Interaction Of Shear Waves Research Articles

Shear Wave Interaction of Two Collinear Finite Cracks in an Infinite Magnetoelastic Orthotropic Media

Shear Wave Interaction of Two Collinear Finite Cracks in an Infinite Magnetoelastic Orthotropic Media

Interaction of shear waves with semi-infinite moving crack inside of a orthotropic media

The present work investigates the motion of a semi-infinite moving crack inside a semi-infinite half-space of orthotropic medium subjected to anti-plane shear wave. The crack is located at a finite depth from the surface of semi-infinite orthotropic medium. Our aim is to examine how such anisotropy and geometric parameters can be adjusted to reduce the magnitude of stress intensity factor (SIF) to control the crack propagation near the crack tip region. As mathematical tools, Fourier transformation and inverse Fourier transformation techniques are employed to convert the governing mixed boundary value problem to the well-known Weiner-Hopf equation with suitable boundary conditions. Some physical quantities such as SIF at the crack tip and crack opening displacement (COD) around the crack tip have been derived. Graphical exhibition has been carried out to show the impact of relevant parameters such as crack velocity, layer depth from the surface to crack and orthotropic material properties on SIF and COD. The numerical results show that SIF decay with crack depth from the layer. It is also observed that SIF decreases with an increase in crack velocity and finally tends to zero as crack velocity approches near SH-wave velocity. Also, the value of COD decays as we move along the damage near the crack tip along negative x-axis and finally tends to zero at the crack tip. This behavior of COD is consistent with the physical nature of the semi-infinite crack of the problem. The results are validated for isotropic material with some reported work and are well in agreement. The study of these physical quantities (SIF, COD) ensures the arrest of onset of crack expansion by monitoring geometric parameters and wave velocity to avoid fracture.

Numerical and experimental study of the nonlinear interaction between a shear wave and a frictional interface.

The nonlinear interaction of shear waves with a frictional interface are presented and modeled using simple Coulomb friction. Analytical and finite difference implementations are proposed with both in agreement and showing a unique trend in terms of the generated nonlinearity. A dimensionless parameter ξ is proposed to uniquely quantify the nonlinearity produced. The trends produced in the numerical study are then validated with good agreement experimentally. This is carried out loading an interface between two steel blocks and exciting this interface with different amplitude normal incidence shear waves. The experimental results are in good agreement with the numerical results, suggesting the simple friction model does a reasonable job of capturing the fundamental physics. The resulting approach offers a potential way to characterize a contacting interface; however, the difficulty in activating that interface may ultimately limit its applicability.

Tracking shear waves in turbid medium by light: theory, simulation, and experiment

Shear wave propagation provides rich information for material mechanical characterization, including elasticity and viscosity. This Letter reports tracking of shear wave propagation in turbid media by laser-speckle-contrast analysis. The theory is described, and a Monte Carlo simulation of light shear wave interaction was developed. Simulation and experiments on tissue-mimicking phantoms agree well and show tracking of shear wave at the phantom surface and at depth as well as multiple shear waves interacting within the object. The relationship between speckle contrast value and shear wave amplitude is also investigated.

Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb’s law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.

Imaging fractures and sedimentary fabrics using shear wave splitting measurements made on passive seismic data

SUMMARY The ability to detect aligned fractures using seismic anisotropy provides a valuable tool for exploiting hydrocarbon reservoirs better. Perhaps the most direct way of identifying anisotropy is by observing shear wave splitting. However, the interaction of shear waves with subsurface structure is often complicated. Although fractures in hydrocarbon reservoirs are usually subvertical, shear waves recorded on downhole receivers from microseismic events in or near the reservoir are not likely to have travelled vertically. As such, interpreting splitting measurements made on such waves is a non-trivial problem. Here we develop an approach to model the effects of subsurface structure on non-vertically propagating shear waves. Rock physics theory is used to model the effects of sedimentary fabrics as well as fractures, allowing us to use shear wave splitting measurements to invert for aligned fractures. We use synthetic examples to demonstrate how it is possible to assess in advance how well splitting measurements will image structures, and how this is highly dependent on the available range of ray coverage. Finally, we demonstrate the inversion technique on a passive seismic data set collected during hydraulic fracture stimulation. Despite an unfavourable source–receiver geometry, the strike of an aligned fracture set is accurately identified.

Assessment of site effects of a shallow and wide basin using geotechnical information-based spatial characterization

The site effects relating to the amplification of ground motion under earthquake loading are strongly influenced by both the subsurface soil condition and the geologic structure. For site characterization at the Gyeongju area in Korea, in this study, site investigations were carried out, including borehole drilling and in-situ seismic tests. In addition, geologic information of ground surface obtained by site visits and pre-existing site investigation data were combined into a geo-knowledge database. The subsurface of this area, which has a history of abundant historical earthquakes, is composed of an alluvial soil deposited up to 40 m thick, overlying weathered residual soils, which rest on bedrock. A geotechnical information system (GTIS), based on a geographic information system (GIS) framework, was implemented to effectively determine the spatial geologic structure of the study area. The results indicated that the Gyeongju basin has a shallow and wide shape. Based on this GTIS, two-dimensional (2D) finite-element (FE) analyses were performed to evaluate the site effects related mainly to the subsurface geologic structure of two typical basin sections in the study area. The resulting seismic responses show that the earthquake ground motions were amplified during the propagation of shear waves through the soil layer overlying the bedrock, and the duration of shaking near the basin edges was prolonged owing to the surface waves generated by interactions of shear waves with basin geometry. Furthermore, one-dimensional (1D) FE seismic response analyses for representative soil sites in the basin were additionally conducted. The results of the 2D seismic responses at most sites in the basin are similar, except for the sites near the basin edges, because the basin in this study is very shallow and wide.

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.

Analysis of contrast in images generated with transient acoustic radiation force

Several mechanical imaging methods are under investigation that use focused ultrasound (US) as a source of mechanical excitation. Images are then generated of the tissue response to this localized excitation. One such method, acoustic radiation force impulse (ARFI) imaging, utilizes a single US transducer on a commercial US system to transmit brief, high-energy, focused acoustic pulses to generate radiation force in tissue and correlation-based US methods to detect the resulting tissue displacements. Local displacements reflect relative mechanical properties of tissue. The resolution of these images is comparable with that of conventional B-mode imaging. The response of tissue to focused radiation force excitation is complex and depends upon tissue geometry, forcing function geometry ( i.e., region of excitation, or ROE) and tissue mechanical and acoustic properties. Finite element method (FEM) simulations using an experimentally validated model and phantom experiments have been performed using varying systems, system configurations and tissue-mimicking phantoms to determine their impact on image quality. Image quality is assessed by lesion contrast. Due to the dynamic nature of ARFI excitation, lesion contrast is temporally-dependent. Contrast of spherical inclusions is highest immediately after force cessation, decreases with time postforce and then reverses, due to shear wave interaction with internal boundaries, differences in shear modulus between lesions and background and inertial effects. In images generated immediately after force cessation, contrast does not vary with applied force, increases with lesion stiffness and increases as the ROE size decreases relative to the size of the structure being imaged. These studies indicate that improved contrast in radiation force-generated images will be achieved as ROE size decreases; however, frame rate and thermal considerations present trade-offs with small ROE size. (E-mail: kathy.nightingale@duke.edu)

Finite frequency tomography of D″ shear velocity heterogeneity beneath the Caribbean

The shear velocity structure in the lowermost 500 km of the mantle beneath the Caribbean and surrounding areas is determined by seismic tomography applied to a suite of Sd‐SKS, ScS‐S, (Scd + Sbc)‐S, and ScS‐(Scd + Sbc) differential times, where (Scd + Sbc) is a pair of overlapping triplication arrivals produced by shear wave interaction with an abrupt velocity increase at the top of the D″ region. The inclusion of the triplication arrivals in the inversion, a first for a deep mantle tomographic model, is possible because of the widespread presence of a D″ velocity discontinuity in the region. The improved ray path sampling provided by the triplication arrivals yields improved vertical resolution of velocity heterogeneity within and above the D″ region. The reference velocity model, taken from a prior study of waveforms in the region, has a 2.9% shear velocity discontinuity 250 km above the core‐mantle boundary (CMB). Effects of aspherical structure in the mantle at shallower depths than the inversion volume are suppressed by applying corrections for several different long‐wavelength shear velocity tomography models. Born‐Fréchet kernels are used to characterize how the finite frequency data sample the structure for all of the differential arrival time combinations; inversions are performed with and without the kernels. The use of three‐dimensional kernels stabilizes the tomographic inversion relative to a ray theory parameterization, and a final model with 60‐ and 50‐km correlation lengths in the lateral and radial dimensions, respectively, is retrieved. The resolution of the model is higher than that of prior inversions, with 3–4% velocity fluctuations being resolved within what is commonly described as a circum‐Pacific ring of high velocities. A broad zone of relatively high shear velocity material extends throughout the lower mantle volume beneath the Gulf of Mexico, with several percent lower shear velocities being found beneath northern South America. Concentrated low‐velocity regions extend through the D″ layer under the Caribbean, Colombia, and Ecuador, suggestive of small‐scale plumes in the boundary layer and possible lateral variations of the D″ discontinuity. One scenario consistent with the imaged features involves subducted Farallon plate ponding at the base of the mantle and laterally displacing hot boundary layer material that piles up and destabilizes on its margins.

Interaction of shear waves and propagating cracks.

Shear waves generated from an ultrasonic transducer are used to twist dynamically growing crack fronts; the response of crack front to such external perturbations is examined in order to investigate the primary cause of surface roughening in brittle materials. The response of the crack front is found to be linear in amplitude and frequency of the perturbing wave and without persistence. The response to random perturbations, e.g., by localized material inhomogeneities at the free surface, is also discussed.

Interaction of shear wave with fiber orientations in composite laminate: model and experiment

Linearly polarized transverse (shear) waves propagating in the thickness direction of a composite laminate interact strongly with the fiber directions in the discrete plies of the laminate. Shear waves transmitted through or reflected from a laminate therefore contain information about its stacking sequence and layup orientation. In the case of transmission, one can also exploit the analogy with the polarizer-analyzer configuration in optics. It has been shown that the interaction between shear waves and fiber directions can lead to high sensitivity for the detection of certain errors in the layup or stacking sequence of a laminate. This paper describes a complete analytical model for the propagation of shear waves in a laminate using local and global transfer matrices. Transmitted and reflected signal amplitude as a function of angle and time (or frequency) can be predicted for a given input. Experimental results are also shown for a transmission setup that uses electromagnetic acoustic transducers (EMATs) for the generation and reception of normal incidence shear waves in cured and uncured composite laminates.

Experimental investigation of acoustic band structures in tetragonal periodic particulate composite structures

Transmission of a longitudinal elastic wave through periodic particulate composites, consisting of heavy spherical inclusions in a tetragonal arrangement in an elastic matrix, was measured experimentally. Several band gaps were identified, each having an associated jump in the phase velocity spectrum, near two sets of frequencies: frequencies at which the rigid body (dipole) resonance of particles are enhanced through shear wave interaction within a layer; and frequencies determined by the inter-layer spacing. An approximate theory is developed which shows good correlation with experimental results.

Interaction of a shear wave with a moving domain wall in an iron garnet crystal

The boundary-value problem of the interaction of a plane monochromatic shear wave with a moving Bloch wall in an iron garnet crystal is solved in the framework of the nonexchange magnetostatic approximation on the basis of the method of phase invariants for wave problems with moving boundaries. For a shear wave incident on the domain wall, the possibility of the reflectionless birefringence is demonstrated. Numerical results illustrating the resonance properties of the magnetic subsystem are presented. It is established that, at the upper bound of the reflectionless birefringence range, the interaction of the shear wave with the domain wall manifests itself as a degenerate resonance with the solution in the form of two combined antiphase, collinearly propagating shear waves of infinitely large amplitudes, which form a zero resulting field.

The interaction of a magnetoelastic shear wave with longitudinal cavities in a conducting layer

We study the influence of a strong magnetic field on the interaction of a shear wave with longitudinal cylindrical cavities in an elastic ideally conducting layer. The resulting singular integral equation of the boundary-value problem under consideration is implemented numerically for the case of a single cavity. We present the results of computation of the stresses on the edge of a circular cavity and an elliptical cavity.

A note on start-up and large amplitude oscillatory shear flow of multimode viscoelastic fluids

Start up of plane Couette flow and large amplitude oscillatory shear flow of single and multimode Maxwell fluids as well as Oldroyd-B fluids have been analyzed by analytical or semi-analytical procedures. The result of our analysis indicates that if a single or a multimode Maxwell fluid has a relaxation time comparable or smaller than the rate of change of force imparted on the fluid, then the fluid response is not singular as Elasticity Number (E → ∞ ). However, if this is not the case, as E → ∞, perturbations of single and multimode Maxwell fluids give rise to highly oscillatory velocity and stress fields. Hence, their behavior is singular in this limit. Moreover, we have observed that transients in velocity and stresses that are caused by propagation of shear waves in Maxwell fluids are damped much more quickly in the presence of faster and faster relaxing modes. In addition, we have shown that the Oldroyd-B model gives rise to results quantitatively similar to multimode Maxwell fluids at times larger than the fastest relaxation time of the multimode Maxwell fluid. This suggests that the effect of fast relaxing modes is equivalent to viscous effects at times larger than the fastest relaxation time of the fluid. Moreover, the analysis of shear wave propagation in multimode Maxwell fluids clearly show that the dynamics of wave propagation are governed by an effective relaxation and viscosity spectra. Finally, no quasi-periodic or chaotic flows were observed as a result of interaction of shear waves in large amplitude oscillatory shear flows for any combination of frequency and amplitudes.

A HYBRID METHOD FOR SIZING RADIAL CRACKS IN PRESSURE TUBES

Abstract A testing method is described for the depth measurement of defects that can occur in CANDU nuclear reactor pressure tubes. Experiments are reported which use immersion transducers, to study the interaction of shear waves with both artificial and real defects. A hybrid system, based on both time and amplitude measurements, is proposed for the estimation of defect depth.

Effects of the internal shear wave window: Comparison with anisotropy induced splitting

In the absence of anisotropy, the observed polarizations of shear waves should be those radiated from the source, modified only by interaction with internal interfaces and free surface topography. It has been suggested that shear wave polarizations may be systematically distorted by internal interfaces, which could lead to difficulties in interpreting anisotropy‐induced shear wave splitting. Since the literature now reports many investigations of shear wave splitting, possible complications caused by internal interfaces would be important and need to be assessed. In this paper, we investigate the polarization of shear waves in full‐wave synthetic seismograms incident from a point source at an isotropic‐to‐isotropic interface, over a range of angles of incidence. Particle motion due to plane and curved wave fronts has different characteristics. Internal shear wave windows can be defined, analogous to the shear wave window at the free surface. Within the innermost window, the polarizations at subsurface geophones (as in vertical seismic profiles) are recorded with little distortion, but outside this window the waveforms become increasingly distorted for larger angles of incidence. This is similar to the behavior of shear waves with respect to the shear wave window at the free surface, except that the behavior at internal interfaces is more complicated because of additional critical angles, and additional windows. We conclude that the interaction of shear waves with internal interfaces is only a serious difficulty when interpretating wide offset vertical seismic profiles, wide angle reflections, and cross‐hole data.

Interaction of shear waves with a periodic array of rigid strips

The interaction of shear waves with a periodic array of rigid strips is investigated. Using conventional analytical techniques the response of the strips is determined as a function of frequency. High amplifications in the strip response are found to occur at particular frequencies. The effects of spacing-to-width ratios and strip-to-matrix mass ratios on these amplifications are examined.

Interaction of shear waves with two coplanar Griffith cracks situated in an infinitely long elastic strip

In an earlier paper [6] we have studied the case of interaction of shear waves with a crack centrally situated in an infinite elastic strip; we, in this paper, extend the study to the case of two coplanar Griffith cracks. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic — elastic material. This method resolves the problem into an integral equation. It has been observed that shear waves with frequencies less than a parameter depending on the width of the wave guide can only propagate. The integral equation is solved numerically for a range of values of wave frequency, width of strip and the inter-crack distance. These solutions are used to calculate the dynamic stress intensity factor. The results are shown graphically.