scholarly journals Reflection and transmission at the boundary surface of modified couple stress thermoelastic media

2016 ◽  
Vol 21 (1) ◽  
pp. 61-81 ◽  
Author(s):  
R. Kumar ◽  
K. Kumar
Keyword(s):  
Couple Stress ◽  
Boundary Surface ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflection And Transmission ◽  
Transverse Waves ◽  
Transmitted Waves ◽  
Special Cases ◽  
Modified Couple Stress ◽  
Thermoelastic Solid

Abstract In this paper the reflection and transmission at a plane interface in modified couple stress generalized thermoelastic solid half spaces in the context of Loard-Shulman (LS) and Green-Lindsay (GL) theories in welded contact are investigated. Amplitude ratios of various reflected and transmitted waves are obtained due to incidence of a set of coupled longitudinal waves and coupled transverse waves. It is found that the amplitude ratios of various reflected and transmitted waves are functions of the angle of incidence, frequency and are affected by the couple stress properties of the media. Some special cases are deduced from the present formulation.

scholarly journals Wave propagation in a microstretch thermoelastic diffusion solid

2015 ◽  
Vol 23 (1) ◽  
pp. 127-170 ◽  
Author(s):  
Rajneesh Kumar
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Inviscid Fluid ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Transverse Waves ◽  
Thermoelastic Diffusion ◽  
Transmitted Waves ◽  
Energy Ratios ◽  
The Media

Abstract The present article deals with the two parts: (i) The propagation of plane waves in a microstretch thermoelastic diffusion solid of infinite extent. (ii) The reflection and transmission of plane waves at a plane interface between inviscid fluid half-space and micropolar thermoelastic diffusion solid half-space. It is found that for two-dimensional model, there exist four coupled longitudinal waves, that is, longitudinal displacement wave (LD), thermal wave (T), mass diffusion wave (MD) and longitudinal microstretch wave (LM) and two coupled transverse waves namely (CD-I and CD-II waves). The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and depicted graphically. In the second part, it is noticed that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency of incident wave and are influenced by the microstretch thermoelastic diffusion properties of the media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios have been computed numerically for a particular model. The variations of energy ratios with angle of incidence for thermoelastic diffusion media in the context of Lord-Shulman (L-S) [1] and Green-Lindsay (G-L) [2] theories are depicted graphically. Some particular cases are also deduced from the present investigation.

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.

Dilatational waves at a microstretch solid/fluid interface

2016 ◽  
Vol 23 (20) ◽  
pp. 3448-3467 ◽  
Author(s):  
Dilbag Singh ◽  
Neela Rani ◽  
Sushil Kumar Tomar
Keyword(s):  
Half Space ◽  
Aluminum Matrix ◽  
Elastic Solid ◽  
Specific Model ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Microstretch Fluid

The present work is concerned with the study of reflection and transmission phenomena of dilatational waves at a plane interface between a microstretch elastic solid half-space and a microstretch liquid half-space. Eringen's theory of micro-continuum materials has been employed for addressing the mathematical analysis. Reflection and transmission coefficients, corresponding to various reflected and transmitted waves, have been obtained when a plane dilatational wave strikes obliquely at the interface after propagating through the solid half-space. It is found that the reflection and transmission coefficients are functions of the angle of incidence, the frequency of the incident wave and the elastic properties of the half-spaces. Numerical calculations have been carried out for a specific model by taking an aluminum matrix with randomly distributed epoxy spheres as the microstretch solid medium, while the microstretch fluid is taken arbitrarily with suitably chosen elastic parameters. The computed results obtained have been depicted graphically. The results of earlier studies have been deduced from the present formulation as special cases.

scholarly journals Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface

2001 ◽  
Vol 26 (11) ◽  
pp. 685-694 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sushil K. Tomar
Keyword(s):  
Viscous Liquid ◽  
Half Space ◽  
Incident Wave ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflection And Transmission ◽  
Special Case

Amplitude ratios of various reflected and transmitted elastic waves from a plane interface separating a viscous liquid half-space and a micropolar elastic solid half-space, are obtained in two cases (i) when longitudinal wave propagating through the solid half-space is made incident at the interface and (ii) when “coupled-wave” propagating through the solid half-space is made incident at the interface. These amplitude ratios have been computed numerically for a specific model and results obtained are presented graphically. It is found that these amplitude ratios depend on the angle of incidence of the incident wave and the effect of viscosity of the liquid on amplitude ratios is noticed. The problem studied by Tomar and Kumar (1995) has been reduced as a special case of our problem.

scholarly journals Resonance of Nanoscale Beam due to Various Sources in Modified Couple Stress Thermoelastic Diffusion with Phase Lags

2019 ◽  
Vol 23 (1) ◽  
pp. 36-49
Author(s):  
Rajneesh Kumar ◽  
Shaloo Devi ◽  
Veena Sharma
Keyword(s):  
Laplace Transform ◽  
Couple Stress ◽  
Chemical Potential ◽  
Inverse Laplace Transform ◽  
Phase Lag ◽  
Thermoelastic Diffusion ◽  
Special Cases ◽  
Laplace Transform Technique ◽  
Modified Couple Stress ◽  
Phase Lags

Abstract This paper deals with the study of thermoelastic thin beam in a modified couple stress with three-phase-lag thermoelastic diffusion model subjected to thermal and chemical potential sources. The governing equations are derived by using the Euler-Bernoulli beam assumption and eigenvalue approach. The Laplace transform technique is employed to obtain the expressions for displacements, lateral deflection, temperature change, axial stress and chemical potential. A particular type of instantaneous and distributed sources is taken to show the utility of the approach. The general algorithm of the inverse Laplace transform is developed to compute the results numerically. The numerical results are depicted graphically to show the effects of phase lags, with and without energy dissipation on the resulting quantities. Some special cases are given.

scholarly journals Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids

2014 ◽  
Vol 22 (2) ◽  
pp. 151-176 ◽  
Author(s):  
Kunal Sharma ◽  
Marin Marin
Keyword(s):  
Amplitude Ratio ◽  
Plane Waves ◽  
Elastic Solid ◽  
Heat Conducting ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transmitted Waves ◽  
Thermally Conducting ◽  
Two Temperature

AbstractThe problem of reflection and transmission of plane waves at an imperfect boundary between two thermally conducting micropolar elastic solid half spaces with two temperature is investigated. Amplitude ratio of various reflected and transmitted waves are presented when a set of coupled longitudinal wave (LD-wave) and thermal wave (T-wave) and a set of coupled transverse wave and microrotation waves (CDI, CDII) is made incident. The expressions for reflection and transmission coefficients which are the ratios of the amplitudes of reflected and transmitted waves at different angles of incident wave are obtained. The corresponding expressions for the normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding has also been included. Stiffness and two temperature e ects on these amplitude ratios with angle of incidence have been depicted graphically. Some special and particular cases are also discussed.

scholarly journals Reflection-Refraction Coefficients and Energy Ratios in Couple Stress Micropolar Thermoviscous Elastic Solid

2021 ◽  
Vol 26 (2) ◽  
pp. 47-69
Author(s):  
Ravinder Kumar Sahrawat ◽  
Poonam
Keyword(s):  
Couple Stress ◽  
Elastic Solid ◽  
Angular Frequency ◽  
Angle Of Incidence ◽  
Transverse Waves ◽  
Reflection And Refraction ◽  
Solid Media ◽  
Energy Ratios ◽  
Perfect Contact ◽  
Propagation Of Waves

Abstract The reflection and refraction phenomenon of propagation of waves in couple stress micropolar thermoviscous elastic solid media with independent viscoelastic and micropolar properties have been studied. The structure of the model has been taken such that the plane interface is divides the given media into two half spaces in perfect contact. Here, we find that there are five waves, one of them is propagating independently while others are set of two coupled waves travelling with different speeds. Energy ratios, reflection and refraction coefficients relative to numerous reflected and refracted waves have been investigated when set of two coupled longitudinal waves and set of two coupled transverse waves strike at the interface through the solid medium. The inequality of energy ratios, refraction coefficients and reflection coefficients are evaluated numerically and presented graphically under three theories of thermoelasticity, namely, Green-Lindsay theory (GL), Lord-Shulman theory (LS), Coupled theory (CT) versus angular frequency and angle of incidence.

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