Diffraction Of SH Waves Research Articles

SH-Wave Diffraction from a Thin Interface Defect of Finite Width in the Joint of an Elastic Layer with a Half-Space

SH-Wave Diffraction from a Thin Interface Defect of Finite Width in the Joint of an Elastic Layer with a Half-Space

Diffraction of SH-Waves on the Interface Defect in the Joint of an Elastic Layer and a Half Space

Diffraction of SH-Waves on the Interface Defect in the Joint of an Elastic Layer and a Half Space

Реализация гибридного численно-аналитического подхода для решения задач дифракции SH-волн на препятствиях произвольной формы

Реализация гибридного численно-аналитического подхода для решения задач дифракции SH-волн на препятствиях произвольной формы

SH-waves interaction with crack at orthotropic interface

ABSTRACT The problem of diffraction of SH-waves by two coplanar Griffith cracks situated at the interface of two different orthotropic media has been analyzed. Fourier transform and integral equation method have been used to solve this problem. The expressions for the stress intensity factors (SIFs) around the crack tips are obtained. Numerical values of SIF and the crack opening displacement for several orthotropic materials have been calculated and plotted graphically to show the effect of material orthotropy.

Shallow tunnel detection using SH-wave diffraction imaging

Clandestine tunnels, used for drug or human trafficking and tactical operations, pose a security threat worldwide and remain elusive targets for detection with geophysical methods. P-wave diffraction imaging is an increasingly common technique for detecting subsurface discontinuities that are smaller than the seismic wavelength (such as faults, pinch outs, and small voids) and has been successfully used to detect shallow tunnels. P-wave diffractions from tunnels typically have very low signal-to-noise ratios and are therefore challenging wavefield components for imaging. Mode-specific amplitude characteristics of theoretical diffractions from a shallow tunnel were evaluated using 9C seismic modeling. Results indicate that SH-wave diffraction has the largest amplitude and coherent phase characteristics along the traveltime hyperbola, making it ideal for diffraction imaging. In real data acquired over a 9.2 m deep tunnel, amplitudes of SH-wave diffractions are 20 dB greater than P-wave diffractions. The tunnel signature on the P-wave diffraction section is of low amplitude relative to the background. The SH-wave diffraction section has a high-amplitude signal focused at the horizontal location and a traveltime consistent with the tunnel location, indicating that the SH-wave may be optimal for diffraction imaging to detect shallow tunnels.

SH-Wave Scattering From the Interface Defect

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Diffraction of SH-waves with cracks in composite media

ABSTRACTThis article addresses the problem of interaction of three co-planar finite cracks, symmetrically positioned at the interface of two bonded dissimilar elastic half spaces. The cracks are excited by anti-plane shear wave. The elastrodynamic problem has been converted into a set of four integral equations using the Fourier transform method. These set of equations have then been solved by using the finite Hilbert transform technique and Cooke’s result. The solutions are used for calculating numerical values of quantities of physical interest, such as the dynamic stress intensity factor and the crack opening displacement for low-frequency vibration, which have been presented graphically for different materials.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

The scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space is investigated by using an indirect boundary element method (IBEM). Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green’s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green’s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

Interface Crack at Orthotropic Media

This paper deals with the diffraction of SH-waves by a Griffith crack located at the interface of two bonded dissimilar orthotropic half spaces. The mixed boundary value problem has been reduced to the solution of Fredholm integral equation of second kind by applying Fourier and Abel transforms. Stress intensity factor at the tip of the crack has been calculated by solving integral equation using perturbation method for low frequency and plotted against dimensionless frequency.

A Series Solution for the Diffraction of SH Waves by a Vertical Edge Crack

Herein, a substitute series solution, which is unavailable in literature, pertaining to the antiplane diffraction problem by a vertical edge crack, is derived via the region-matching technique combining with the method of images. The dynamic stress intensity factor can be straightforwardly extracted from the expression of the radial stress field, fulfilling the crack-tip singularity inherently. Computed results of the extremely near-, near-, and far-field solutions agree well with those of exact analytical solution and available data. The proposed approach can be applied to cope with the diffraction problems by multiple cracks or branched cracks under SH-wave incidence.

SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels

Following the success of seismic analysis of a canyon [1], the problem of SH-wave diffraction by a semi-circular hill is revisited using the null-field boundary integral equation method (BIEM). To fully utilize the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-circular hill scattering problem, the problem is decomposed into two regions to produce circular boundaries using the technique of taking free body. One is the half-plane problem containing a semi-circular boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial full circular boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by a circular boundary. The degenerate kernel in the polar coordinates for two subdomains is utilized for the closed-form fundamental solution. The semi-analytical formulation along with matching boundary conditions yields six constraint equations. Instead of finding admissible wave expansion bases, our null-field BIEM approach in conjunction with degenerate kernels have five features over the conventional BIEM/BEM: (1) free from calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All the numerical results are comparing well with the available results in the literature. It is interesting to find that a focusing phenomenon is also observed in this study.

SH wave diffraction and resonances in periodic structures with super-thin inhomogeneities

Propagation of a time-harmonic plane SH wave and its diffraction in periodic layered elastic composites with both a single infinitesimally thin inhomogeneity and an array of inhomogeneities (cracks, rigid inclusions) are analyzed. The mathematical model is based on an integral approach, a system of boundary integral equations, and a T-matrix; the commonly used spring model is also applied for a damaged composite. The resonances and wave localization in the vicinity of obstacles are focused.

SH Waves Diffusion in Fluid-Saturated Medium

Problem statement: Characteristics of the seismic waves have been studied mainly the amplitudes, attenuation, frequency, porosity and the velocity of the waves. In this study, the SH-waves were studied for the diffusion which was related to the diffraction of SH-waves in the saturated medium. Approach: The elastic wave equation was being used to show the SH-waves. A comparison was made of the propagating SH-waves in the fluid-saturated mediums that were categorized into two distinct groups: Insoluble and soluble mediums. Results: The discussions on fluid density in the mediums showed that high density fluid promotes diffusive characteristic while low density fluid endorses non diffusive SH-wave. However, the diffraction had induced significant shock wave in the medium saturated with low density fluid. Conclusion: These results indicated that the linear seismic waves are able to transform into nonlinear waves.

Diffraction of SH-waves by an Interfacial Crack Between a Magnetoelectroelastic Solid and an Elastic Material

Within the framework of the dynamic theory of linear magnetoelectroelasticity, the scattering of anti-plane shear waves by an interfacial crack is investigated. It is assumed that a crack of finite length is located at the interface of a magnetoelectroelastic material and an elastic solid, and SH-waves are directed at an angle relative to the crack face. The Fourier transform is applied to solve the governing differential equations. Singular integral equations with Cauchy kernel of the first kind are reduced for fully electromagnetically permeable and impermeable boundary conditions, respectively. Numerical computations are carried out for several special bi-materials. Obtained results are presented for the dynamic field intensity factors and energy release rates, and the influences of the normalized frequency and incident angle θ are illustrated graphically.

Diffraction of SH-waves on interface cracks under the action of concentrated forces

In the mathematically rigorous statement, we solve the problem of diffraction of elastic SH-waves on a finite (semiinfinite) crack located on the plane boundary of two perfectly joined materials. As a sounding field, we consider the field of a point source. The problem is reduced to the Wiener – Hopf functional equation, which is solved by the method of factorization. An approximate solution of this equation is obtained. We numerically study the distribution of the field in the radiation zone and the distinctive features of its formation depending on the location of the source of radiation.

Interaction of plane SH-waves with the tips of interface cracks

On the basis of the solution of the problem of diffraction of SH-waves on the interface crack obtained earlier, we study the specific features of the far radiated field for very small and critical sounding angles. The effects of multiple diffraction of waves on the crack tips and the formation of the scattered field of displacements are analyzed. It is shown that, in these cases, the dependence of the amplitude of the field on the crack length for very small and critical angles of irradiation is monotonic. This fact can be used for the determination of the crack sizes.

3648 非一様剛性をもつ半無限閉口亀裂による弾性SH波の散乱(S24-3 非定常応答(2),S24 数理・数値解析による先端材料評価)

3648 非一様剛性をもつ半無限閉口亀裂による弾性SH波の散乱(S24-3 非定常応答(2),S24 数理・数値解析による先端材料評価)

SH-wave diffraction by an interfacial flaw in monoclinic bimaterials

A system of incident, reflected and transmitted plane SH-waves is diffracted by an interface flaw in two dissimilar linearly elastic anisotropic half-spaces. The half-space solids have single planes of material symmetry. These coincide, but the two sets of principal material axes in the common plane have arbitrary orientations with respect to each other and to the interface. Exact transient solutions show the effects of material properties and orientation. Increasing the degree of non-orthotropy causes the maximum and minimum shear wave speeds in each solid to deviate more from the isotropic limit. For a non-orthotropic/isotropic bimaterial, this also causes the dynamic stress intensity factor to decrease, and the factor always falls below the factor value arising for a homogeneous solid with properties identical to those of the isotropic constituent.

Scattering and diffraction ofSHwaves by a finite crack: an analytical solution

The diffraction of SH waves by a finite plane crack is studied. The classical Sommerfeld solution for a semi infinite straight reflecting screen is used as a building block to calculate the diffracted field generated by a finite crack. The solution is derived from the analysis of the behaviour of diffracted waves. These waves, which are first generated at the edges of the crack, travel along the surfaces and are diffracted/reflected at the opposite edge. By iteratively taking into account the contribution to the total field of these travelling waves, an infinite series with a known limit is constructed, leading to an approximate analytical solution for the case of a finite plane crack. This solution is virtually exact for large frequencies and it is very good for incoming wavelengths of up to four times the size of the crack. Since the solution is explicit the computational cost is very low. Both frequency and time domain results are included.

Diffraction of SH-waves across a mixed boundary in a plate

The diffraction of SH-waves in an infinite elastic plate is studied under general boundary conditions using the Wiener-Hopf technique. A mixed interface boundary value problem is solved as an illustration.