scholarly journals The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Fractional Order ◽  
Radial Distance ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Temperature Function ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Diagonalization Method ◽  
Temperature Parameter ◽  
Two Temperature

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

scholarly journals Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Mechanical Damage ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Temperature Parameter ◽  
Thermoelastic Solid ◽  
The One ◽  
Parameter Values ◽  
Two Temperature

AbstractThis work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

scholarly journals Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

Crystals ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1014
Author(s):  
Eman A. N. Al-Lehaibi
Keyword(s):  
Mechanical Damage ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Damage Parameter ◽  
Damage Effect ◽  
Principal Stresses ◽  
Diagonalization Method ◽  
Temperature Parameter ◽  
Thermoelastic Solid ◽  
Two Temperature

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

scholarly journals Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

2021 ◽  
Vol 26 (4) ◽  
pp. 78
Author(s):  
Hamzah Abdulrahman Alharthi
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Strain Theory ◽  
Aspect Ratios ◽  
The Laplace Transform ◽  
Beam Thickness ◽  
Novel Model ◽  
Two Temperature

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

Rotation of Two-Temperature Generalized Thermoelastic Half-Space Subjected to Thermal Shock and Without Energy Dissipation

2017 ◽  
Vol 14 (1) ◽  
pp. 529-535
Author(s):  
Eman A. N Al-Lehaibi
Keyword(s):  
Mathematical Model ◽  
Energy Dissipation ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Laplace Transforms ◽  
Temperature Parameter ◽  
Without Energy Dissipation ◽  
The Impact ◽  
The Mathematical Model ◽  
Two Temperature

In this work, a mathematical model for the thermoelastic medium with constant elastic parameters in the context of two-temperature generalized thermoelasticity without energy dissipation has been constructed. The governing equations of the mathematical model will be taken when the medium 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 particular model when the medium is subjected to a thermal load by using stat-space approach. The inversion of the Laplace transforms will be calculated numerically and after that we’ll present the results graphically with some comparisons to study the impact of thermal or mechanical load on the speed of progress of mechanical and thermal waves through the medium. Also, to studying the effect of the two-temperature parameter rotation parameter on all the studied field.

scholarly journals Propagation of Rayleigh Wave in a Two-Temperature Generalized Thermoelastic Solid Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Special Cases ◽  
Temperature Parameter ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Two Temperature

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous two-temperature thermoelastic solid half-space in the context of Lord and Shulman theory of generalized thermoelasticity. The governing equations of a two-temperature generalized thermoelastic medium are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The speed of Rayleigh wave is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.

scholarly journals Effect of rotation on a semiconducting medium with two-temperatures under L-S theory

2017 ◽  
Vol 38 (2) ◽  
pp. 101-122 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ramadan S. Tantawi ◽  
Ebtesam E.M. Eraki
Keyword(s):  
Relaxation Time ◽  
Angular Velocity ◽  
Elastic Medium ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Temperature Parameter ◽  
Two Temperatures ◽  
Two Temperature

AbstractThe model of the equations of generalized thermoelasticity in a semi-conducting medium with two-temperature is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under Lord-Schulman theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the considered variables. Also some particular cases are discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted in the absence and presence of rotation as well as two-temperature parameter.

scholarly journals Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Renu Yadav ◽  
Kapil Kumar Kalkal ◽  
Sunita Deswal
Keyword(s):  
Heat Source ◽  
State Space ◽  
Fractional Order ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Conductive Temperature ◽  
Special Cases ◽  
Two Temperature

The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented.

scholarly journals Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Sudip Mondal ◽  
Sadek Hossain Mallik ◽  
M. Kanoria
Keyword(s):  
Thermal Conductivity ◽  
Fractional Order ◽  
Generalized Thermoelasticity ◽  
Variable Thermal Conductivity ◽  
Fourier Series Expansion ◽  
Phase Lag ◽  
Dual Phase ◽  
The Laplace Transform ◽  
Matrix Differential ◽  
Two Temperature

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter.

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