scholarly journals State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem

2007 ◽  
Vol 44 (5) ◽  
pp. 1550-1562 ◽  
Author(s):  
H.M. Youssef ◽  
Eman A. Al-Lehaibi
Keyword(s):  
State Space ◽  
Generalized Thermoelasticity ◽  
Dimensional Problem ◽  
State Space Approach ◽  
One Dimensional ◽  
Two Temperature ◽  
Space Approach

State space approach to one-dimensional magneto-thermoelasticity under the Green–Naghdi theories

2009 ◽  
Vol 87 (8) ◽  
pp. 867-878 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. S. El-Karamany ◽  
A.A. Bary
Keyword(s):  
State Space ◽  
Generalized Thermoelasticity ◽  
Heat Sources ◽  
State Space Approach ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
Isotropic Media ◽  
The Laplace Transform ◽  
Space Approach ◽  
Coupled Theory

A model of the equations of generalized magneto-thermoelasticity for perfectly conducting isotropic media is given. The formulation is applied to the generalized thermoelasticity theories: Green–Naghdi of type II and type III as well as to the dynamic coupled theory. The state space approach is adopted for the solution of one-dimensional problems in the absence of heat sources with time-dependent heating on the boundary. The Laplace-transform technique is used. Numerical results are given and illustrated graphically employing numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the three theories.

Modeling of memory-dependent derivatives with the state-space approach

2019 ◽  
Vol 16 (4) ◽  
pp. 657-677
Author(s):  
Siddhartha Biswas
Keyword(s):  
Time Delay ◽  
State Space ◽  
Kernel Function ◽  
Generalized Thermoelasticity ◽  
Inversion Method ◽  
Two Dimensional ◽  
State Space Approach ◽  
Content Type ◽  
Coupled Equations ◽  
Space Approach

Purpose The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD). Design/methodology/approach The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms. Findings The solutions are presented graphically for different values of time delay and kernel function. Originality/value The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of an isotropic plate.

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