Interaction due to Mechanical and Thermal Sources in Thermoelastic Half-Space with Voids

2005 ◽  
Vol 11 (4) ◽  
pp. 499-517 ◽  
Author(s):  
Rajneesh Kumar ◽  
Leena Rani
Keyword(s):  
Half Space ◽  
Normal Force ◽  
Volume Fraction ◽  
Thermal Source ◽  
Physical Domain ◽  
Coupled Thermoelasticity ◽  
Time Harmonic ◽  
The Fourier Transform ◽  
Mechanical And Thermal Sources ◽  
Thermal Sources

The dynamic response of a homogeneous, isotropic, thermoelastic half-space with voids subjected to time harmonic normal force and thermal source is investigated by applying the Fourier transform. The displacements, stresses, temperature distribution, and change in volume fraction field obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the voids effect for the theory of coupled thermoelasticity and uncoupled thermoelasticity for an insulated boundary and temperature gradient boundary.

Deformation due to various sources in a fibre-reinforced anisotropic generalized thermoelastic medium

2009 ◽  
Vol 87 (2) ◽  
pp. 179-187 ◽  
Author(s):  
Rajneesh Kumar ◽  
Raj Rani Gupta
Keyword(s):  
Fourier Transforms ◽  
Plane Surface ◽  
Thermal Relaxation ◽  
Numerical Inversion ◽  
Physical Domain ◽  
Thermoelastic Medium ◽  
Generalized Thermoelastic ◽  
Mechanical And Thermal Sources ◽  
Close Form ◽  
Thermal Sources

The present investigation is concerned with the deformation of a fibre-reinforced, anisotropic, generalized thermoelastic medium subjected to mechanical and thermal sources acting on the plane surface. Close-form solutions for stresses and temperature distribution are derived using Laplace transforms for time and Fourier transforms for space. As an application of the approach concentrated, uniformly distributed, and linearly distributed sources are taken. A numerical inversion technique is applied to obtain the solution in the physical domain. Effects of anisotropy and thermal relaxation are shown graphically on the resulting quantities.

Axi-symmetric deformation in the micropolar porous generalized thermoelastic medium

2010 ◽  
Vol 58 (1) ◽  
pp. 129-139 ◽  
Author(s):  
R. Kumar ◽  
R. Gupta
Keyword(s):  
Normal Force ◽  
Volume Fraction ◽  
Specific Model ◽  
Numerical Inversion ◽  
Thermal Source ◽  
Field Equations ◽  
Thermoelastic Medium ◽  
Symmetric Deformation ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

Axi-symmetric deformation in the micropolar porous generalized thermoelastic mediumIn the present article we studied the thermodynamical theory of micropolar porous material and derived the equations of the linear theory of microploar porous generalized thermoelastic solid. Then the general solution to the field equations for plane axi-symmetric problem are obtained. The Laplace and Hankel transforms have been employed to study the problem, which are inverted numerically by using numerical inversion technique. An application of normal force and thermal source has been taken to show the utility of the approach. The technique developed in the present paper is simple, straightforward and convenient for numerical computation. Effect of micropolarity and porosity on the components of stress, temperature distribution and volume fraction field together with the effect of generalized theory of thermoelasticity have been depicted graphically for a specific model. Some particular cases are also deduced from the present problem.

scholarly journals Eigen Value Approach in Micropolar Elastic Medium with Voids

2013 ◽  
Vol 18 (2) ◽  
pp. 521-536
Author(s):  
R. Singh ◽  
K. Singh
Keyword(s):  
Elastic Medium ◽  
Normal Force ◽  
Volume Fraction ◽  
Tangential Force ◽  
Normal Displacement ◽  
Physical Domain ◽  
Field Equations ◽  
Hankel Transformation ◽  
Eigen Value ◽  
Stress Components

The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.

Approximate Solutions in Linear, Coupled Thermoelasticity

1968 ◽  
Vol 35 (2) ◽  
pp. 255-266 ◽  
Author(s):  
R. E. Nickell ◽  
J. L. Sackman
Keyword(s):  
Half Space ◽  
Rapid Heating ◽  
Ritz Method ◽  
Gaussian Quadrature ◽  
Boundary Surface ◽  
Initial Boundary ◽  
Approximate Solutions ◽  
Coupled Thermoelasticity ◽  
Initial Boundary Value ◽  
Thermally Conducting

A method for obtaining approximate solutions to initial-boundary-value problems in the linear theory of coupled thermoelasticity is developed. This procedure is a direct variational method representing an extension of the Ritz method. As an illustration of the procedure, it is applied to a class of one-dimensional, transient problems involving weak thermal shocks. The problems considered are: (a) Rapid heating of a half space through a thermally conducting boundary layer, and (b) gradual heating of the boundary surface of a half space. The solutions generated by the extended Ritz method are compared, for accuracy, to solutions obtained from a numerical inversion scheme for the Laplace transform based on Gaussian quadrature. These comparisons indicate that the variational procedure developed here can yield accurate results.

Electromagnetic Induction in a Stratified Conducting Half-Space by an Arbitrary Periodic Source

1973 ◽  
Vol 51 (10) ◽  
pp. 1064-1074 ◽  
Author(s):  
D. M. Summers ◽  
J. T. Weaver
Keyword(s):  
Half Space ◽  
Recursion Formula ◽  
Electric And Magnetic Fields ◽  
Hertz Potential ◽  
Infinite Line ◽  
The Fourier Transform ◽  
The One ◽  
External Time ◽  
Entire Theory ◽  
Time Periodic

A general theory of induction in a horizontally stratified plane conductor by an external, time-periodic, magnetic source is presented. The analysis is a generalization to the case of an N-layered conductor of a previously published theory for induction in a uniform conducting half-space, in which the electromagnetic field was expressed in terms of electric and magnetic Hertz vectors oriented normally to the surface of the conductor. With the aid of this representation the entire theory is developed in terms of the one scalar component of the magnetic Hertz vector. Solutions for the electric and magnetic fields above and within the conductor are obtained in the form of double integrals whose integrands are related through a recursion formula to the Fourier transform of the magnetic Hertz potential of the source evaluated at the surface of the conductor. Special formulas applicable to 1- and 2-layer conductors are derived and the form of solution for some elementary sources is also discussed. As an illustration of the theory, numerical calculations are given for an infinite line current above a 10-layer conductor whose conductivity increases (i) linearly and (ii) exponentially with depth.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

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