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.

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.

Two-dimensional scattering of a plane compressional wave by surface imperfections

1969 ◽  
Vol 59 (3) ◽  
pp. 1349-1364
Author(s):  
Ivor K. McIvor
Keyword(s):  
Order Approximation ◽  
Strong Dependence ◽  
Plane Waves ◽  
Compressional Wave ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
The Body ◽  
Angle Of Incidence ◽  
Small Surface ◽  
Surface Imperfections

abstract A perturbation method for treating the scattering of plane waves by small surface imperfections on an elastic half space is presented. The solution to the first order approximation is given as convolution integrals of the surface imperfection with kernel functions defined by Fourier inversion integrals. The evaluation of these integrals is discussed and their asymptotic representations determined. The far field scattered displacements are explicitly obtained for arbitrary imperfections. The scattered field consists of a Rayleigh surface wave and four body phases which at the free surface travel with the speed of dilational or distortional waves. Numerical examples are given. In particular the error in the apparent angle of emergence due to the scattered waves is obtained. The body phases exhibit the familiar 3/2 geometric attenuation, but still may make a significant contribution at moderately long distances. A strong dependence of the magnitude of the error on the angle of incidence is demonstrated.

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.

scholarly journals Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Baljeet Singh ◽  
Ritu Sindhu ◽  
Jagdish Singh
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Rotation Frequency ◽  
Frequency Equation ◽  
Governing Equations ◽  
Wave Solutions ◽  
Effects Of Rotation ◽  
Micropolar Material

A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

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 Influence of Diffusion and Impedence Parameters on Wave Propagation in Thermoelastic Medium

2021 ◽  
Vol 26 (4) ◽  
pp. 99-112
Author(s):  
Sachin Kaushal ◽  
Rajneesh Kumar ◽  
Kulwinder Parmar
Keyword(s):  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Thermoelastic Medium ◽  
Impedance Boundary ◽  
Reflected Waves ◽  
Diffusion Relaxation ◽  
Impedance Parameters ◽  
The Impact ◽  
Coupled Theory

Abstract The aim of the present paper is to study the impact of diffusion and impedance parameters on the propagation of plane waves in a thermoelastic medium for Green and Lindsay theory (G-L) and the Coupled theory (C-T) of thermoelasticity. Results are demonstrated for impedance boundary conditions and the amplitude ratios of various reflected waves against the angle of incidence are calculated numerically. The characteristics of diffusion, relaxation time and impedence parameter on amplitude ratios have been depicted graphically. Some cases of interest are also derived from the present investigation.

Reflection and refraction of thermo-viscoelastic waves at the interface between two micropolar viscoelastic media without energy dissipation

2007 ◽  
Vol 85 (7) ◽  
pp. 797-812 ◽  
Author(s):  
M I Othman ◽  
Y Q Song
Keyword(s):  
Energy Dissipation ◽  
Harmonic Wave ◽  
Angle Of Incidence ◽  
Viscoelastic Media ◽  
Reflection And Refraction ◽  
Viscoelastic Waves ◽  
Viscoelastic Theory ◽  
Continuous Boundary ◽  
Without Energy Dissipation ◽  
62.20 Dc

Reflection and refraction of a plane harmonic wave at the interface between two viscoelastic media are studied under generalized thermo-viscoelastic theory. Using potential function, the governing equations reduce to two fourth-order ifferential equations. Coefficient ratios of reflection and refraction of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection and refraction with the angle of incidence are illustrated graphically for aluminium–epoxy and magnesium crystal micropolar viscoelastic materials. Also, the effects of viscous and micropolar elastic are illustrated by numerical results in the theory of thermo-viscoelasticity without energy dissipation. PACS No.: 62.20.Dc

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Nihar Sarkar ◽  
Soumen De ◽  
Narayan Das ◽  
Nantu Sarkar
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Half Space ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Energy Ratios ◽  
Thermally Conducting ◽  
Stress Free Boundary

Abstract This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

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