scholarly journals Three-Dimensional Piezothermoelastic Stress of a Finite Functionally Graded Cylindrical Shell with Piezoelectric Layer

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yong-gang Kang ◽  
Zhong-qi Wang ◽  
Gongnan Xie
Keyword(s):  
Cylindrical Shell ◽  
Fourier Series ◽  
Material Properties ◽  
Piezoelectric Layer ◽  
Radial Direction ◽  
Electric Displacement ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers

Three-dimensional piezothermoelastic solutions for a finite functionally graded cylindrical shell with piezoelectric layer are carried out in this paper. The cylindrical shell is simply supported at four end edges and is subjected to axisymmetric thermomechanical loads. The piezoelectric layers are polarized along radial direction as a sensor. The material properties are assumed to be temperature independent and radially dependent but are assumed to be homogeneous in each layer; the variables are expanded in Fourier series to satisfy the boundary conditions and multilayer approach is used. Numerical results of mullite/molybdenum functionally graded cylindrical shell are presented; the temperature change, stresses, electric potential, and electric displacement distributions are given and briefly discussed.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

scholarly journals Mechanical and Thermal Stresses in a FGPM Hollow Cylinder due to Radially Symmetric Loads

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Steady State ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Functionally Graded ◽  
Power Functions ◽  
One Dimensional ◽  
Complex Fourier Series

The general solution of steady-state on one-dimensional Axisymmetric mechanical and thermal stresses for a hollow thick made of cylinder Functionally Graded porous material is developed. Temperature, as functions of the radial direction with general thermal and mechanical boundary-conditions on the inside and outside surfaces. A standard method is used to solve a nonhomogenous system of partial differential Navier equations with nonconstant coefficients, using complex Fourier series, rather power functions method and solve the heat conduction. The material properties, except poisson's ratio, are assumed to depend on the variable , and they are expressed as power functions of .

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.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Functionally Graded Hollow Sphere With Piezoelectric Internal and External Layers Under Asymmetric Transient Thermomechanical Loads

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Hollow Sphere ◽  
Legendre Polynomials ◽  
Radial Direction ◽  
Energy Equation ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Piezoelectric Layers ◽  
Transient Thermal

In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

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