scholarly journals Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores

2017 ◽  
Vol 4 (2) ◽  
pp. 160511 ◽  
Author(s):  
Deepak Kr. Pandit ◽  
Santimoy Kundu ◽  
Shishir Gupta
Keyword(s):  
Phase Velocity ◽  
Closed Form ◽  
Volume Fraction ◽  
Separation Of Variables ◽  
Theoretical Work ◽  
Sh Wave ◽  
Sh Waves ◽  
Analysis Of Dispersion ◽  
Void Pores ◽  
Absorption Characteristics

This theoretical work reports the dispersion and absorption characteristics of horizontally polarized shear wave (SH-wave) in a corrugated medium with void pores sandwiched between two dissimilar half-spaces. The dispersion and absorption equations have been derived in a closed form using the method of separation of variables. It has been established that there are two different kinds of wavefronts propagating in the proposed media. One of the wavefronts depends on the modulus of rigidity of elastic matrix of the medium and satisfies the dispersion equation of SH-waves. The second wavefront depends on the changes in volume fraction of the pores. Numerical computation of the obtained relations has been performed and the results are depicted graphically. The influence of corrugation, sandiness on the phase velocity and the damped velocity of SH-wave has been studied extensively.

scholarly journals Influence of Uniaxial Pressure on the Characteristics of Lamb and SH-wave Propagation in LiNbO₃ Crystalline Plates

2021 ◽  
pp. 105-116
Author(s):  
Sergey I. Burkov ◽  
Oleg N. Pletnev ◽  
Pavel P. Turchin ◽  
Olga P. Zolotova ◽  
Boris P. Sorokin
Keyword(s):  
Wave Propagation ◽  
Lithium Niobate ◽  
Phase Velocity ◽  
Electromechanical Coupling ◽  
Theoretical Study ◽  
Uniaxial Pressure ◽  
Coupling Coefficients ◽  
Propagation Characteristics ◽  
Sh Wave ◽  
Sh Waves

Theoretical study of uniaxial pressure influence on the propagation characteristics of Lamb and SH-waves in lithium niobate plate is carried out. Electromechanical coupling coefficients and controlling coefficients of the pressure influence on phase velocity are calculated in various directions. Transformation and hybridization of acoustic modes upon a pressure influence have been derived in details. PACS: 43.25.Fe; 43.35.Cg; 77.65.-j

Impacts on the Propagation of SH-Waves in a Heterogeneous Viscoelastic Layer Sandwiched between an Anisotropic Porous Layer and an Initially Stressed Isotropic Half Space

2016 ◽  
Vol 33 (1) ◽  
pp. 13-22 ◽  
Author(s):  
S. Kundu ◽  
P. Alam ◽  
S. Gupta ◽  
D. Kr. Pandit
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
Porous Layer ◽  
Separation Of Variables ◽  
Finite Thickness ◽  
Wave Number ◽  
Viscoelastic Layer ◽  
Sh Wave ◽  
Sh Waves

AbstractThe present study deals with the affected behaviour of SH-wave propagation through a viscoelastic layer sandwiched between an anisotropic porous layer of finite thickness and an isotropic half space. The sandwiched viscoelastic layer is considered as heterogeneous medium of finite thickness and isotropic half-space is considered as initially stressed medium. The method of separation of variables has been applied to obtain the dispersion equation of SH-wave in their respective media. The obtained complex dispersion relation has been separated into real and imaginary parts. Moreover, the dispersion relation has been satisfied with the classical condition of Love waves. The effects of heterogeneity, attenuation constant, dissipation factor of viscoelasticity, initial stress (compressive), thickness ratio of two layers and porosity on the propagation of SH-waves have been shown by number of graphs. Graphs have been plotted for the dimensionless phase and damping velocity on the propagation of SH-waves with respect to the dimensionless real wave number. The results may be useful to explore the nature and peculiarity of SH-wave propagation in the viscoelastic structure.

Scattering of SH Wave on Periodic Cracks in an Infinite Plane of Piezoelectric/Piezomagnic Composite Materials

2012 ◽  
Vol 166-169 ◽  
pp. 3364-3368
Author(s):  
Wei Shi ◽  
Li Xia Ma
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Composite Materials ◽  
Piezoelectric Materials ◽  
Infinite Plane ◽  
Sh Wave ◽  
Scattering Problems ◽  
Sh Waves ◽  
Periodic Cracks ◽  
The Fourier Transform

In this paper, the scattering problems of SH waves on periodic cracks in an infinite of piezoelectric/piezomagnic composite materials bonded to an infinite of homogeneous piezoelectric materials is investigated, the Fourier transform techniques are used to reduce the problem to the solution of Hilbert singular integral equation, the latter is solved by Lobotto-Chebyshev and Gauss integral equation, at last, numerical results showed the effect of the frequency of wave, sizes and so on upon the normalized stress intensity factor.

scholarly journals Nondestructive Evaluation of Functionally Graded Subsurface Damage on Cylinders in Nuclear Installations Based on Circumferential SH Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhen Qu ◽  
Xiaoqin Shen ◽  
Xiaoshan Cao
Keyword(s):  
Mechanical Properties ◽  
Phase Velocity ◽  
Nondestructive Evaluation ◽  
Surface Damage ◽  
Subsurface Damage ◽  
Functionally Graded ◽  
Horizontal Shear ◽  
Steel Cylinder ◽  
Sh Waves ◽  
Subsurface Layers

Subsurface damage could affect the service life of structures. In nuclear engineering, nondestructive evaluation and detection of the evaluation of the subsurface damage region are of great importance to ensure the safety of nuclear installations. In this paper, we propose the use of circumferential horizontal shear (SH) waves to detect mechanical properties of subsurface regions of damage on cylindrical structures. The regions of surface damage are considered to be functionally graded material (FGM) and the cylinder is considered to be a layered structure. The Bessel functions and the power series technique are employed to solve the governing equations. By analyzing the SH waves in the 12Cr-ODS ferritic steel cylinder, which is frequently applied in the nuclear installations, we discuss the relationship between the phase velocities of SH waves in the cylinder with subsurface layers of damage and the mechanical properties of the subsurface damaged regions. The results show that the subsurface damage could lead to decrease of the SH waves’ phase velocity. The gradient parameters, which represent the degree of subsurface damage, can be evaluated by the variation of the SH waves’ phase velocity. Research results of this study can provide theoretical guidance in nondestructive evaluation for use in the analysis of the reliability and durability of nuclear installations.

Reflection of SH waves from anisotropic transition layer

1974 ◽  
Vol 64 (6) ◽  
pp. 1979-1991 ◽  
Author(s):  
V. Thapliyal
Keyword(s):  
Reflection Coefficient ◽  
Incident Wave ◽  
Transition Layer ◽  
Seismic Energy ◽  
Considerable Effect ◽  
Anisotropy Factor ◽  
Sh Wave ◽  
Sh Waves ◽  
Obliquely Incident ◽  
Order Discontinuity

abstract The effects of anisotropy on the reflection of SH-waves (horizontally polarized shear waves) from a transition layer are studied. The transition layer is sand-wiched between two isotropic homogeneous half-spaces and is constituted by a medium which is both anisotropic and inhomogeneous. The SH-wave potentials are obtained for an anisotropic inhomogeneous medium in which both the anisotropy factor (ratio of the horizontal rigidity to the vertical rigidity) and vertical velocity vary with depth. An expression for the reflection coefficient of SH waves is obtained when the material mentioned above forms a finite transition zone between two isotropic homogeneous half-spaces. For further generalization, a second-order discontinuity along with the first-order on eis being assumed in the material properties, at the boundaries of the transition layer. The mathematical and numerical analyses show that the anisotropy factor, found at the top of the transition layer (N0/M0) produces considerable effect on the reflection coefficient for an obliquely incident SH wave. It has been noted that the greater the thickness of the transition layer, the greater is the dependence of the reflection coefficient upon the value of the anisotropy (N0/M0). The minima and maxima of the reflection of seismic energy are found dependent on the value of anisotropy. For greater values of the anisotropy, these maxima and minima shift toward the lower values of the wavelength of the propagating wave (or toward the higher values of the thickness of the transition layer). In fact, the values of the reflection coefficient at which these maxima and minima of seismic energy occur are found greater for the higher values of anisotropy. The effects of anisotropy are found more pronounced for the larger angles of incidence. This remains so until the angle of refraction becomes imaginary. However, no effects of the anistropy factor are found on the reflection coefficients for a normally incident wave. The results, mentioned above, are therefore discussed only for the obliquely incident wave. A geophysically interesting situation has been chosen for studying, quantitatively, the effects of the anisotropy factor on the reflection of SH waves.

Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

2021 ◽  
pp. 1-24
Author(s):  
Liguo Jin ◽  
Liting Du ◽  
Haiyan Wang
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Half Space ◽  
Strong Interaction ◽  
Rigid Foundation ◽  
Structural Stiffness ◽  
Sh Waves ◽  
Closed Form Analytical Solution ◽  
Flexible Foundation ◽  
Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1774-1779 ◽  
Author(s):  
Joe Dellinger ◽  
Lev Vernik
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Elastic Constants ◽  
Near Field ◽  
Frequency Dispersion ◽  
Transversely Isotropic ◽  
Sh Waves ◽  
Phase Velocities ◽  
Pulse Transmission ◽  
Transmission Technique

The elastic properties of layered rocks are often measured using the pulse through‐transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first‐break traveltimes of P, SV, and SH‐waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near‐field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

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