ibrabbas7

Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.

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Vibrational analysis for an axially moving microbeam with two temperatures

2015 | Keywords microbeam, axially moving, wo temperatures,
Vibrational analysis for an axially moving microbeam with two temperatures
In this article, the effect of two temperatures on an axially moving microbeam subjected to ramp-type heating is studied. The generalized thermoelasticity theory with one relaxation time model is used. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique, the inversion of Laplace transform is done numerically. Some comparisons have been shown in figures ... Read more

Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere

2015 | Keywords analytical solution, free vibration, Thermoelastic, Hollow Sphere,
Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere
For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible ... Read more

The effects of relaxation times and moving heat source on two-temperature generalized thermoelastic thin slim strip

2015 | Keywords thin slim strip, Thermoelastic, Two-temperature, moving heat source, Relaxation Times,
The effects of relaxation times and moving heat source on two-temperature generalized thermoelastic thin slim strip
The problem of two-temperature generalized thermoelastic thin slim strip is investigated in the context of Green and Lindsay theory. As an application of the problem, a particular type of moving heat source is considered and the problem is solved analytically by using the eigenvalue approach in the Laplace transforms domain. The displacement, conductive temperature, thermodynamic temperature, and stress are obtained. ... Read more

Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source

2015 | Keywords eigenvalue approach, moving heat source, Magneto-Thermoelastic, fractional order,
Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source
In the present work, we consider the problem of fractional order thermoelastic interaction in a material placed in a magnetic field and subjected to a moving plane of heat source. The basic equations have been written in the form of a vector–matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. The inverse Laplace ... Read more

Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator

2015 | Keywords Nano-Beam Resonator, Frequency Shifts, Thermoelastic Damping, Exact solution,
Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator
In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in ... Read more

Free vibration of a thermoelastic hollow cylinder with one relaxation time

2015 | Keywords Thermoelastic, relaxation time, free vibration,
Free vibration of a thermoelastic hollow cylinder with one relaxation time
The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the ... Read more

A GN model for thermoelastic interaction in a microscale beam subjected to a moving heat source

2015 | Keywords Thermoelastic, microscale beam, moving heat source,
A GN model for thermoelastic interaction in a microscale beam subjected to a moving heat source
In this study, the problem of thermoelastic interaction in a microscale beam subjected to a moving heat source in the context of Green and Naghdi theory type III is investigated. The both ends of the microscale beam are clamped and thermally isolated. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform ... Read more

Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer

2015 | Keywords Thermoelastic, three-phase lag heat transfer, Functional Graded Material,
Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer
The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials (FGM) (i.e., material with spatially varying material properties) are established. The ... Read more

Three-dimensional interaction in thermoelastic medium with two relaxation time due to thermal source

2015 | Keywords Three-dimensional, two relaxation time, Thermoelastic, Thermal Source,
Three-dimensional interaction in thermoelastic medium with two relaxation time due to thermal source
The present study is concerned with the interaction in thermoelastic medium with two relaxation times due to thermal source. The finite element technique under normal mode analysis is used to solve the resulting nondimensional coupled equations. As an application of the approach, the particular type of thermal source has been considered. The components of displacement, stress and temperature change are ... Read more

A Green and Naghdi Model in a Two-Dimensional Thermoelastic Diffusion Problem for a Half Space

2015 | Keywords Half Space, Thermoelastic Diffusion, Two-Dimensional, Green and Naghdi Model,
A Green and Naghdi Model in a Two-Dimensional Thermoelastic Diffusion Problem for a Half Space
The present investigation is concerned with the wave propagation of generalized thermoelastic diffusion on a half space with energy dissipation. The surface of the half-space is taken to be traction free and a thermal shock applied on the surface. The problem has been solved numerically using a finite element method. The expressions for displacement components, stresses, temperature, concentration and chemical ... Read more