Thermopiezoelectric Response of a One-Dimensional Functionally Graded Piezoelectric Medium to a Moving Heat Source - A Review

2012 ◽  
Vol 151 ◽  
pp. 396-400 ◽  
Author(s):  
Zeng Tao Chen ◽  
Hamid Akbarzadeh ◽  
Hossein Babaei
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Smart Materials ◽  
Thermal Gradient ◽  
Functionally Graded ◽  
Moving Heat Source ◽  
One Dimensional ◽  
Smart Materials And Structures ◽  
Conduction Theory ◽  
Fourier Heat Conduction

The multi-physics of piezoelectric materials under different environmental conditions has been an active research subject for a few decades. Particularly, the thermoelastic behaviour of smart materials and structures is of great importance to their reliability in different applications. Traditionally, the Fourier heat conduction theory was introduced in dealing with the thermoelastic reactions of smart materials and structures. This may lead to reasonable analyses and useful guidelines in design of smart structures, especially when no severe thermal gradient is involved. However, when a severe thermal gradient is indeed involved in the service environment of a smart structure, the analysing results based on the Fourier heat conduction theory is unrealistic and usually rendered useless. Non-Fourier heat conduction theories have been introduced in the thermoelastic analysis of smart materials and structures in recent years and resulted in reasonable results. In this paper, we review the recent results of a thermopiezoelectric problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source using both the Fourier and Non-Fourier heat conduction theories. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results.

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.

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

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.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

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