scholarly journals Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Pramod Kumar Vaishnav ◽  
Santimoy Kundu ◽  
Shishir Gupta ◽  
Anup Saha
Keyword(s):  
Porous Medium ◽  
Dispersion Relation ◽  
Initial Stress ◽  
Half Space ◽  
Love Wave ◽  
Separation Of Variables ◽  
Infinite Medium ◽  
Type Wave ◽  
Bounded Below ◽  
Irregular Interface

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

Effect of corrugation on the dispersion of Love-type wave in a layer with monoclinic symmetry, overlying an initially stressed transversely isotropic half-space

2017 ◽  
Vol 13 (2) ◽  
pp. 308-325
Author(s):  
Abhishek Kumar Singh ◽  
Amrita Das ◽  
Kshitish Ch. Mistri ◽  
Shreyas Nimishe ◽  
Siddhartha Koley
Keyword(s):  
Dispersion Relation ◽  
Phase Velocity ◽  
Comparative Study ◽  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Transversely Isotropic ◽  
Wave Number ◽  
Content Type ◽  
Type Wave

Purpose The purpose of this paper is to investigate the effect of corrugation, wave number, initial stress and the heterogeneity of the media on the phase velocity of the Love-type wave. Moreover, the paper aims to have a comparative study of the presence and absence of anisotropy, heterogeneity, corrugation and initial stress in the half-space, which serve as a focal theme of the study. Design/methodology/approach The present paper modelled the propagation of the Love-type wave in a corrugated heterogeneous monoclinic layer lying over an initially stressed heterogeneous transversely isotropic half-space. The method of separation of variables is used to procure the dispersion relation. Findings The closed form of dispersion relation is obtained and found to be in well agreement to the classical Love wave equation. Neglecting the corrugation at either of the boundary surfaces, expressions of the phase velocity of the Love-type wave are deduced in closed form as special cases of the problem. It is established through the numerical computation of the obtained relation that the concerned affecting parameters have significant impact on the phase velocity of the Love-type wave. Also, a comparative study shows that the anisotropic case favours more to the phase velocity as comparison to the isotropic case. Originality/value Although many attempts have been made to study the effect of corrugated boundaries on reflection and refraction of seismic waves, but the effect of corrugated boundaries on the dispersion of surface wave (which are dispersive in nature) propagating through mediums pertaining various incredible features still needs to be investigated.

scholarly journals Effect of Initial Stress on an SH Wave in a Monoclinic Layer over a Heterogeneous Monoclinic Half-Space

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3243
Author(s):  
Ambreen Afsar Khan ◽  
Anum Dilshad ◽  
Mohammad Rahimi-Gorji ◽  
Mohammad Mahtab Alam
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Phase Velocity ◽  
Initial Stress ◽  
Half Space ◽  
Love Wave ◽  
Coupling Parameter ◽  
Sh Wave ◽  
Special Cases ◽  
Parameter Coupling

Considering the propagation of an SH wave at a corrugated interface between a monoclinic layer and heterogeneous half-space in the presence of initial stress. The inhomogeneity in the half-space is the causation of an exponential function of depth. Whittaker’s function is employed to find the half-space solution. The dispersion relation has been established in closed form. The special cases are discussed, and the classical Love wave equation is one of the special cases. The influence of nonhomogeneity parameter, coupling parameter, and depth of irregularity on the phase velocity was studied.

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.

Propagation of Love-Type Wave in a Corrugated Fibre-Reinforced Layer

2016 ◽  
Vol 32 (6) ◽  
pp. 693-708 ◽  
Author(s):  
A. K. Singh ◽  
K. C. Mistri ◽  
A. Das
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Phase Velocity ◽  
Comparative Study ◽  
Love Wave ◽  
Substantial Effect ◽  
Free Layer ◽  
Type Wave ◽  
State Of Stress ◽  
Boundary Surfaces

AbstractThe present paper investigates the propagation of Love-type waves in an initially stressed heterogeneous fibre-reinforced layer with corrugated boundary surfaces, lying over a viscoelastic half-space under hydrostatic state of stress. The dispersion relation is obtained in closed form and found to be in well-agreement with the classical Love wave equation. The substantial effect of reinforcement, position and undulation parameters (i.e. corrugation), heterogeneity, horizontal initial stress and hydrostatic state of stress are discussed briefly. It is established through comparative study that reinforced layer supports more to phase velocity of Love-type wave as compare to reinforced free layer.

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

2014 ◽  
Vol 06 (05) ◽  
pp. 1450050 ◽  
Author(s):  
SANTIMOY KUNDU ◽  
SHISHIR GUPTA ◽  
SANTANU MANNA ◽  
PRALAY DOLAI
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Graphical Representation ◽  
Separation Of Variables ◽  
Classical Equation ◽  
Wave Number ◽  
Fiber Reinforced

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

scholarly journals Torsional Wave Propagation in a Pre-Stressed Structure with Corrugated and Loosely Bonded Surfaces

2017 ◽  
Vol 47 (4) ◽  
pp. 48-74 ◽  
Author(s):  
Manoj K. Singh ◽  
Sanjeev A. Sahu
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Analytical Model ◽  
Wave Number ◽  
Smooth Interface ◽  
Notable Effect ◽  
Heterogeneity Parameter ◽  
Torsional Surface Waves

AbstractAn analytical model is presented to study the behaviour of propagation of torsional surface waves in initially stressed porous layer, sandwiched between an orthotropic half-space with initial stress and pre-stressed inhomogeneous anisotropic half-space. The boundary surfaces of the layer and halfspaces are taken as corrugated, as well as loosely bonded. The heterogeneity of the lower half-space is due to trigonometric variation in elastic parameters of the pre-stressed inhomogeneous anisotropic medium. Expression for dispersion relation has been obtained in closed form for the present analytical model to observe the effect of undulation parameter, flatness parameter and porosity on the propagation of torsional surface waves. The obtained dispersion relation is found to be in well agreement with classical Love wave equation for a particular case. The cases of ideally smooth interface and welded interface have also been analysed. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, wave number, heterogeneity parameter and initial stress on the phase velocity of torsional surface waves.

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.

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