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.

scholarly journals Reflection of Plane Waves from Surface of a Generalized Thermo-Viscoelastic Porous Solid Half-Space with Impedance Boundary Conditions

2020 ◽  
Vol 22 (4) ◽  
pp. 1483-1496
Author(s):  
Baljeet Singh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Impedance Boundary ◽  
Reflected Waves ◽  
Material Parameters ◽  
Impedance Boundary Conditions ◽  
Impedance Parameter

AbstractA phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x–z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

scholarly journals Effect of Two Temperatures on Reflection Coefficient in Micropolar Thermoelastic with and without Energy Dissipation Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Rajneesh Kumar ◽  
K. D. Sharma ◽  
S. K. Garg
Keyword(s):  
Energy Dissipation ◽  
Temperature Effects ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflected Waves ◽  
Two Temperatures ◽  
Thermally Conducting ◽  
Without Energy Dissipation ◽  
Two Temperature

The reflection of plane waves at the free surface of thermally conducting micropolar elastic medium with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected waves at different angles of incident wave are obtained. Dissipation of energy and two-temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.

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.

Reflection of plane waves in thermoelastic medium with double porosity

2016 ◽  
Vol 12 (4) ◽  
pp. 748-778 ◽  
Author(s):  
Rajneesh Kumar ◽  
Richa Vohra ◽  
M.G. Gorla
Keyword(s):  
Relaxation Time ◽  
Earthquake Engineering ◽  
Plane Waves ◽  
Practical Importance ◽  
Double Porosity ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Thermoelastic Medium ◽  
Content Type ◽  
The Earth

Purpose The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure. Design/methodology/approach A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV). Findings The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model. Originality/value Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

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.

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space

2012 ◽  
Vol 42 (3) ◽  
pp. 33-60 ◽  
Author(s):  
Baljeet Singh ◽  
Anand Yadav
Keyword(s):  
Magnetic Fields ◽  
Half Space ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Thermoelastic Medium ◽  
Reflected Waves ◽  
Velocity Equation ◽  
Thermoelastic Solid

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-SpaceThe governing equations of a rotating transversely isotropic magneto-thermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation, thermal and magnetic fields are shown graphically on these coefficients.

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 Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids

2016 ◽  
Vol 21 (2) ◽  
pp. 285-301 ◽  
Author(s):  
R. Bijarnia ◽  
B. Singh
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Reflected Waves ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Two Temperature

AbstractThe paper is concerned with the propagation of plane waves in a transversely isotropic two temperature generalized thermoelastic solid half-space with voids and rotation. The governing equations are modified in the context of Lord and Shulman theory of generalized thermoelasticity and solved to show the existence of four plane waves in thex – zplane. Reflection of these plane waves from thermally insulated stress free surface is also studied to obtain a system of four non-homogeneous equations. For numerical computations of speed and reflection coefficients, a particular material is modelled as transversely isotropic generalized thermoelastic solid half-space. The speeds of plane waves are computed against the angle of propagation to observe the effects of two temperature and rotation. Reflection coefficients of various reflected waves are also computed against the angle of incidence to observe the effects of various parameters.

Reflection of spherical seismic waves in elastic layered media

Geophysics ◽  
1983 ◽  
Vol 48 (6) ◽  
pp. 655-664 ◽  
Author(s):  
Paul M. Krail ◽  
Henry Brysk
Keyword(s):  
Plane Wave ◽  
Seismic Waves ◽  
Plane Waves ◽  
Spherical Wave ◽  
Bright Spot ◽  
Angle Of Incidence ◽  
Complicated Manner ◽  
Plane Wave Incident ◽  
Wave Limit ◽  
The Impact

The solution of the elastic wave equation for a plane wave incident on a plane interface has been known since the turn of the century. For reflections from reasonably shallow beds, however, it is necessary to treat the incident wave as spherical rather than plane. The formalism for expressing spherical wavefronts as contour integrals over plane waves goes back to Sommerfeld (1909) and Weyl (1919). Brekhovskikh (1960) performed a steepest descent evaluation of the integrals to attain analytic results in the acoustic case. We have extended his approach to elastic waves to obtain spherical‐wave Zoeppritz coefficients. We illustrate the impact of the curvature correction parametrically (as the velocity and density contrasts and Poisson’s ratios are varied). In particular, we examine conditions appropriate to “bright spot” analysis; expectedly, the situation becomes less simple than in the plane‐wave limit. The curvature‐corrected Zoeppritz coefficients vary more strongly (and in a more complicated manner) with the angle of incidence than do the original ones. The determination of material properties (velocities and densities) from the reflection coefficients is feasible in principle, with exacting prestack processing and interpretation. For orientation, we outline the procedure for the simple case of a separated single source and detector pair over a multilayered horizontal earth.

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