General Solution for Equation of Transient Heat Conduction in Functionally Graded Material Hollow Cylinder With Piezoelectric Internal and External Layers

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Functionally Graded Material ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Two Dimensions ◽  
Functionally Graded ◽  
Power Functions ◽  
Generalized Bessel Function ◽  
Graded Material

In this paper, the exact solution of the equation of transient heat conduction in two dimensions for a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers is developed. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. The FGM properties are assumed to depend on the variable r, and they are expressed as power functions of r.

Solution for Equation of Two-Dimensional Transient Heat Conduction in Functionally Graded Material Hollow Sphere With Piezoelectric Internal and External Layers

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Power Functions ◽  
Legendre Series ◽  
Graded Material

In this paper, an exact solution for the equation of two-dimensional transient heat conduction in a hollow sphere made of functionally graded material (FGM) and piezoelectric layers is developed. Transient temperature distribution, as a function of radial and circumferential directions and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and Legendre series. The results are the sum of transient and steady-state solutions that depend upon the initial condition for temperature and heat source, respectively. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r.

One-Dimensional Moving Heat Source in a Hollow FGM Cylinder

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
M. Jabbari ◽  
A. H. Mohazzab ◽  
A. Bahtui
Keyword(s):  
Heat Source ◽  
Hollow Cylinder ◽  
Thermal Stresses ◽  
Direct Method ◽  
Functionally Graded ◽  
Moving Heat Source ◽  
Power Functions ◽  
One Dimensional ◽  
Generalized Bessel Function ◽  
Graded Material

This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to the power functions of radial direction. Temperature distribution is symmetric and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of a hollow cylinder. The thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.

One Dimensional Moving Heat Source in Hollow FGM Cylinder

2006 ◽  
Author(s):  
Mohsen Jabbari ◽  
Amir Hossein Mohazzab ◽  
Ali Bahtui
Keyword(s):  
Heat Source ◽  
Hollow Cylinder ◽  
Thermal Stresses ◽  
Direct Method ◽  
Functionally Graded ◽  
Moving Heat Source ◽  
Power Functions ◽  
One Dimensional ◽  
Generalized Bessel Function ◽  
Graded Material

This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to power functions of radial direction. Temperature distribution is symmetric, and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of hollow cylinder. Thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.

Analysis of Thermoelastic Damping of Functionally Graded Material Micro Plate Based on the Mindlin Plate Theory

2020 ◽  
Vol 865 ◽  
pp. 67-71
Author(s):  
Shi Rong Li ◽  
Peng Xiong ◽  
Da Fu Cao
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Heat Conduction Equation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Conduction Equation ◽  
Mindlin Plate ◽  
Thermoelastic Damping ◽  
Graded Material ◽  
Mindlin Plate Theory

In this paper, thermoelastic damping (TED) in a simply supported rectangular functionally graded material (FGM) micro plate with continuous variation of the material properties along the thickness direction is performed. The equations of motion and the heat conduction equation coupled with the thermal effects are derived based on the Mindlin plate theory and the one-way coupled heat conduction theory, respectively. The heat conduction equation with variable coefficients is solved by using the layer-wise homogenization approach. Analytical solution of TED is obtained by complex frequency method. Numerical results of TED are presented for the rectangular FGM micro plate made of ceramic-metal constituents with the power-law gradient profile. The effects of the shear deformation, the material gradient index, the plate thickness on the TED of the FGM micro plate are studied.

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