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.

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: IX. Love waves in a porous internal stratum

1965 ◽  
Vol 55 (5) ◽  
pp. 919-923
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Porous Layer ◽  
Shear Waves ◽  
Love Waves ◽  
Porous Solid ◽  
Transverse Waves ◽  
Phase Velocities ◽  
Impermeable Layer

abstract The dispersion equation in the second approximation for small porosity is deduced for the problem of transverse waves in a porous layer separating two impermeable elastic half-spaces, and the expression for the dissipation per cycle displayed. It is shown that Love waves can be propagated in a porous layer only with phase velocities smaller than that of body shear waves in either of the half-spaces, whereas in an impermeable layer Love waves may exist having phase velocity equal to that of body shear waves in one of the half-spaces.

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.

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.

Love Wave Propagation in a Layered Piezoelectric Structure Immersed in a Viscous Fluid

2006 ◽  
Vol 306-308 ◽  
pp. 1211-1216 ◽  
Author(s):  
Fei Peng ◽  
Hua Rui Liu ◽  
S.Y. Hu
Keyword(s):  
Wave Propagation ◽  
Viscous Fluid ◽  
Love Wave ◽  
Mass Density ◽  
Transversely Isotropic ◽  
Love Waves ◽  
Perturbation Approach ◽  
Isotropic Layer ◽  
Piezoelectric Structure ◽  
Wave Sensors

This paper is addressed to the Love wave propagation in a layered piezoelectric structure immersed in a viscous fluid. The layered piezoelectric structure consists of an isotropic layer and a relatively thicker transversely isotropic piezoelectric substrate. The velocity of the Love waves changes due to the presence of the viscous fluid. The exact theory is accurate but not convenient to apply because it is generally difficult to get an explicit relation between the quantities we interest. In this paper, the perturbation approach is applied to obtain the explicit relations for the phase velocity and attenuation of Love waves. The result is useful for the measurement of the viscosity and mass density in Love wave sensors.

A new method for the analysis of multi-mode surface-wave dispersion: Application to Love-wave propagation in the east Pacific

1975 ◽  
Vol 65 (2) ◽  
pp. 323-342 ◽  
Author(s):  
Donald W. Forsyth
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Phase Velocity ◽  
Love Wave ◽  
Wave Dispersion ◽  
Oceanic Lithosphere ◽  
Surface Wave Dispersion ◽  
Earthquake Sources ◽  
East Pacific ◽  
The Difference

abstract A new technique is presented for simultaneously measuring the average, regional phase velocity of two or more surface-wave modes, even if they travel with the same group velocity. Many observations are required over paths of varying length with earthquake sources of known focal mechanism. The phase of the signal observed at each station can be predicted if the initial phase of the source and the phase velocity and relative amplitude of each mode is known. The square of the difference between the observed phase and the predicted phase is summed over all paths for a set of trial phase velocities. The trial velocities which give the minimum sum correspond to the average phase velocity of each mode. By applying this technique to Love-wave data from the east Pacific, the dispersion of the first higher Love mode was measured for the first time in an oceanic area. The phase velocity of the fundamental mode was found to increase with increasing age of the sea floor, probably as a result of the cooling of the oceanic lithosphere. The region was found to be anisotropic for Love-wave propagation, with the fastest velocities roughly perpendicular to the ridge. The degree of anisotropy appears to increase with increasing period.

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 Propagation in Prestressed Piezoelectric Layered Structure

2016 ◽  
Vol 08 (04) ◽  
pp. 1650045 ◽  
Author(s):  
Shishir Gupta ◽  
Abhijit Pramanik ◽  
Mostaid Ahmed ◽  
Arun Kumar Verma
Keyword(s):  
Wave Propagation ◽  
Initial Stress ◽  
Layered Structure ◽  
Love Wave ◽  
Love Waves ◽  
Piezoelectric Film ◽  
Elastic Substrate ◽  
Open Case ◽  
Piezoelectric Layered Structure ◽  
General Dispersion

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.

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.

scholarly journals Field investigation of Love waves in near-surface seismology

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. G1-G6 ◽  
Author(s):  
Robert Eslick ◽  
Georgios Tsoflias ◽  
Don Steeples
Keyword(s):  
Surface Layer ◽  
Data Acquisition ◽  
Love Wave ◽  
Field Data ◽  
Field Investigation ◽  
Love Waves ◽  
Frequency Range ◽  
Minimum Thickness ◽  
Near Surface ◽  
Wave Data

We examine subsurface conditions and survey parameters suitable for successful exploitation of Love waves in near-surface investigations. Love-wave generation requires the existence of a low shear-velocity surface layer. We examined the minimum thickness of the near-surface layer necessary to generate and record usable Love-wave data sets in the frequency range of [Formula: see text]. We acquired field data on a hillside with flat-lying limestone and shale layers that allowed for the direct testing of varying overburden thicknesses as well as varying acquisition geometry. The resulting seismic records and dispersion images were analyzed, and the Love-wave dispersion relation for two layers was examined analytically. We concluded through theoretical and field data analysis that a minimum thickness of [Formula: see text] of low-velocity material is needed to record usable data in the frequency range of interest in near-surface Love-wave surveys. The results of this study indicate that existing guidelines for Rayleigh-wave data acquisition, such as receiver interval and line length, are also applicable to Love-wave data acquisition.

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