Reflection of plane waves from a thermo-microstretch elastic solid with temperature dependent elastic properties

2014 ◽  
Vol 10 (2) ◽  
pp. 228-249 ◽  
Author(s):  
Ya Qin Song ◽  
Mohamed I.A. Othman ◽  
Zheng Zhao
Keyword(s):  
Reflection Coefficient ◽  
Harmonic Wave ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Angle Of Incidence ◽  
Temperature Dependent ◽  
Content Type

Purpose – The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation. Design/methodology/approach – Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories. Findings – The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory. Originality/value – The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Devender Sheoran ◽  
Ramesh Kumar ◽  
Sunil Kumar ◽  
Kapil Kumar Kalkal
Keyword(s):  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Conservation Of Energy ◽  
Content Type ◽  
Reflected Waves ◽  
Diffusive Medium ◽  
Energy Ratios ◽  
Two Temperature

Purpose The purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature. Design/methodology/approach A two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB. Findings The problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material. Originality/value The modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

Effect of rotation on plane waves in generalized thermomicrostretch elastic solid: comparison of different theories using finite element method

2014 ◽  
Vol 92 (10) ◽  
pp. 1269-1277 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ibrahim A. Abbas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Waves ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Presence And Absence ◽  
Effects Of Rotation ◽  
Coupled Theory ◽  
Element Method

The present investigation is aimed at studying the effect of rotation on the thermomicrostretch elastic solid. The formulation is applied in the context of the generalized thermoelasticity Lord–Şhulman theory with one relaxation time and Green–Lindsay’s theory with two relaxation times, as well as the classical dynamical coupled theory. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, the force stresses, the couple stresses, and the microstress distribution are represented graphically. The results indicate that the effects of rotation are very pronounced. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories.

scholarly journals The reflection phenomena ofSV-waves in a generalized thermoelastic medium

2000 ◽  
Vol 23 (8) ◽  
pp. 529-546 ◽  
Author(s):  
Abo-El-Nour N. Abd-Alla ◽  
Amira A. S. Al-Dawy
Keyword(s):  
Thermal Effect ◽  
Elastic Waves ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Generalized Thermoelastic

We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.

Reflection of plane waves from a thermo-microstretch elastic solid under the effect of rotation

2014 ◽  
Vol 92 (6) ◽  
pp. 488-496 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ya Qin Song
Keyword(s):  
Harmonic Wave ◽  
Plane Waves ◽  
Elastic Solid ◽  
Elastic Half Space ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Plane Harmonic Wave ◽  
Continuous Boundary ◽  
Coupled Theory ◽  
Micropolar Material

A reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space is studied. The formulation is applied to generalized thermo-elasticity theories, the Lord–Şhulman and Green–Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten differential equations. Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically in magnesium crystal micropolar material under three theories. Also the effect of frequency and rotation on the coefficient ratios of reflection is illustrated graphically in the context of Lord–Shulman theory.

scholarly journals Reflection at Free Surface in Micropolar Thermoelastic Solid with two Temperatures

2013 ◽  
Vol 18 (1) ◽  
pp. 217-234 ◽  
Author(s):  
K. Sharma
Keyword(s):  
Half Space ◽  
Plane Surface ◽  
Plane Waves ◽  
Relaxation Times ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Two Temperatures ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

The present investigation is concerned with the effect of two temperatures on reflection coefficients in a micropolar thermoelastic solid half space. With two relaxation times, reflection of plane waves impinging obliquely at a plane interface of the micropolar generalized thermoelastic solid half space with two temperatures is investigated. The incident wave is assumed to be striking at the plane surface after propagating through the micropolar generalized thermoelastic solid with two temperatures. Amplitude ratios of the various reflected waves are obtained in closed form and it is found that these are functions of angle of incidence, frequency and are affected by the elastic properties of the media. The effect of two temperatures is shown on these amplitude ratios for a specific model.

Reflection of Plane Waves in a Rotating Temperature-Dependent Thermoelastic Solid with Diffusion

2012 ◽  
Vol 28 (4) ◽  
pp. 599-606
Author(s):  
B. Singh ◽  
L. Singh ◽  
S. Deswal
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Reflected Waves ◽  
Energy Ratios ◽  
Rotation Parameters ◽  
Thermoelastic Solid

ABSTRACTThe governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing equations indicates the existence of four coupled plane waves in x-z plane. The reflection of plane waves from the free surface of a rotating temperature-dependent thermoelastic solid half-space with diffusion is considered. The required boundary conditions are satisfied by the appropriate potentials for incident and reflected waves in the half-space to obtain a system of four non-homogeneous equations in the reflection coefficients. The expressions for energy ratios of the reflected waves are also obtained. The reflection coefficients and energy ratios are found to depend upon the angle of incidence, reference temperature, thermodiffusion and rotation parameters. Aluminum material is modeled as the half-space to compute the absolute values of the reflection coefficients and the energy ratios. Effects of temperature dependence and rotation parameters on the reflection coefficients and energy ratios are shown graphically for a certain range of the angle of incidence of the incident plane wave.

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

scholarly journals Generalized Photo-Thermo-Microstretch Elastic Solid Semiconductor Medium Due To Excitation Process

2021 ◽  
Author(s):  
kh. lotfy ◽  
A. El-Bary
Keyword(s):  
Mechanical Load ◽  
Harmonic Wave ◽  
Plane Waves ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Load Force ◽  
Normal Displacement ◽  
Physical Fields ◽  
Novel Model ◽  
Coupled Stress

Abstract A novel model in the theory of photo-thermoelasticity with microstretch properties is studied. The plasma-elastic-thermal plane waves are propagated in a linear isotropic generalized photo-thermo-microstretch elastic semiconductor solid medium. The photothermal excitation occurs in the context of the microinertia of microelement process during two dimensions (2D) deformation. The harmonic wave techniques are used to get the solutions for the basic variables. The analytical solution of the main physical fields; carrier intensity, normal displacement components, temperature, stress load force, microstress and tangential coupled stress can be obtained. Some graphics illustrated when using the plasma, thermal and mechanical load boundary conditions, which they apply at the outer free surface of the elastic medium. Some semiconductor materials as silicon (Si) and Germanium (Ge) are used to make the numerical simulation and some comparisons in different thermal memories are made. The main physical variables with new parameters are discussed theoretically and shown graphically.

State-space approach to generalized thermoelasticity plane waves with two relaxation times under dependence of the modulus of elasticity on reference temperature

2003 ◽  
Vol 81 (12) ◽  
pp. 1403-1418 ◽  
Author(s):  
M IA Othman
Keyword(s):  
State Space ◽  
Modulus Of Elasticity ◽  
Plane Waves ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Fourier Integral ◽  
Reference Temperature ◽  
Modern Theory ◽  
State Space Approach ◽  
Space Approach

We construct a model of the two-dimensional equations of generalized thermoelasticity with two relaxation times in an isotropic elastic medium with the modulus of elasticity being dependent on the reference temperature. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern theory, is applied to the nondimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate, varying exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature. PACS No.: 46.25.Hf

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