Shear Research Articles

Influence of an impulsive source on shear wave propagation in a mounted porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate under initial stress

The present paper articulates a mathematical model for the propagation of horizontally polarised shear (SH) wave in an initially stressed composite layered structure under the influence of an impulsive line source. The initially stressed composite structure is comprised of a transversely isotropic fluid saturated porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate (semi-infinite medium) in which the bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. Green's functions are derived for the composite layered structure by taking a line force/charge density (Dirac delta function) at the lower interface of intermediate stratum into the account. An efficient analytical treatment involving Green's function technique along with Fourier's transform has been employed to establish the closed form of dispersion equation for the propagating wave. As a special case of the problem, the closed form of dispersion equation has been deduced for a structure with a single layer overlying a semi-infinite medium. These deduced results are validated with pre-established results and classical Love wave equation. Numerical computation has been carried out to demonstrate graphically the effect of various affecting parameters, viz. wave number, initial stress, porosity, sandiness parameter, width ratio, imperfect bonding parameters and functional gradient parameters on the phase velocity of shear wave. Some remarkable results regarding the propagation behaviour of shear wave in the considered composite layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering.

Pervasive low-velocity layer atop the 410-km discontinuity beneath the northwest Pacific subduction zone: Implications for rheology and geodynamics

Regional triplication waveforms of five intermediate-depth events are modeled to simultaneously obtain the compressional (P) and shear (SH) wave velocity structure beneath northwestern Pacific subduction zone. Both the P- and SH-wave velocity models for three different sub-regions show a low-velocity layer (LVL) with a thickness of ∼55-80 km lying above the 410-km discontinuity with a ∼900 km lateral extent from the Japan Sea to the northeastern Asian continental margin. With the dihedral angle approaching to zero around 400 km, a minute amount of melt atop the 410-km discontinuity caused by the hydrous slab might completely wet olivine grain boundaries and result in a low seismic velocity layer in this specific subduction zone. This mechanism suggests that the 410-LVL is a low viscosity zone that would partially decouple the upper mantle from the transition zone. We infer that the widespread 410-LVL provides evidence for a water-bearing mantle transition zone beneath the western Pacific subduction zone.

Influence of doubly loaded elastic void pores and distinct inhomogeneity in the sandwiched layered composite structure

This research article deals with the study of shear (SH) wave propagation in two dissimilar layered elastic medium with void pores over an inhomogeneous semi-infinite medium. The casewise study is carried out by assuming two types of inhomogeneity varies exponentially and linearly with depth. Solving the equation of motions and taking account of boundary conditions, two dispersion relations have been identified which indicating the existence of two types of shear waves. One dispersion relation corresponds to the first kind of SH wave associated with a change in void volume fraction. Another relation corresponds to the second kind of SH wave associated with the elastic properties of the matrix part of material medium. We notified the result that the first kind of wavefront is same for both the cases. Moreover, the deduced result obtained is in well-agreement with pre-established and classical results. The influence of concerned parameters on both kinds of wavefront is shown graphically and discussed in the section of numerical simulation of the proposed model. The present problem is meaningful and may find applications in various fields such as geophysics, geology, mechanical engineering, earthquake engineering, and civil engineering.

Transcervical superior wedge resection (osteotomy) and fixation with contoured plate for the non- union of femoral neck fractures.

Study was conducted to determine the healing rate of non-union femoral neck fractures following a new transcervical superior based wedge resection and fixation with contoured plate. This study is based on a concept, that the presence of a residual part of the femoral neck on the trochanteric side of the non-union and removal of a wedge with a superior base not only converts shearing forces into compression forces but also provides fresh bone with an osteogenic potential. This is a descriptive case series 'one group pre-test post-test design', conducted from 2010 to 2016 with a sample size of 18, convenience sampling technique with a minimum follow up of 12 months. Eighteen patients with a mean age of 32.44±8.8 years were operated with transcervical wedge resection and fixation. However, only 14 completed a minimum follow up of twelve months. Thirteen (93%) patients achieved union while, one had stable fibrous union which later on developed avascular necrosis and underwent a total hip replacement. There was a mean shortening of 2.05±0.4 cm. Seven (50%) had post-operative Lurch and 4 (28.6%) required shoe raise while 1 had low grade infection.

Method of Green’s Function for Characterization of SH Waves in Porous-Piezo Composite Structure with a Point Source

An approach of Green’s function is adopted to solve the inhomogeneous linear differential equations representing wave equations in piezo-composite materials. In particular, transference of horizontally polarised shear (SH) waves is considered in bedded structure comprising of porous-piezo electric layer lying over a heterogeneous half-space. Propagation of SH-waves is considered to be influenced by point source, situated in the heterogeneous substrate. A closed form analytical solution is obtained to establish the dispersion relation. Remarkable influence of different parameters (like elastic constant, piezoelectric constant, heterogeneity parameter, initial stress and layers thickness) on the phase and group velocity are shown graphically. Moreover, a special case of present study is shown by replacing the porous piezoelectric material with piezoelectric material. Some numerical examples are illustrated by taking the material constants of Lead Zirconate Titanate (PZT-1, PZT-5H and PZT-7) for the porous piezoelectric layer where the phase velocity of SH waves is high rather than that of piezoelectric layer.

S-band delay lines in suspended lithium niobate

Thin-film lithium niobate is an attractive platform for GHz-frequency applications in low-power RF analog signal processing, optomechanics, and quantum devices due to its high coupling, low loss, excellent optical properties, and compatibility with superconducting quantum circuits. We demonstrate aluminum interdigitated transducers (IDTs) in this platform for horizontal shear (SH) waves between 1.2 and 3.3 GHz and longitudinal waves between 2.1 and 5.4 GHz. For the SH waves, we measure a piezoelectric coupling coefficient of 13% and 6.0 dB/mm propagation losses in delay lines up to 1.2 mm with a 300 ns delay in air at room temperature. In these high keff2 transducers, electrical loading gives rise to large reflections and resonances. Finite element method models and an experimental finger-pair sweep are used to characterize the role of resonance in these transducers, illuminating the physics behind the large motional admittances of these small-footprint IDTs.

Green’s function technique to study the influence of heterogeneity on horizontally polarised shear-wave propagation due to a line source in composite layered structure

The present paper investigates Green’s function technique to study the impact of the non-linear heterogeneity on the propagation of the horizontally polarised shear (SH) wave in a composite layered structure due to the line source. The composite structure is comprised of two distinct isotropic homogeneous elastic layers of finite width lying over an isotropic heterogeneous semi-infinite elastic medium. A general quadratic heterogeneity (including the linear heterogeneity term) in the rigidity of the semi-infinite medium has been taken into account. An efficient analytical treatment involving Green’s function technique along with the application of Fourier transformation has been employed to establish the closed form of the dispersion equation for the propagating wave. As a special case of the problem, the closed form of the dispersion equation has been found in well agreement with the pre-established and classical results. The influence of linear and non-linear heterogeneities on the phase velocity of the horizontally polarised shear-wave has been analysed comparatively for numerous cases associated with the considered model and the corresponding single layer half-space model. It is reported that the phase velocity of the horizontally polarised shear-wave is more pronounced in the case of the corresponding single layer half-space structure as compared to the considered structure. Also, the impact of the general quadratic heterogeneity (supported by the linear heterogeneity) enhances the phase velocity most favourably as compared to the case of the simple quadratic heterogeneity, linear heterogeneity and homogeneity in the semi-infinite medium.

Effect of interfacial imperfection on shear wave propagation in a piezoelectric composite structure: Wentzel–Kramers–Brillouin asymptotic approach

The primary objective of this article is to investigate the behaviour of horizontally polarized shear (SH) wave propagation in piezoelectric composite structure consisting of functionally graded piezoelectric material layer imperfectly bonded to functionally graded porous piezoelectric material half-space. The linear form of functional gradedness varying continuously along with depth is considered in both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. The interface of the composite structure is considered to be damaged mechanically and/or electrically. Wentzel–Kramers–Brillouin asymptotic approach is adopted to solve the coupled electromechanical field differential equations of both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. An analytical treatment has been employed to determine the dispersion relations of propagating SH-wave for both electrically short and electrically open conditions, which further reduced to the pre-established and classical results as special case of the problem. The effect of various affecting parameters, namely, functional gradedness, wave number, mechanical/electrical imperfection parameters in the presence and absence of porosity on the phase velocity of SH-wave, has been reported through numerical computation and graphical demonstration. In addition, the variation of the coupled electromechanical factor with dimensionless wave number and cut-off frequency with different modes of propagation of wave for electrically short and electrically open cases has also been discussed.

Detection of tunnels and boulders using shallow SH-SH reflected seismic waves

We present three case studies on detecting buried glacial boulders, a sewage tunnel, and abandoned coal mine tunnels using shear-wave reflection methods. The seismic signature of such subsurface features is in the form of an isolated diffraction, distinctly recognized on seismic sections obtained from shallow seismic surveys using a transverse horizontal (H2) source and a multichannel landstreamer that consists of H2 geophones. We used H2 impulsive and vibrator sources with varying bandwidth. Based on field experiments with multicomponent recordings, we determined that the H2-H2 source-receiver configuration is the most optimal to generate downgoing horizontally polarized shear (SH) waves and upcoming SH reflected and diffracted waves. A shallow SH-SH image using a microvibe high-frequency sweep exhibits a wavelength between 1 and 2 m, which is comparable to that of a ground-penetrating radar image with the additional advantage of deeper penetration.

Method to simulate waveelds from ambient-noise sources

The shear (SH)-wave transfer function and the horizontal-to-vertical (HV) spectral ratio are essential to estimate the S-wave velocity pro- le and thickness of surface layers overlying a bedrock on the basis of resonance frequencies. In practice, it is the second method the most used. In this work, we propose a full-wave numerical method, based on a pseudospectral spatial differentiation, to simulate SH and P-S waves generated by random sources distributed spatially and temporally (ambient noise). The modeling allows us to implement seis- mic attenuation, surface waves and causal source radiation patterns, based on random values of the angles of the moment tensor at each source location. We focus on the location of the resonance peaks, since this property is strictly related to the thickness of the layers. First, we analyze Lamb’s problem for which an analytical P-S solution exists. The modeling algorithm is veri ed for a Ricker time history, but the analy- sis can be performed by using spikes as sources. The experiments based on ambient noise are compared to those of a coherent line source as a reference spectrum (e.g., an earthquake event far away from the receivers). SH-wave resonance frequencies can be identi ed in the spectra only when the random sources are located below the bedrock. In the case of P-S waves, the SH-wave transfer function is a good approximation to the HV spectrum, mainly when the noise is generated in the bedrock. Finally, we have assumed a square basin and found that coherent (e.g., earthquake-type) sources may yield identi able peaks but ambient noise gives unreliable results.

Conformational Changes of Soy Proteins under High-Intensity Ultrasound and High-Speed Shearing Treatments

Inspired by denatured globular protein conformational structures, soy protein isolate (SPI) aqueous solutions under neutral pH without the addition of any chemicals were studied under different mechanical treatments. Compared with the traditional magnetic stirring treatment (MS), high-intensity ultrasonication (US), high-speed mechanical shearing (SH), and their combined treatments (USSH, SHUS) were able to better dissolve SPI and further swell and deform the globular conformation. Higher solubility, lower turbidity, enlarged particle size, much uniform particle size distribution, higher free sulfhydryl groups content, increased fluorescence intensity, higher surface hydrophobicity, and higher viscosity SPI solution properties were detected from all these US and SH treated protein samples. Among them, the USSH treated SPI solution was characterized to have the proteins in the best modified conformational structure. The polymer chain relaxation and degradation were also observed from the denatured protein ...

Characterizing horizontally-polarized shear and infragravity vibrational modes in the Arctic sea ice cover using correlation methods.

The deployment of three drifting seismic stations on the Arctic sea ice during the winter of 2014-2015 with station inter-spacing between 30 and 80 km enables the characterization of the coherent seismic wavefield at these scales through the use of array methods. Two distinct vibrational modes are observed, corresponding to the fast and non-dispersive horizontally-polarized shear (SH) mode and the slow and dispersive flexural, infragravity mode (ice swell). The excitation of these two modes is not synchronous. The activation of the infragravity mode is linked to the arrival of energetic, dispersive wavetrains that can be readily seen on individual spectrograms, and that, as previous studies have shown, are likely to have their origins in distant storms. In contrast, the SH mode is excited at other time intervals and cannot be isolated on the recording of single stations due to the broadband and emergent nature of these wavetrains; given the horizontal polarization of these waves, the authors hypothesize that SH waves are caused by episodes of rapid SH deformation along major leads located outside the station network. The existence of horizontally-polarized waves propagating over long distances opens the possibility of monitoring ice deformation at the scale of the Arctic basin with unprecedented time resolution.

Analysis on propagation characteristics of the shear wave in a triple layered concentric infinite long cylindrical structure: An analytical approach

The present work delves into the propagation of a horizontally polarised shear (SH) wave in an infinitely long cylindrical structure comprised of three concentric isotropic layered media. The model has been formulated in cylindrical co-ordinates and an analytical approach is employed to achieve the closed form of the dispersion relation. The application of the Debye Asymptotic Analysis to tackle the complexity arisen due to the involvement of Hankel’s function in the solution treatment is one of the key features of the present article. With the aid of the Debye Asymptotic Analysis, the dispersion equation is shown to be in well agreement with the classical Love wave equation in the absence of the outermost layer medium. The present analysis highlights the influence of the wave number and various radii ratios of the concentric cylindrical layered elastic medium on the phase velocity of the shear wave propagating in the embraced structure. Numerical computations have been carried out to accomplish the graphical demonstration unravelling some important peculiarities associated with the propagation characteristics of the shear wave in the considered cylindrical structure.

Microstructural considerations on SH-wave propagation in a piezoelectric layered structure

Shear wave based acoustic devices are being used in gaseous and liquid environments because of their high-sensitivity. The theoretical study of horizontally polarized shear (SH) waves in a layered structure consisting of a piezoelectric ceramic of PZT − 5H or BaT iO3 material overlying a couple stress substrate is presented in this paper. The considered substrate is supposed to be exhibiting microstructural properties. The closed form expression of dispersion relations are derived analytically for electrically open and short conditions. The effects of internal microstructures of the couple stress substrate, thickness of PZT − 5H or BaT iO3 ceramic, piezoelectric and dielectric constants are illustrated graphically on the phase velocity of the piezoelectric layer under electrically open and short conditions.

Horizontally polarized shear waves in stratified anisotropic (monoclinic) media

The dispersion relations are derived for the horizontally polarized shear (SH) waves in stratified anisotropic plates with arbitrary elastic anisotropy. Analytical expressions for the vectorial group and ray velocities of SH waves propagating in anisotropic layers with monoclinic symmetry are obtained. Closed form relations between velocities and specific kinetic and strain energy for SH waves are derived and analyzed.

Optimization of a Focusable and Rotatable Shear-Wave Periodic Permanent Magnet Electromagnetic Acoustic Transducers for Plates Inspection.

Due to the symmetry of conventional periodic-permanent-magnet electromagnetic acoustic transducers (PPM EMATs), two shear (SH) waves can be generated and propagated simultaneously in opposite directions, which makes the signal recognition and interpretation complicatedly. Thus, this work presents a new SH wave PPM EMAT design, rotating the parallel line sources to realize the wave beam focusing in a single-direction. The theoretical model of distributed line sources was deduced firstly, and the effects of some parameters, such as the inner coil width, adjacent line sources spacing and the angle between parallel line sources, on SH wave focusing and directivity were studied mainly with the help of 3D FEM. Employing the proposed PPM EMATs, some experiments are carried out to verify the reliability of FEM simulation. The results indicate that rotating the parallel line sources can strength the wave on the closing side of line sources, decreasing the inner coil width and the adjacent line sources spacing can improve the amplitude and directivity of signals excited by transducers. Compared with traditional PPM EMATs, both the capacity of unidirectional excitation and directivity of the proposed PPM EMATs are improved significantly.

Analysis of axis symmetric circular crested elastic wave generated during crack propagation in a plate: A Helmholtz potential technique

This paper presents cylindrical coordinate solutions of axis symmetric circular crested elastic waves that appear due to sudden energy release during incremental crack propagation in a plate. Axis symmetric assumption decouples the elastic wave problem to Lamb (P+SV) and shear (SH) horizontal waves. Helmholtz decomposition principle was used to decompose displacement field in to unknown scalar and vector potentials; and body force vectors to known excitation scalar and vector potentials respectively. Therefore, Navier–Lame equations yield a set of four inhomogeneous wave equations of unknown potentials Φ, Hr, Hθ, Hz and known excitation potentials A*,Br*,Bθ*,Bz*. There are two types of potentials exist in a plate for axis symmetric circular crested Lamb wave: pressure potentials Φ, A* and shear potentials Hθ, Bθ*. Inhomogeneous wave equations for Φ and Hθ were solved due to generalized excitation potentials A* and Bθ* in a form, suitable for numerical calculation. The theoretical formulation shows that elastic waves generated in a plate using excitation potentials follow the Rayleigh-Lamb equations. The resulting solution is a series expansion containing the superposition of all the Lamb wave modes existing for the particular frequency-thickness combination under consideration. In addition, bulk wave solution is also recovered due to the effect of the excitation potentials. The numerical studies modeled the two-dimensional (2D) (circular crested) AE elastic wave propagation in order to simulate the out-of-plane displacement that would be recorded by an AE sensor placed on the plate surface at some distance away from the source. Parameter studies were performed to evaluate: (a) the effect of the pressure and shear potentials; (b) the effect of the thickness-wise location of the excitation potential sources varying from mid-plane to the top surface (source depth effect); (c) the effect of peak time (d) the effect of propagating distance away from the source. A Gaussian pulse is used to model the growth of the excitation potentials during the AE event; as a result, the actual excitation potential follows the error function variation in the time domain. The numerical studies show that the peak amplitude of A0 signal is higher than the peak amplitude of S0 signal and the peak amplitude of bulk wave is not significant compared to S0, A0 peak signals.

Scattering of shear waves by a two-phase multiferroic sensor embedded in a piezoelectric/piezomagnetic medium

In this paper, a robust methodology with several desirable features is developed for the determination of the magneto-electro-elastic fields of a shear (SH) wave scattered by a two-phase multiferroic fiber embedded in an infinite transversely isotropic piezoelectric or piezomagnetic medium. While the traditional wave-function expansion approach commonly used in the literature ceases to hold when the geometry of the obstacle is not symmetric, the present theory is capable of treating eccentric coating-fiber ensemble. To put its wide range of applicability in perspective, my analytical methodology is applied to several descriptive examples with various degrees of complexity. The calculated results reveals the profound influence of material properties of constituent phases, the thickness and eccentricity of coating layer, as well as the frequency of propagating SH-wave on the pertinent scattered fields induced by the multiferroic fiber. It is expected that the formulation and numerical results of this paper serve as a useful reference for the design and manufacture of multiferroic materials with a durable and yet reliable performance under dynamics loadings.

Unified homogenization of photonic/phononic crystals with first-band negative refraction

It is shown, for the first time, that negative refraction with positive phase velocity refraction can be realized (and controlled) on a wide frequency-range of the first (lowest) pass band of simple photonic and phononic crystals.First a unified approach is presented to accurately, efficiently, and uniquely produce the homogenized effective material properties of doubly periodic phononic crystals for anti-plane shear (SH) and photonic crystals for transverse electric (TE) and transverse magnetic (TM) electromagnetic Bloch-form waves in such a manner that they exactly reproduce the band structure of the composite over any desired frequency band. Then the correspondence between phononic and photonic field equations is established and their effective homogenized material parameters are calculated. Finally the actual calculation procedure is detailed and illustrative examples are worked out for each case, revealing a rich body of refractive characteristics of these crystals, and showing by means of illustrative examples that the homogenized effective parameters do in fact yield the exact results. Thus the resulting homogenized solid embodies exactly the actual band structure and dispersive properties of the considered phononic/photonic crystal, which clearly distinguishes it from any anisotropic normal material.When in contact with a normal homogeneous half-space, the homogenized medium would display positive, negative, or even no energy refraction depending on the frequency and wave vector of plane waves incident from the normal homogeneous solid to the interface. Remarkably, using the same volume fraction of the same constituents, it is possible to design a (homogenized) material that would display negative energy refraction with positive phase velocity refraction even on the first (acoustic) pass band. The window of the frequency and the range of wave-vector values at which, say, the negative energy refraction would occur can be controlled by judicious selection and design of the unit cell’s constituent geometry and properties.The unit cell of the crystal may consist of anisotropic constituents of any constant or variable properties that may also admit large discontinuities. For elliptical and rectangular inclusion geometries, analytical expressions are given for the calculation of the key quantities.

Edge waves in a 3D plate: Two solutions based on plate mode matching

Edge waves in a three-dimensional plate are considered as the singularity cases of the obliquely incident and reflection fields of Lamb modes and horizontally polarized shear (SH) modes, solved by mode matching based on a real orthogonal relation or the boundary collocation technique. With that, the dispersion curves of the edge waves in a duralumin plate are evaluated. The leaky edge waves are predicted and the one corresponding to quasi-resonance at free-edge in a plane strain plate are verified together with the pure edge waves. The high-frequency features of the dispersion curves are discussed.