scholarly journals Thermoelastic waves without energy dissipation in an unbounded body with a spherical cavity

2000 ◽  
Vol 23 (8) ◽  
pp. 555-562 ◽  
Author(s):  
D. S. Chandrasekharaiah ◽  
K. S. Srinath
Keyword(s):  
Energy Dissipation ◽  
Spherical Cavity ◽  
Small Time ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Thermoelastic Body ◽  
Without Energy Dissipation ◽  
The Waves ◽  
Thermoelastic Waves ◽  
Stress Free Boundary

The linear theory of thermoelasticity without energy dissipation is employed to study waves emanating from the boundary of a spherical cavity in a homogeneous and isotropic unbounded thermoelastic body. The waves are supposed to be spherically symmetric and caused by a constant step in temperature applied to the stress-free boundary of the cavity. Small-time solutions for the displacement, temperature, and stress fields are obtained by using the Laplace transform technique. It is found that there exist two coupled waves, of which one is predominantly elastic and the other is predominantly thermal, both propagating with finite speeds but with no exponential attenuation. Exact expressions for discontinuities in the field functions that occur at the wavefronts are computed and analysed. The results are compared with those obtained earlier in the contexts of some other models of thermoelasticity.

scholarly journals The Effect of a Hyperbolic Two-Temperature Model with and without Energy Dissipation in a Semiconductor Material

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1711
Author(s):  
Faris Alzahrani ◽  
Ibrahim Abbas
Keyword(s):  
Energy Dissipation ◽  
Thermodynamic Temperature ◽  
Temperature Model ◽  
Conductive Temperature ◽  
Mechanical Waves ◽  
Without Energy Dissipation ◽  
Thermoelastic Waves ◽  
Analytical Expressions ◽  
Thermoelastic Theory ◽  
Two Temperature

In this work, the new model of photothermal and elastic waves, with and without energy dissipation, under a hyperbolic two-temperature model, is used to compute the displacement, carrier density, thermodynamic temperature, conductive temperature and stress in a semiconductor medium. The medium is considered in the presence of the coupling of plasma and thermoelastic waves. To get the complete analytical expressions of the main physical fields, Laplace transforms and the eigenvalue scheme are used. The outcomes are presented graphically to display the differences between the classical two-temperature theory and the new hyperbolic two-temperature theory, with and without energy dissipation. Based on the numerical results, the hyperbolic two-temperature thermoelastic theory offers a finite speed of mechanical waves and propagation of thermal waves.

scholarly journals On generalized thermoelastic disturbances in an elastic solid with a spherical cavity

1991 ◽  
Vol 4 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Basudeb Mukhopadhyay ◽  
Rasajit Bera ◽  
Lokenath Debnath
Keyword(s):  
Laplace Transform ◽  
Classical Theory ◽  
Spherical Cavity ◽  
Dynamic Pressure ◽  
Elastic Solid ◽  
Dynamical Theory ◽  
The Laplace Transform ◽  
Generalized Thermoelastic ◽  
Short Time ◽  
The Waves

In this paper, a generalized dynamical theory of thermoelasticity is employed to study disturbances in an infinite elastic solid containing a spherical cavity which is subjected to step rise in temperature in its inner boundary and an impulsive dynamic pressure on its surface. The problem is solved by the use of the Laplace transform on time. The short time approximations for the stress, displacement and temperature are obtained to examine their discontinuities at the respective wavefronts. It is shown that the instantaneous change in pressure and temperature at the cavity wall gives rise to elastic and thermal disturbances which travel with finite velocities v1 and v2(>v1) respectively. The stress, displacement and temperature are found to experience discontinuities at the respective wavefronts. One of the significant findings of the present analysis is that there is no diffusive nature of the waves as found in classical theory.

scholarly journals Eigen Value Approach to Generalized Thermoelastic Interactions in an Unbounded Body with Circular Cylindrical Cavity without Energy Dissipation

2017 ◽  
Vol 22 (4) ◽  
pp. 811-825 ◽  
Author(s):  
S. Chakraborty
Keyword(s):  
Energy Dissipation ◽  
Cylindrical Cavity ◽  
Generalized Thermoelasticity ◽  
Displacement Component ◽  
Eigen Value ◽  
The Laplace Transform ◽  
Circular Cylindrical Cavity ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Without Energy Dissipation

Abstract The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

scholarly journals Exact Solution of Thermoelastic Problem for a One-Dimensional Bar without Energy Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. Abd El-Latief ◽  
S. E. Khader
Keyword(s):  
Exact Solution ◽  
Relaxation Time ◽  
Thermal Stress ◽  
Energy Dissipation ◽  
Heat Source ◽  
Half Space ◽  
Time Dependent ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Without Energy Dissipation

We consider a homogeneous isotropic thermoelastic half-space in the context of the theory of thermoelasticity without energy dissipation. There are no body forces or heat source acting on the half-space. The surface of the half-space is affected by a time dependent thermal shock and is traction free. The Laplace transform with respect to time is used. The inverse transforms are obtained in an exact manner for the temperature, thermal stress, and displacement distributions. These solutions are represented graphically and discussed for several cases of the applied heating. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.

Sign in / Sign up

Export Citation Format

Share Document