Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.



Publications Which contain the keyword: eigenvalue approach

Eigenvalue approach for generalized thermoelastic porous medium under the effect of thermal loading due to a laser pulse in DPL model
The aim of the present study is concerned with the thermal loading due to laser pulse on thermoelastic porous medium under dual-phase-lag model DPL. The material is a homogeneous isotropic elastic half-space and heated by a non-Gaussian laser beam with the pulse duration of 8 ps. Eigenvalue approach is proposed to analyze the problem and obtain the analytical solutions of ... Read more

2018-10-26 17:31:48 Keywords eigenvalue approach, semiconductor, photo-thermoelastic,
Photo-thermoelastic interactions in a 2D semiconducting medium
Photo-thermoelastic interactions in a two-dimension semiconductor medium are studied by using mathematical methods in the context of coupled thermoelastic theory and plasma waves with one thermal relaxation time. The Laplace-Fourier transformations and eigenvalues approach are used to obtain the general solutions for any set of boundary conditions. The medium is initially assumed to be at rest and due to a ... Read more

2018-10-08 19:23:18 Keywords Thermoelastic, analytical solution, eigenvalue approach,
Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating
In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written ... Read more

2018-10-13 22:40:03 Keywords eigenvalue approach, Thermoelasticity, semiconductor,
Photo-thermal-elastic interaction in an unbounded semiconducting medium with spherical cavity due to pulse heat flux
In this work, the photothermal waves in an unbounded semiconducting medium with spherical cavity are studied. This problem is solved using the theory of coupled plasma, thermal, and elastic wave. An unbounded material, elastic semiconductor containing a spherical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of the cavity is taken traction-free and ... Read more

Eigenvalue Approach in a Generalized Thermal Shock Problem for a Transversely Isotropic Half-Space
In the present work, the investigating of the disturbances in a homogeneous, transversely isotropic elastic medium with generalized thermoelastic theory has been concerned. The formulation is applied to generalized thermoelasticity based on three different theories. Laplace and Fourier transforms are used to solve the problem analytically. The essential equations have been written as a vector-matrix differential equation in the Laplace ... Read more

2018-10-06 21:06:26 Keywords wave propagation, Thermoelastic, eigenvalue approach,
Wave propagation in a generalized thermoelastic plate using eigenvalue approach
In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain ... Read more

Eigenvalue approach on a two-dimensional thermal shock problem with weak, normal and strong conductivity
The present paper is devoted to the study of a two-dimensional thermal shock problem with weak, normal and strong conductivity using the eigenvalue approach. The governing equations are taken in the context of the new consideration of heat conduction with fractional order generalized thermoelasticity with the Lord-Shulman model (LS model). The bounding surface of the half-space is taken to be ... Read more

2018-10-06 07:38:29 Keywords eigenvalue approach, Thermoelastic, Fractional-Order,
Fractional-Order Generalized Thermoelastic Interaction in an Unbounded Media by Pulsed Laser Heating
In this work, the influence of fractional-order derivative with two relaxation times in a thermoelastic medium under laser pulse is established. The surface of the half-space with free stresses is considered to be heated by a laser pulse. The exact analytical solution is adopted for the variations of temperature as well as the components of displacement and stress. Based on ... Read more

2018-10-06 07:28:48 Keywords wave propagation, eigenvalue approach, Thermoelastic,
Wave Propagation in a Generalized Thermoelastic Transversely Isotropic Plate Using Eigenvalue Approach
In the present work, frequency equations are obtained for Rayleigh-Lamb wave propagation in a transversely isotropic plate of thermoelastic material, in the context generalized theory of thermoelasticity. The thickness of the plate is taken to be finite and the faces of the plate are assumed isolated and free from stresses. The analytical solution for the temperature, displacement components and stresses ... Read more

Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach
In this paper, the effect of mass diffusion in a thermoelastic nanoscale beam in context Lord and Shulman theory is studied. The analytical solution in the Laplace domain is obtained for lateral deflection, temperature, displacement, concentration, stress and chemical potential. The both ends of the nanoscale beam are simply supported. The basic equations have been written in the form of ... Read more