scholarly journals Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Chunbao Xiong ◽  
Ying Guo
Keyword(s):  
Heat Source ◽  
Fractional Order ◽  
Axial Direction ◽  
Moving Heat Source ◽  
Variable Properties ◽  
Governing Equations ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Temperature Dependent Properties ◽  
Nondimensional Temperature

A one-dimensional generalized magnetothermoelastic problem of a thermoelastic rod with finite length is investigated in the context of the fractional order thermoelasticity. The rod with variable properties, which are temperature-dependent, is fixed at both ends and placed in an initial magnetic field, and the rod is subjected to a moving heat source along the axial direction. The governing equations of the problem in the fractional order thermoelasticity are formulated and solved by means of Laplace transform in tandem with its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress in the rod are obtained and illustrated graphically. The effects of the temperature-dependent properties, the velocity of the moving heat source, the fractional order parameter, and so forth on the considered variables are concerned and discussed in detail, and the results show that they significantly influence the variations of the considered variables.

scholarly journals A One-Dimensional Thermoelastic Problem due to a Moving Heat Source under Fractional Order Theory of Thermoelasticity

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Tianhu He ◽  
Ying Guo
Keyword(s):  
Heat Source ◽  
Laplace Transform ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Moving Heat Source ◽  
Dimensional Problem ◽  
Governing Equations ◽  
One Dimensional

The dynamic response of a one-dimensional problem for a thermoelastic rod with finite length is investigated in the context of the fractional order theory of thermoelasticity in the present work. The rod is fixed at both ends and subjected to a moving heat source. The fractional order thermoelastic coupled governing equations for the rod are formulated. Laplace transform as well as its numerical inversion is applied to solving the governing equations. The variations of the considered temperature, displacement, and stress in the rod are obtained and demonstrated graphically. The effects of time, velocity of the moving heat source, and fractional order parameter on the distributions of the considered variables are of concern and discussed in detail.

Generalized Thermoelastic Responses of a Piezoelectric Rod Subjected to a Moving Heat Source

2007 ◽  
Vol 353-358 ◽  
pp. 1149-1152
Author(s):  
Tian Hu He ◽  
Li Cao
Keyword(s):  
Numerical Calculation ◽  
Heat Source ◽  
Laplace Transformation ◽  
Moving Heat Source ◽  
Governing Equations ◽  
Laplace Inversion ◽  
Thermally Induced ◽  
Numerical Laplace Inversion ◽  
Generalized Thermoelastic ◽  
Elastic Responses

Based on the Lord and Shulman generalized thermo-elastic theory, the dynamic thermal and elastic responses of a piezoelectric rod fixed at both ends and subjected to a moving heat source are investigated. The generalized piezoelectric-thermoelastic coupled governing equations are formulated. By means of Laplace transformation and numerical Laplace inversion the governing equations are solved. Numerical calculation for stress, displacement and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed.

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300 ◽  
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

A Fractional-Order Generalized Thermoelastic Problem of a Bilayer Piezoelectric Plate for Vibration Control

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Yeshou Xu ◽  
Zhao-Dong Xu ◽  
Tianhu He ◽  
Jinxiang Chen ◽  
Chao Xu
Keyword(s):  
Contact Resistance ◽  
Vibration Control ◽  
Fractional Order ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Elastic Behavior ◽  
Temperature Dependent ◽  
Riemann Sum ◽  
Thermoelastic Plate ◽  
Temperature Dependent Properties

Multilayered piezoelectric structures have special applications for vibration control, and they often serve in a thermoelastic coupling environment. In this work, the fractional-order generalized thermoelasticity theory is used to investigate the dynamic thermal and elastic behavior of a bilayer piezoelectric–thermoelastic plate with temperature-dependent properties. The thermal contact resistance is implemented to describe the interfacial thermal wave propagation. The governing equations for the bilayer piezoelectric–thermoelastic plate with temperature-dependent properties are formulated and then solved by means of Laplace transformation and Riemann-sum approximation. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. According to the numerical results, the effects of the thermal contact resistance, the ratio of the material properties between different layers, the temperature-dependent properties, and the fractional-order parameters on the distributions of the considered quantities are revealed in different cases and some remarkable conclusions are obtained. The investigation helps gain insights into the optimal design of actuators, sensors, which are made of piezoelectric materials.

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

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.

Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

1964 ◽  
Vol 31 (3) ◽  
pp. 423-429 ◽  
Author(s):  
Robert C. Petrof ◽  
Serge Gratch
Keyword(s):  
Wave Propagation ◽  
Elastic System ◽  
Thermomechanical Coupling ◽  
Temperature Dependent ◽  
Stress Variation ◽  
Single Degree Of Freedom ◽  
One Dimensional ◽  
Stress Strain Relation ◽  
Longitudinal Wave Propagation ◽  
Temperature Dependent Properties

A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.

scholarly journals Development of Finite Element Solver for Welding Analysis

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Abid Ali Khan ◽  
Farzeen Shahid ◽  
Ihtzaz Qamar
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Heat Conduction ◽  
Heat Source ◽  
Welding Process ◽  
Transient Heat Conduction ◽  
Moving Heat Source ◽  
Structural Members ◽  
Final Solution ◽  
Governing Equations

Welding is a process of joining the similar or different metals. Improper welding process leads to inaccuracies and misalignments of structural members, causing high cost and delays in work. Therefore, it is essential to predict the temperature field during welding process. Different techniques can be used to predict the temperature field, which may lead to structure distortion. The present study aims to develop a finite element solver for transient heat conduction analysis. The final solution is calculated from the assumed solution and compared with the numerical computations. The solver is then modified for use of moving heat source. The modification comprise, change in governing equations with the inclusion of phase change. The moving heat source continuously increases the temperature during motion. When the heat source completes a pass, model is allowed to cool down in order to study the temperature distribution during cooling.

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