scholarly journals Study of Axi-Symmetric Vibrations in a Micropolar Transversely Isotropic Layer

2019 ◽  
Vol 24 (2) ◽  
pp. 259-268
Author(s):  
R.R. Gupta ◽  
R.R. Gupta
Keyword(s):  
Wave Propagation ◽  
Isotropic Medium ◽  
Lamb Waves ◽  
Transversely Isotropic ◽  
Isotropic Layer ◽  
Transversely Isotropic Medium ◽  
Symmetric Wave ◽  
Special Cases ◽  
Secular Equations ◽  
Transversely Isotropic Layer

Abstract The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.

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.

scholarly journals Effect of rotation on wave propagation in a transversely isotropic medium

2001 ◽  
Vol 7 (2) ◽  
pp. 147-154 ◽  
Author(s):  
F. Ahmad ◽  
A. Khan
Keyword(s):  
Wave Propagation ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Slow Waves ◽  
Fast Wave ◽  
Transversely Isotropic Medium ◽  
High Frequencies ◽  
Unbounded Medium ◽  
Axis Of Symmetry ◽  
Effects Of Rotation

Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry is studied. For propagation at high frequencies, effects of rotation are negligible but for a frequency which is much smaller than the frequency of rotation, there is a fast wave and two very slow waves. When the two frequencies are equal, the speed of a wave becomes unbounded.

Analytic study of the geometrical spreading of P-waves in a layered transversely isotropic medium with a vertical symmetry axis

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1305-1315 ◽  
Author(s):  
Hongbo Zhou ◽  
George A. McMechan
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Transversely Isotropic ◽  
P Wave ◽  
Geometrical Spreading ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Special Cases

An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis (VTI). With this expression, geometrical spreading can be determined using only the anisotropy parameters in the first layer, the traveltime derivatives, and the source‐receiver offset. Explicit, numerically feasible expressions for geometrical spreading are obtained for special cases of transverse isotropy (weak anisotropy and elliptic anisotropy). Geometrical spreading can be calculated for transversly isotropic (TI) media by using picked traveltimes of primary nonhyperbolic P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading. For media with a few (4–5) layers, relative errors in the computed geometrical spreading remain less than 0.5% for offset/depth ratios less than 1.0. Errors that change with offset are attributed to inaccuracy in the expression used for nonhyberbolic moveout. Geometrical spreading is most sensitive to errors in NMO velocity, followed by errors in zero‐offset reflection time, followed by errors in anisotropy of the surface layer. New relations between group and phase velocities and between group and phase angles are shown in appendices.

scholarly journals The influence of heterogeneity and initial stress on the propagation of Love-type wave in a transversely isotropic layer subjected to rotation

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110414
Author(s):  
Fatimah Salem Bayones ◽  
Nahed Sayed Hussein ◽  
Abdelmooty Mohamed Abd-Alla ◽  
Amnah Mohamed Alharbi
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Dispersion Equation ◽  
Initial Stress ◽  
Transversely Isotropic ◽  
Wave Number ◽  
Isotropic Layer ◽  
Rigid Foundation ◽  
Type Wave ◽  
Transversely Isotropic Layer

Introduction: In this paper, a mathematical model of Love-type wave propagation in a heterogeneous transversely isotropic elastic layer subjected to initial stress and rotation of the resting on a rigid foundation. Frequency equation of Love-type wave is obtained in closed form. The material constants and initial stress have been taken as space dependent and arbitrary functions of depth in the respective media. Objectives: The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, rotation, wave number, the phase velocity on the Love-type wave propagation. Methods: The analytical solution has been obtained, we have used the separation of variables, method and the numerical solution using the bisection method implemented in MATLAB. Results: We present a general dispersion relation to describe the impacts as the propagation of Love-type waves in the structures. Numerical results analyzing the dispersion equation are discussed and presented graphically. Moreover, the obtained dispersion relation is found in well agreement with the classical case in isotropic and transversely isotropic layer resting on a rigid foundation. Finally, some graphical presentations have been made to assess the effects of various parameters in the plane wave propagation in elastic media of different nature.

Generalized moveout approximation for qP- and qSV-waves in a homogeneous transversely isotropic medium

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. D79-D84 ◽  
Author(s):  
Alexey Stovas
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Velocity Analysis ◽  
Kinematic Modeling ◽  
Transversely Isotropic Medium ◽  
Time Migration ◽  
Special Cases ◽  
Higher Order Terms ◽  
Vti Medium

The moveout approximations can be used in kinematic modeling, velocity analysis, and time migration. The generalized moveout approximation involves five approximation parameters and has several known approximations as special cases. A method is demonstrated for determining parameters of the generalized nonhyperbolic moveout approximation for qP- and qSV-waves in a homogeneous transversely isotropic medium with vertical symmetry axis (VTI medium). The additional parameters for the generalized approximation are computed from the hyperbolic asymptote at infinite offset. Comparison with a few well-known moveout approximations for higher-order terms in the Taylor series and asymptotic behavior shows that the generalized moveout approximation is superior to other nonhyperbolic approximations. A few numerical examples for qP- and qSV-waves in a VTI medium also indicate that the generalized approximation performs the best.

Effect of undulation on SH-wave propagation in corrugated magneto-elastic transversely isotropic layer

2016 ◽  
Vol 24 (3) ◽  
pp. 200-211 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Kshitish Ch. Mistri ◽  
Tanupreet Kaur ◽  
A. Chattopadhyay
Keyword(s):  
Wave Propagation ◽  
Transversely Isotropic ◽  
Isotropic Layer ◽  
Sh Wave ◽  
Transversely Isotropic Layer

Effect of anisotropy on Love wave propagation

1968 ◽  
Vol 58 (1) ◽  
pp. 259-266
Author(s):  
Janardan G. Negi ◽  
S. K. Upadhyay
Keyword(s):  
Wave Propagation ◽  
Frequency Dependence ◽  
Characteristic Frequency ◽  
Love Wave ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Isotropic Case ◽  
Rigid Base ◽  
Isotropic Layer ◽  
Transversely Isotropic Layer

abstract A study on Love wave propagation in a transversely isotropic layer with stress free upper surface and underlying rigid base, is presented. The characteristic frequency equation is obtained and frequency dependence of the velocity parameters for different modes is analysed in detail. Several distinctive propagation phenomena which differ considerably from those in isotropic case are listed below:

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.

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