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 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.

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.

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.

Propagation of Cylindrical Rayleigh Waves in a Transversly Isotropic Thermoelastic Diffusive Solid Half-Space

2013 ◽  
Vol 43 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Boundary Conditions ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Attenuation Coefficients ◽  
Special Cases ◽  
Phase Velocity And Attenuation

Abstract The propagation of cylindrical Rayleigh waves in a trans- versely isotropic thermoelastic diffusive solid half-space subjected to stress free, isothermal/insulated and impermeable or isoconcentrated boundary conditions is investigated in the framework of different theories of ther- moelastic diffusion. The dispersion equation of cylindrical Rayleigh waves has been derived. The phase velocity and attenuation coefficients have been computed from the dispersion equation by using Muller’s method. Some special cases of dispersion equation are also deduced

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.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Latha Madhuri Poonem ◽  
Rajitha Gurijala ◽  
Sindhuja Ala ◽  
Malla Reddy Perati
Keyword(s):  
Phase Velocity ◽  
Initial Stress ◽  
Half Space ◽  
Frequency Equation ◽  
Poroelastic Medium ◽  
Content Type ◽  
Torsional Waves ◽  
Reinforcement Parameter ◽  
Dry Sand ◽  
Phase Velocity And Attenuation

PurposeThe purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.Design/methodology/approachTorsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.FindingsPhase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.Originality/valueInitial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

scholarly journals Wave Propagation in a Micropolar Transversely Isotropic Generalized Thermoelastic Half-Space

2014 ◽  
Vol 19 (2) ◽  
pp. 247-257
Author(s):  
R.R. Gupta
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Rayleigh Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Thermoelastic Properties ◽  
Special Cases ◽  
Generalized Thermoelastic ◽  
Phase Velocity And Attenuation

Abstract Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

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.

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