scholarly journals Two Temperature Magneto-Thermoelasticity with Initial Stress: State Space Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Sunita Deswal ◽  
Kapil Kumar Kalkal
Keyword(s):  
State Space ◽  
Generalized Thermoelasticity ◽  
Elastic Half Space ◽  
Mathematical Methods ◽  
Initial Stress State ◽  
Numerical Work ◽  
Displacement Potential ◽  
Suitable Material ◽  
Space Formulation ◽  
Propagation Of Waves

Magneto-thermoelastic interactions in an initially stressed isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the L-S model of linear theory of generalized thermoelasticity. The formalism deals with the state space approach with the purpose of counteracting the difficulties of handling the displacement potential functions. Of specific concern here is the propagation of waves owing to ramp type increase in temperature and load. The medium is considered to be permeated by a uniform magnetic field. The expressions for different field parameters such as displacement, temperature, strain, and stress in the physical domain are obtained by applying a numerical inversion technique. Results of some earlier workers have been deduced from the present formulation. Numerical work is also performed for a suitable material with the aim of illustrating the results.

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

State space formulation: A solution to modal parameter estimation

1991 ◽  
Vol 148 (2) ◽  
pp. 329-342 ◽  
Author(s):  
M. Prevosto ◽  
M. Olagnon ◽  
A. Benveniste ◽  
M. Basseville ◽  
G. Le Vey
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
Modal Parameter ◽  
Space Formulation ◽  
Modal Parameter Estimation

Asymmetric Wave Propagation in an Elastic Half-Space by a Method of Potentials

1987 ◽  
Vol 54 (1) ◽  
pp. 121-126 ◽  
Author(s):  
R. Y. S. Pak
Keyword(s):  
Wave Propagation ◽  
Dynamic Response ◽  
Half Space ◽  
Elastic Half Space ◽  
Displacement Potential ◽  
Uniform Distributions ◽  
Time Harmonic ◽  
Method Of Potentials ◽  
Transformed Stress ◽  
Asymmetric Wave

A method of potentials is presented for the derivation of the dynamic response of an elastic half-space to an arbitrary, time-harmonic, finite, buried source. The development includes a set of transformed stress-potential and displacement-potential relations which are apt to be useful in a variety of wave propagation problems. Specific results for an embedded source of uniform distributions are also included.

ASSESSING PRE-CRISIS FUNDAMENTALS IN SELECTED ASIAN STOCK MARKETS

2005 ◽  
Vol 50 (02) ◽  
pp. 175-196 ◽  
Author(s):  
EE LENG LAU ◽  
G. K. RANDOLPH TAN ◽  
SHAHIDUR RAHMAN
Keyword(s):  
Kalman Filter ◽  
Emerging Markets ◽  
State Space ◽  
Stock Prices ◽  
Stock Markets ◽  
Bubble Formation ◽  
State Space Model ◽  
Space Model ◽  
Rational Bubbles ◽  
Space Formulation

In the folklore of emerging markets, there is a popular belief that bubbles are inevitable. In this paper, our objective is to estimate a state-space model for rational bubbles in selected Asian economies with the aid of the Kalman Filter. For each economy, we derive a possible picture of the bubble formation process that is implied by the state-space formulation. The estimation is based on the rational valuation formula for stock prices. Our results provide a possible way of defining the presence of rational bubbles in the stock markets of Taiwan, Singapore, Korea, and Malaysia.

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