A Study on Free Vibrational Response of Functionally Graded Nanocomposite Sandwich Plates Reinforced by Randomly Oriented Straight Carbon Nanotubes

2016 ◽  
Vol 880 ◽  
pp. 77-82
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotube ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Reinforced Composites ◽  
Technical Literature ◽  
Simply Supported ◽  
Vibrational Response ◽  
Three Dimensional Elasticity

This paper is motivated by the lack of studies in the technical literature concerning to the three dimensional vibration analysis of thick laminated rectangular plates with continuously graded carbon nanotube-reinforced (CGCNTR) sheets. The formulations are based on the three-dimensional elasticity theory. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The structure is supported by an elastic foundation with Winkler’s (normal) and Pasternak’s (shear) coefficients. The material properties of the functionally graded carbon nanotube reinforced composites are graded along the thickness and estimated through Mori-Tanaka method.

Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

2009 ◽  
Vol 44 (4) ◽  
pp. 249-261 ◽  
Author(s):  
Y P Xu ◽  
D Zhou
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Lower Surface ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Line ◽  
Simply Supported ◽  
Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

Dynamic analysis of functionally graded plate integrated with two piezoelectric layers, based on a three-dimensional elasticity solution

2009 ◽  
Vol 223 (6) ◽  
pp. 1297-1309 ◽  
Author(s):  
M Shakeri ◽  
S N Sadeghi ◽  
M Javanbakht ◽  
H Hatamikian
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Series Expansion ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates ◽  
Piezoelectric Layers ◽  
Three Dimensional Elasticity

In this article, dynamic analysis of functionally graded (FG) plates integrated with two piezoelectric layers has been carried out. The rectangular plate is simply supported at four edges and exposed to dynamic excitation. Three-dimensional elasticity equations have been considered. Using a series expansion of mechanical and electrical displacements, the partial differential equations have been reduced to ordinary differential equations (ODEs) with variable coefficients. The solution of the resulting system of ODEs has been carried out using the Galerkin method. The final result is obtained by taking just one term in the series expansion. The Newmark method has been used to move forward in the time domain for a dynamic solution. Finally, numerical results have been presented for a simply supported rectangular FG plate integrated with two piezoelectric layers. In some cases, results have been compared to previously published works.

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