scholarly journals Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory

2010 ◽  
Vol 34 (5) ◽  
pp. 1276-1291 ◽  
Author(s):  
Sh. Hosseini-Hashemi ◽  
H. Rokni Damavandi Taher ◽  
H. Akhavan ◽  
M. Omidi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
First Order ◽  
Shear Deformation Plate Theory

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

2013 ◽  
Vol 5 (1) ◽  
pp. 90-112 ◽  
Author(s):  
S. Jafari Mehrabadi ◽  
B. Sobhaniaragh ◽  
V. Pourdonya
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Effective Material Properties

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2193-2209
Author(s):  
Ehsan Ansari ◽  
AliReza Setoodeh
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Predictions ◽  
Shear Deformation Plate Theory

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

scholarly journals Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 1: Governing equations establishment

2015 ◽  
Vol 37 (3) ◽  
pp. 187-204
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Buckling Load ◽  
Thermal Loads ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling ◽  
Analysis Of Stability

In this paper, the buckling and post-buckling behaviors of eccentrically  stiffened functionally graded material (ES-FGM) plates on elastic  foundations subjected to in-plane compressive loads or thermal loads are  investigated by an analytical solution. The novelty of this work is that FGM  plates are reinforced by FGM stiffeners and the temperature, stiffener,  foundation are considered. The first-order shear deformation  plate theory is used. The thermal elements of plate and stiffeners in  fundamental equations are introduced. Theoretical formulations based on the  smeared stiffeners technique and the first-order shear deformation plate  theory, are derived. The analytical expressions to determine the static  critical buckling load and post-buckling load-deflection curves are  obtained.

scholarly journals Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

2019 ◽  
Vol 69 (4) ◽  
pp. 9-24 ◽  
Author(s):  
Chikh Abdelbaki
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Power Law ◽  
Material Properties ◽  
Scale Effects ◽  
Plate Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Simply Supported ◽  
Shear Deformation Plate Theory

AbstractThis paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

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