidirectional functionally graded sandwich (BFGSW) plates are studied in this paper for the first time by using an efficient nine-node quadrilateral (Q9) element. The core of the sandwich plates is pure ceramic, while the two skin layers are of a three-phase bidirectional functionally graded material. The element is derived on the basis of the Mindlin plate theory and linked interpolations. Fundamental frequencies and buckling loads are computed for the plates with various boundary conditions. Numerical result shows that convergence of the linked interpolation element is faster compared to the conventional Lagrangian interpolation Q9 element. Numerical investigations are carried out to highlight the influence of the material gradation and the side-to-thickness ratio on the vibration and buckling behaviour of the plates.

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

2011 ◽  
Vol 32 (7) ◽  
pp. 925-942 ◽  
Author(s):  
L. Hadji ◽  
H. A. Atmane ◽  
A. Tounsi ◽  
I. Mechab ◽  
E. A. Adda Bedia
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Plate Theory

scholarly journals Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

2014 ◽  
Vol 229 (5) ◽  
pp. 818-839 ◽  
Author(s):  
A Asanjarani ◽  
S Satouri ◽  
A Alizadeh ◽  
MH Kargarnovin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Conical Shell ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Graded Material ◽  
Truncated Conical Shell

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory

2018 ◽  
Vol 233 (6) ◽  
pp. 2056-2073 ◽  
Author(s):  
S Parida ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Material

In the present article, a higher order shear deformation theory is used to develop a finite element model for the free vibration analysis of a rotating functionally graded material plate in the thermal environment. The model is based on an eight-noded isoparametric element with seven degrees-of-freedom per node. The material properties are temperature dependent and graded along its thickness according to a simple power law distribution in terms of volume fraction of the constituents. The general displacement equation provides C0 continuity, and the transverse shear strain undergoes parabolic variation through the thickness of the plate. Therefore, the shear correction factor is not used in this theory. The obtained results are compared with the published results in the literature to determine the accuracy of the method. The effects of various parameters like hub radius, rotation speed, aspect ratio, thickness ratio, volume fraction index, and temperature on the frequency of rotating plate are investigated.

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

On Free Vibration of Functionally Graded Mindlin Plate and Effect of In-Plane Displacements

2013 ◽  
Vol 29 (2) ◽  
pp. 373-384 ◽  
Author(s):  
A. Hasani Baferani ◽  
A.R. Saidi ◽  
H. Ehteshami
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Aspect Ratios

AbstractIn this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.

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