scholarly journals Effect of Rotation on Propagation of Waves in Transversely Isotropic Thermoelastic Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Raj Rani Gupta ◽  
Rajani Rani Gupta
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Thermal Wave ◽  
Isotropic Medium ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transversely Isotropic Medium ◽  
Propagation Of Waves

The present study is concerned with the effect of rotation on the propagation of plane waves in a transversely isotropic medium in the context of thermoelasticity theory of GN theory of types II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasilongitudinal wave. The slowest of them is a thermal wave. The remaining is called quasitransverse wave. The prefix “quasi” refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of rotation and anisotropy.

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.

Wave propagation in an initially stressed transversely isotropic thermoelastic half-space

2014 ◽  
Vol 23 (5-6) ◽  
pp. 185-190 ◽  
Author(s):  
Raj Rani Gupta ◽  
M.S. Saroa
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Half Space ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Type Ii ◽  
Transversely Isotropic Medium ◽  
Temperature Distributions ◽  
Thermoelasticity Theory

AbstractThe present paper deals with the study of reflection waves in an initially stressed transversely isotropic medium, in the context of Green and Naghdi (GN) thermoelasticity theory type II and III. The components of displacement, stresses and temperature distributions are determined through the solution of the wave equation by imposing the appropriate boundary conditions. Numerically simulated results are plotted graphically with respect to frequency in order to show the effect of anisotropy.

scholarly journals Propagation of waves in the layer of a thermo-viscoelastic transversely isotropic medium

2016 ◽  
Vol 21 (1) ◽  
pp. 21-35
Author(s):  
R.R. Gupta ◽  
R.R. Gupta
Keyword(s):  
Wave Propagation ◽  
Temperature Distribution ◽  
Isotropic Medium ◽  
Lamb Waves ◽  
Transversely Isotropic ◽  
Type Ii ◽  
Transversely Isotropic Medium ◽  
Symmetric Wave ◽  
Secular Equations ◽  
Propagation Of Waves

Abstract The article is presented to enhance our knowledge about the propagation of Lamb waves in the layer of a viscoelastic transversely isotropic medium in the context of thermoelasticity with GN theory of type-II and III. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for cobalt and the dispersion curves, amplitudes of displacements and temperature distribution for symmetric and skew-symmetric wave modes are presented to evince the effect of anisotropy. Some particular cases are also deduced.

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.

Exact elastic impedance matrices for transversely isotropic medium

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. C1-C15 ◽  
Author(s):  
Feng Zhang ◽  
Xiang-Yang Li
Keyword(s):  
Shale Gas ◽  
Isotropic Medium ◽  
Seismic Reflection ◽  
Transversely Isotropic ◽  
Seismic Inversion ◽  
P Wave ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Transversely Isotropic Medium ◽  
Anisotropy Parameters

Conventional elastic impedances are derived as scalars by means of the integration of reflectivity. In this sense, they are attributes of the seismic reflection but not the intrinsic physical property of the subsurface media. The derivation of these expressions shares the same assumptions as the reflectivity approximations, such as weak impedance contrast, small angle of incidence, or weak anisotropic media, and thus it limits the accuracy and interpretation capability. The exact P/SV impedance matrices relating the stress and strain represent the mechanical property of the subsurface media and yield reflection coefficients at an arbitrary angle of incidence. We have extended the impedance matrices to a transversely isotropic medium. The resulting elastic impedances (stress/velocity ratios) can be used to characterize those unconventional reservoir formations with strong seismic anisotropy, such as shale-gas and coal-bed methane. Our numerical analyses determined their variations with the phase angle and anisotropy parameters. The exact expressions of the P- and S-wave elastic impedances are used to model the seismic reflection coefficients, and thus they can be inverted simultaneously if all of the types of reflection waves are available. We then derive approximations of quasi-P-wave elastic impedances for seismic inversion of anisotropy parameters and further interpretation. Our applications on real logs and seismic data for a turbidite fan reservoir and a shale-gas reservoir determined the robust interpretation capability of derived elastic impedances in lithology characterizations.

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.

Approximate polarization of plane waves in a medium having weak transverse isotropy

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1605-1612 ◽  
Author(s):  
Björn E. Rommel
Keyword(s):  
Isotropic Medium ◽  
Transverse Isotropy ◽  
Full Range ◽  
Velocity Ratio ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Seismic Exploration ◽  
Transversely Isotropic Medium ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Many real rocks and sediments relevant to seismic exploration can be described by elastic, transversely isotropic media. The properties of plane waves propagating in a transversely isotropic medium can be given in an analytically exact form. Here the polarization is recast into a comprehensive form that includes Daley and Hron’s normalization and Helbig’s full range of elastic constants. But these formulas are rather lengthy and do not easily reveal the features caused by anisotropy. Hence Thomsen suggested an approximation scheme for weak transverse isotropy. His derivation of the approximate polarization, however, is based on a property that is not suitable to measure small differences between an isotropic and a weakly transversely isotropic medium. Therefore the approximation of the polarization is recast. The corrected approximation does show a dependence on weak transverse isotropy. This feature can be viewed as an additional rotation of the polarization with respect to the wavenormal. It depends on the anisotropy as well as the inverse velocity ratio. An approximate condition of pure polarization, which occurs in certain directions, is also obtained. The corrected approximation results in a better match of the approximate polarization with the exact one, providing the assumption of weak transverse isotropy is met. When comparing the additional rotation with the deviation of the (observable) ray direction from the wavenormal, the qSV‐wave indicates transverse isotropy most clearly.

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