Hamdy M. Youssef

Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity

The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity. The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach. The inverse Laplace transforms was obtained numerically. The temperature, displacement and stress distributions are represented graphically.

Two-Temperature Theory in Three-Dimensional Problem for Thermoelastic Half Space Subjected to Ramp Type Heating

A three-dimensional model of the two-temperature generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and duple Fourier transforms techniques are applied to a specific problem of a half space subjected to ramp-type heating and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the conductive temperature, the dynamical temperature, the stress, the strain, and the displacement distributions are represented graphically.

Two-Temperature Generalized Thermoelasticity with Variable Thermal Conductivity

In this work, the consideration of variable thermal conductivity as a linear function of temperature has been taken into account in the context of two-temperature generalized thermoelasticity (Youssefs model). The governing equations have been derived and used to solve the one-dimensional problems of an elastic half-space. The governing equations have been cast into a matrix form by using Bahar–Hetnarski method, and Laplace transform is used to get the general solution for any set of boundary conditions. The solution has been applied for a thermally shocked medium that has no strain on its bounding plane. The numerical inversion of the Laplace transform has been calculated by using the Riemann-sum approximation method. The distribution of the conductive temperature, the thermo-dynamical temperature, the strain, the displacement, and the stress have been shown graphically with some comparisons.

Thermoelastic Material Response Due to Laser Pulse Heating in Context of Four Theorems of Thermoelasticity

This article describes the study of induced temperature and stress fields in an elastic half-space in the context of classical coupled thermoelasticity (Biot) and generalized thermoelasticity (Lord–Shulman, Green–Lindsay and Green–Naghdi) in a unified system of equations. The medium is considered to be made of an isotropic homogeneous thermoelastic half-space. The bounding plane of the surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Because the response is of more interest in the transient state, the inversion of Laplace transforms were carried out numerically. The derived expressions were computed numerically for copper, and the results are presented in graphical form.

Three-dimensional thermo-viscoelastic material

ABSTRACT A three-dimensional model of the generalized thermo-viscoelasticity is established. The formulation is applied to the generalized thermo-viscoelasticity theories: Lord–Shulman and Green–Lindsay as well as to the dynamic coupled theory. The resulting nondimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction-free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain, and displacement distributions are represented graphically.

Thermoelastic Damping in Nanomechanical Resonators Based on Two-Temperature Generalized Thermoelasticity Theory

This work is concerned with the study of the thermoelastic damping of nanobeam resonators in the context of the two-temperature generalized thermoelasticity theory. An explicit formula of thermoelastic damping has been derived. Influences of the beam height, the relaxation time parameter, the two-temperature parameter and the isothermal value of frequency have been studied with some comparisons between the Biot model and Lord–Shulman model (L–S). Numerical results show that the values of thermal relaxation parameter and the two-temperature parameter have a strong influence on thermoelastic damping in nanoscales.

On the theory of two-temperature thermoelasticity without energy dissipation of Green–Naghdi model

This work introduces one-dimensional numerical application of an elastic and isotropic half space in which the governing equations have been taken in the context of the two-temperature thermoelasticity without energy dissipation theory to show the effects of the two-temperature parameter on all the studied fields and to stand on the contributions of this theory. The results of this work confirmed that the two-temperature thermoelasticity without energy dissipation is valid when the thermo-dynamical temperature and the temperature of the heat conduction are not coinciding.

Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam

In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact of thermal load and the effect of the fractional order parameter on the speed of progress of mechanical and thermal waves through the beam.© 2013 ASME