Shear Wave Phase Velocity Research Articles

Determination of Shear Wave Velocity by Bender Elements using Variable-Path Length Method

For determining shear wave velocity by bender elements, several types of travel time methods have been proposed and are being used commonly. Although the methods have been established over a period of time, there are still many aspects that need to be improved. For example, the ambiguity of arrival time due to near-field effect and the distance measurement for soft sample during testing installation. This study seeks to propose an alternative method which could minimise such ambiguities. In this regard, a method called variable-path length method is proposed, which uses a continuous sinusoidal wave instead of a pulse wave, is applied to a series of tests on reconstituted Kasaoka clay in a modified triaxial apparatus. Based on the results, it is verified that the proposed method can measure shear wave velocity without the ambiguity of arrival time and independent of initial distance between transmitter and receiver. In addition, the proposed method has an advantage to determine phase velocity of shear wave at arbitrary frequency which is useful to study the frequency dependence of geomaterials.

Propagation Velocity and Attenuation of a Shear Wave Pulse Measured by Ultrasound Detection in Agarose and Polyacrylamide Gels

The aim of our research was to measure and analyze phase velocity and pulse attenuation of a shear wave in two media: well-known agarose-gelatin gel and seldom-used polyacrylamide gel. These quantities were determined at three temperatures by the method of transmission sonoelastography described by Catheline et al. (1999). The shear wave was generated with a shaker stimulated by an electric pulse, with a length of one sinusoidal period with a preset frequency. The calculation method is based on a cross-correlation algorithm used for consecutive A-scans of signals of backwards scattered ultrasonic pulses. It allows determination of the local displacement of scattering elements in the medium, caused by a propagating shear wave, and determination of viscoelastic properties of gels. The results of the measurements of shear wave phase velocity and attenuation, obtained for agarose-gelatin and polyacrylamide gels that simulate biological systems depending on frequency and amplitude of vibrations, are presented. The comparison of the measured characteristic properties of gels has revealed that polyacrylamide gel is more useful in viscoelastic investigations of tissue-like phantoms. (E-mail: fiztom@univ.gda.pl)

Rayleigh waves in a double porosity half-space

Based on the governing equations of double-porosity media extended from Biot's theory, the propagation characteristics of Rayleigh waves are discussed in this paper. Characteristic equations of Rayleigh waves in a double porosity half-space with the pervious boundary are derived by assuming that both the coupling mass coefficient ρ 23 and coupling permeability term k (12) are equal to zeros. The dispersion and attenuation properties of Rayleigh waves in a double porosity medium are analyzed numerically. The effects of the porosity and fracture permeability on the behavior of the propagation of Rayleigh waves are investigated. It is found that Rayleigh waves in a double porosity half-space are dispersive and attenuated during propagation. The Rayleigh wave speed is always less than the phase velocity of P1 and shear waves, and always higher than the phase velocity of P3 wave.

The interaction of ultrasound with particulate composites

The longitudinal and shear wave phase velocities and attenuation are measured as function of frequency for random particulate composites, consisting of near mono-disperse spherical glass particles imbedded in a homogeneous epoxy matrix. Experimental results are compared to two theoretical scattering models: the Waterman and Truell method (WT) and the dynamic generalized self-consistent model (DGSCM). It is observed that both models work well in the case of a low inclusion concentration. At higher concentrations both the WT and DGSCM matched the phase velocity, in most cases, within the range of experimental error of about 3%. The WT agrees with the attenuation data only at low concentrations, and the disparity between theory and measured values increase with increasing concentration. The DGSCM agrees well with the attenuation data.

Shear-wave Mach cones in a strongly coupled dusty plasma

Shear-wave Mach cones excited in a strongly coupled dusty plasma in the fluid regime are studied using the generalized hydrodynamic model. The Mach cones are excited by a laser beam that is modeled to sweep the three-dimensional dusty plasma with a velocity that is supersonic with respect to the phase velocity of the transverse shear waves. The formation of single Mach cone structures in vorticity maps reveals that they are formed due to shear motion. It is found that an asymmetry in the wake excitation technique gives rise to certain asymmetries in the Mach cone patterns.

Relating the relaxation spectrum to wave dispersion data

This paper addresses the problem of determining the relaxation spectrum of a viscoelastic fluid from knowledge of the phase velocity of shear waves propagated in the fluid. Theoretical constraints are obtained which guarantee solvability of the problem. Questions of ill-posedness are identified and it is shown how to include additional information into the problem from independent measurements of group velocity. Alternative integro-differential and integro-algebraic systems are derived which are closed with respect to the original and additional data. A simple iterative algorithm which involves updating estimates of a moment ratio is proposed and tested against two model problems. The algorithm determines an n-mode relaxation spectrum and the corresponding storage and loss moduli.

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF m (ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.

Shear waves in a fluid saturated elastic plate

In the present context, we consider the propagation of shear waves in the transverse isotropic fluid saturated porous plate. The frequency spectrum for SH-modes in the plate has been studied. It is observed that the frequency of the propagation is damped due to the two-phase character of the porous medium. The dimensionless phase velocities of the shear waves have also been calculated and presented graphically. It is interesting to note that the frequency and phase velocity of shear waves in porous media differ significantly in comparison to that in isotropic elastic media.

Acoustic anisotropy and birefringence in fibre-reinforced composite materials

All nine elastic moduli of an orthotropic composite material, namely, polypropylene reinforced with glass fiber, are determined from the measured values of the bulk acoustic wave velocities along specific directions in the planes of symmetry of the material. These data are used to calculate the angular dependences of phase velocities, polarization vectors, and directions of ray velocities of bulk waves in the composite. It is demonstrated that the difference in the velocities of shear waves polarized along and across the glass fiber gives rise to an acoustic birefringence and can lead to an elliptical polarization of waves. The measurement of the phase velocities of shear waves as functions of the wave polarization is suggested as a method for the determination of the fiber orientation in a composite material.

Estimation of five elastic stiffness coefficients of unidirectional glass fiber reinforced plastic by laser generated ultrasonic

Five elastic stiffness coefficients of UD-GFRP were estimated by using a laser iso-angular scanning method. Four stiffness coefficients C 33, C 11, C 66 and C 44 (direction 3 being the fiber direction) were first accurately determined by using phase velocities of longitudinal and shear waves in the fiber and fiber-normal directions. The stiffness C 13 was estimated by iteration so that the slowness curve of quasi-shear waves computed to an assumed C 13 best matches the measured one. The estimated stiffness coefficients agreed quite well with those estimated by the through-transmission method in water.

Scattering of Antiplane Shear Waves in a Piezoelectric Fibrous Composite Medium with Slip at Interfaces

This study considers the phase velocity and attenuation of time harmonic axial shear waves in a piezoelectric fibrous composite with slip at interfaces subjected to a steady-state in-plane electrical load. Scattering of plane axial shear waves by a circular piezoelectric fiber with slip is analyzed. We apply the results of the single scattering problem to the propagation of any desired finite frequency waves in a composite containing a dilute concentration of circular piezoelectric fibers. Numerical results for some piezoelectric fibrous composites are obtained and the effects of interfacial slippages and electroelastic interactions on the phase velocity and attenuation of coherent plane waves are discussed in detail.

Shear wave dispersion and mechanical relaxation spectra

It is shown that a mechanical stress relaxation spectrum may be obtained directly from measurements of the dispersion of shear waves in viscoelastic media. The effectiveness of this spectrum, in terms of its sensitivity and accuracy in parametrizing distributions of stress relaxation in the frequency domain, is demonstrated with reference to several published spectra. Of the three different forms of stress relaxation spectrum which may be obtained directly from oscillatory shear measurements, only that based on the group and phase velocities of shear waves is found adequate in terms of sensitivity to the presence of adjacent relaxation mechanisms in the systems considered herein.

Combined compression and shear wave ultrasonic measurements on curing adhesive

This paper describes an ultrasonic technique to study the propagation of wide bandwidth compression and shear wave pulses in a curing adhesive. A temperature controlled water filled test cell with transducers placed at either end is used to couple ultrasound into a thin sample of adhesive. A novel sample holder is employed to contain the uncured liquid adhesive between thin polymer films to stop water ingress and a high-precision goniometer is used to align the sample with respect to the transducers. Consecutive normal and oblique incidence measurements are made at intervals during the adhesive cure. The oblique angle is selected to enable a shear wave to be excited in the adhesive sample by mode conversion. This occurs as soon as the adhesive is able to support shear displacements and hence the detection of the transition from liquid to solid state is possible. The compression and shear wave pulses are analysed in the frequency domain using Fourier analysis and this facilitates calculation of the frequency-dependent compression and shear wave absorption coefficients and phase velocities. From these measurements it is possible to calculate the complex bulk and shear moduli. Results are presented for a number of commercially available adhesives, and it is shown that ultrasound data signatures can be related to aspects of cure such as its rate and `gel point', as well as providing quantitative measurement of the elastic moduli.

Dynamics of viscous amphiphilic films supported by elastic solid substrates

The dynamics of amphiphilic films deposited on a solid surface is analysed for the case in which shear oscillations of the solid surface are excited. The two cases of surface and bulk shear waves are studied with the film exposed to a gas or to a liquid. By solving the corresponding dispersion equation and the wave equation while maintaining the energy balance, we are able to connect the surface density and the shear viscosity of a fluid amphiphilic overlayer with the experimentally accessible damping coefficient, phase velocity, dissipation factor, and resonant frequency shifts of shear waves.

Acoustoelasticity in cracked solids

SUMMARY A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov’s approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated.

Measurement of velocity and attenuation of shear waves in bovine compact bone using ultrasonic spectroscopy

The ultrasonic spectroscopy (broadband pulse) technique was applied to simultaneously measure phase velocity and attenuation coefficient of shear waves in bovine compact bone at frequencies ranging from 4.0–10.0 MHz. It was found that the ratio of attenuation coefficient of shear waves to that of longitudinal waves at a particular frequency for bovine compact bone was smaller than that of other polymer synthesizing materials. The anisotropy of phase velocity and attenuation coefficient of compact bone was also experimentally examined.

Studies of gel viscoelasticity by a wave interference technique

A new technique involving high-frequency shear wave interferometry has been used to investigate the viscoelastic properties of gels formed from aqueous dispersions of a synthetic hectorite-type clay colloid. The technique facilitates studies of stress relaxation phenomena under a range of strains and strain rates, in both linear and nonlinear deformation regimes. Measurements of the group and phase velocities of frequency-multiplexed shear waves, conducted in the presence and absence of steady shear fields, provide visco elastic-solid-like relaxation spectra. Under shear, the relaxation spectra indicate a trend to fluidization of the system as shear rate increases. A viscoelastic solid model is used to interpret the wave dispersion and the results, which constitute the first rheometrical exploitation of the `beat' phenomenon, support conclusions drawn from light scattering and small-angle neutron scattering studies concerning the origin of viscoelasticity in this system.

Determination of velocity and attenuation of shear waves using ultrasonic spectroscopy

The ultrasonic spectroscopy (broadband pulse) technique was applied to simultaneously measure phase velocity and attenuation coefficient of shear waves in a solid at frequencies ranging from 2.2 to 7.6 MHz. This technique is an extension of the ultrasonic spectropy technique currently used in determining dispersion of longitudinal waves.

Determination of velocity and attenuation of shear waves using broadband pulse technique.

The ultrasonic spectroscopy (broadband pulse) technique was applied to simultaneously measure phase velocity and attenuation coefficient of shear waves in a solid in the megahertz frequencies. This technique is an extension of the ultrasonic spectroscopy technique currently used in determining dispersion of longitudinal waves. Sources of error in measurements including diffraction loss and nonlinear distortion will be discussed. [Work supported by Hewlett–Packard Co.]

The influence of wave dispersion characteristics on the determination of mechanical relaxation spectra

A new rheometrical technique has been developed to determine the mechanical relaxation spectra of viscoelastic materials by measurement of shear wave group and phase velocities in a virtual gap rheometer. The technique’s sensitivity and accuracy in providing relaxation spectra directly from measurements arises from exploitation of marked changes in wave dispersion characteristics in the vicinity of stress relaxation mechanisms. The new technique is compared with two conventional, wave‐based rheometrical techniques (based on pulse‐propagation and resonance measurements), which are adversely affected by wave dispersion. The superior accuracy and sensitivity of the new technique over conventional rheometry is demonstrated with reference to the Maxwell model and published relaxation spectra. Experimental results obtained on a concentrated colloidal dispersion serve to demonstrate the measurement principles.