Rheological model of Love wave propagation in viscoelastic layered media under gravity

2015 ◽  
Vol 11 (3) ◽  
pp. 424-436
Author(s):  
Rajneesh Kakar
Keyword(s):  
Internal Friction ◽  
Phase Velocity ◽  
Love Wave ◽  
Velocity Ratio ◽  
Love Waves ◽  
Wave Number ◽  
Viscoelastic Layer ◽  
Content Type ◽  
Surface Plot ◽  
Inhomogeneity Factor

Purpose – The purpose of this paper is to deal with the propagation of Love waves in inhomogeneous viscoelastic layer overlying a gravitational half-space. It has been observed velocity of Love waves depends on viscosity, gravity, inhomogeneity and initial stress of the layer. Design/methodology/approach – The dispersion relation for the Love wave in closed form is obtained with Whitaker’s function. Findings – The effect of various non-dimensional inhomogeneity factors, gravity factor and internal friction on the non-dimensional Love wave velocity has been shown graphically. The authors observed that the dispersion curve of Love wave increases as the inhomogeneity factor increases. It is seen that increment in gravity, inhomogeneity and internal friction decreases the damping phase velocity of Love waves but it is more prominent in case of internal friction. Originality/value – Surface plot of Love wave reveals that the velocity ratio increases with the increase of non-dimensional phase velocity and non-dimensional wave number. The above results may attract seismologists and geologists.

Analysis of gravity and non-homogeneity on Rayleigh wave in anisotropic elastic-viscoelastic half space of higher order

2015 ◽  
Vol 11 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Mass Density ◽  
Wave Number ◽  
Inhomogeneous Layer ◽  
Third Order ◽  
Content Type ◽  
Anisotropic Elastic ◽  
Mathematical Techniques

Purpose – The purpose of this paper is to illustrate the propagation of Rayleigh waves in an anisotropic inhomogeneous layer placed over an isotropic gravitational viscoelastic half space of third order. Design/methodology/approach – It is considered that the mass density and the elastic coefficients of the layer are space dependent. Dispersion properties of waves are derived with the simple mathematical techniques. Graphs are plotted between phase velocity ‘k’ and wave number ‘c’ for different values of inhomogeneity parameters for a particular model and the effects of inhomogeneity and gravity are studied. Findings – The wave analysis indicates that the phase velocity of Rayleigh waves is affected quite remarkably by the presence of inhomogeneity, gravity and strain rates of strain parameters in the half space. The effects of inhomogeneity and depth on the phase velocity are also shown in corresponding figures. Originality/value – The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

Study of Love-type wave vibrations in double sandy layers on half-space of viscoelastic

2019 ◽  
Vol 16 (4) ◽  
pp. 731-748
Author(s):  
Raju Kumhar ◽  
Santimoy Kundu ◽  
Manisha Maity ◽  
Shishir Gupta
Keyword(s):  
Love Wave ◽  
Hydrostatic Stress ◽  
Separation Of Variables ◽  
Finite Thickness ◽  
Classical Equation ◽  
Frequency Equation ◽  
Wave Number ◽  
Hyperbolic Function ◽  
Complex Frequency ◽  
Content Type

Purpose The purpose of this paper is to examine the dependency of dispersion and damping behavior of Love-type waves on wave number in a heterogeneous dry sandy double layer of finite thickness superimposed on heterogeneous viscoelastic substrate under the influence of hydrostatic initial stress. Design/methodology/approach The mechanical properties of the material of both the dry sandy layers vary with respect to a certain depth as quadratic and hyperbolic function, while it varies as an exponential function for the viscoelastic semi-infinite medium. The method of the separation of variables is employed to obtain the complex frequency equation. Findings The complex frequency equation is separated into real and imaginary components corresponding to dispersion and damping equation. After that, the obtained result coincides with the pre-established classical equation of Love wave, as shown in Section 5. The response of all mechanical parameters such as heterogeneities, sandiness, hydrostatic stress, thickness ratio, attenuation and viscoelasticity on both the phase and damped velocity against real wave number has been discussed with the help of numerical example and graphical demonstrations. Originality/value In this work, a comparative study clarifies that the Love wave propagates with higher speed in an isotropic elastic structure as compared to the proposed model. This study may find its applications in the investigation of mechanical behavior and deformation of the sedimentary rock.

Love Waves in a Viscoelastic Stratum: Explicit Expression for Complex Velocity as a Function of Frequency

2021 ◽  
Author(s):  
Mohan D. Sharma
Keyword(s):  
Phase Velocity ◽  
Love Wave ◽  
Complex Analysis ◽  
Love Waves ◽  
Complex Velocity ◽  
Complex Phase ◽  
Real Frequency ◽  
Analysis Technique ◽  
Layered Stratum ◽  
Complex Dispersion

ABSTRACT Propagation of Love wave is considered in a two-layered stratum of isotropic viscoelastic solids. The complex dispersion equation for this wave is solved through a complex analysis technique. This gets an analytical expression for complex velocity, as a function of real frequency rather than the complex wavenumber. This complex (phase) velocity is used further to calculate the (complex) group velocity. Numerical example is solved to analyze the dispersion in speed and attenuation of the viscoelastic Love waves.

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.

The effect of boundaries on wave propagation in a liquid-filled porous solid: II. Love waves in a porous layer

1961 ◽  
Vol 51 (1) ◽  
pp. 51-59
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Viscous Liquid ◽  
Porous Layer ◽  
Unit Volume ◽  
Transcendental Equation ◽  
Love Waves ◽  
Wave Number ◽  
Velocity Of Propagation ◽  
Approximate Scheme

Abstract The transcendental equation is derived relating frequency and phase velocity of propagation of Love waves in a porous layer containing a viscous liquid. This equation, being complex, can be satisfied only if the wave number of the motion is complex, indicating that the disturbance is dissipative. The general expression being intractable analytically, an approximate scheme is employed to determine the phase velocity and measure of dissipation valid for porous materials in which the mass (per unit volume of aggregate) of the interstitial liquid is smaller than that of the solid.

Love-Wave Phase-Velocity Estimation from Array-Based Rotational Motion Microtremor

2020 ◽  
Author(s):  
Kunikazu Yoshida ◽  
Hirotoshi Uebayashi
Keyword(s):  
Phase Velocity ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Velocity Estimation ◽  
Love Waves ◽  
Phase Velocities ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Spatial Derivatives ◽  
Rotational Motions

ABSTRACT The most popular array-based microtremor survey methods estimate velocity structures from the phase velocities of Rayleigh waves. Using the phase velocity of Love waves improves the resolution of inverted velocity models. In this study, we present a method to estimate the phase velocity of Love waves using rotational array data derived from the horizontal component of microtremors observed using an ordinal nested triangular array. We obtained discretized spatial derivatives from a first-order Taylor series expansion to calculate rotational motions from observed array seismograms. Rotational motions were obtained from a triangular subarray consisting of three receivers using discretized spatial derivatives. Four rotational-motion time histories were calculated from different triangular subarrays in the nested triangular arrays. Phase velocities were estimated from the array of the four rotational motions. We applied the proposed Love-wave phase-velocity estimation technique to observed array microtremor data obtained using a nested triangular array with radii of 25 and 50 m located at the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The phase velocities of rotational and vertical motions were estimated from the observed data, and results showed that the former were smaller than those of the latter. The observed phase velocities obtained from vertical and rotational components agreed well with the theoretical Rayleigh- and Love-wave phase velocities calculated from the velocity structure model derived from nearby PS logs. To show the ability of the rotation to obtain Love wave, we estimated apparent phase velocities from north–south or east–west components. The apparent velocities resulted in between the theoretical velocities of Rayleigh and Love waves. This result indicates that the calculated rotation effectively derived the Love waves from a combination of Love and Rayleigh waves.

SH-wave velocity in a fiber-reinforced anisotropic layer overlying a gravitational heterogeneous half-space

2015 ◽  
Vol 11 (3) ◽  
pp. 386-400 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Elastic Half Space ◽  
Wave Number ◽  
Fiber Reinforced ◽  
Sh Wave ◽  
Dimensionless Wave Number ◽  
Sh Waves ◽  
Content Type

Purpose – The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. Design/methodology/approach – The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave. Findings – Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures. Originality/value – In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

Influence of rectangular and parabolic irregularities on the propagation behavior of transverse wave in a piezoelectric layer

2017 ◽  
Vol 13 (2) ◽  
pp. 188-216 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Santan Kumar ◽  
Dharmender ◽  
Shruti Mahto
Keyword(s):  
Phase Velocity ◽  
Comparative Study ◽  
Piezoelectric Layer ◽  
Perturbation Technique ◽  
Solution Procedure ◽  
Wave Number ◽  
Content Type ◽  
Type Wave ◽  
Propagation Behavior ◽  
The Comparative Study

Purpose The purpose of this paper is to theoretically analyze the propagation of Love-type wave in an irregular piezoelectric layer superimposed on an isotropic elastic substrate. Design/methodology/approach The perturbation technique and Fourier transform have been applied for the solution procedure of the problem. The closed-form expressions of the dispersion relation have been analytically established considering different type of irregularities, namely, rectangular and parabolic for both the cases of electrically open and short conditions. Findings The study reveals that the phase velocity of Love-type wave is prominently influenced by wave number, size of irregularity, piezoelectric constant and dielectric constant of an irregular piezoelectric layer. Numerical simulation and graphical illustrations have been effectuated to depict the pronounced impact of aforementioned affecting parameters on the phase velocity of Love-type wave. The major highlight of the paper is the comparative study carried out for rectangular irregularity and parabolic irregularity in both electrically open and short conditions. Classical Love wave equation has been recovered for both the electrical conditions as the limiting case when both media are elastic and interface between them is regular. Practical implications The consequences of the study can be utilized in the design of surface acoustic wave devices to enhance their efficiency, as the material properties and the type of irregularities present in the piezoelectric layer enable Love-type wave to propagate along the surface of the layer promoting the confinement of wave for a longer duration. Originality/value Up to now, none of the authors have yet studied the propagation of Love waves in a piezoelectric layer overlying an isotropic substrate involving both parabolic and rectangular irregularities. Further, the comparative study of rectangular irregularity and parabolic irregularity for both the cases of electrically open and short conditions elucidating the latent characteristics is among the major highlights and reflects the novelty of the present study.

scholarly journals The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2270
Author(s):  
Olha Hrytsyna ◽  
Jan Sladek ◽  
Vladimir Sladek
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Love Wave ◽  
Short Circuit ◽  
Open Circuit ◽  
Love Waves ◽  
Inertia Effect ◽  
Wave Phase Velocity ◽  
Piezoelectric Structure ◽  
Piezoelectric Structures

The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

scholarly journals Influence of Poroelasticity of the Surface Layer on the Surface Love Wave Propagation

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Adil El Baroudi
Keyword(s):  
Wave Propagation ◽  
Surface Layer ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Love Wave ◽  
Wave Attenuation ◽  
Love Waves ◽  
Velocity Variation ◽  
Fluid Viscosity ◽  
Benchmark Solutions

This work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure–displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. mathematica software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solutions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theoretical resolution, the results in literature in the case of an homogeneous isotropic surface layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

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