Scattering Of SH Waves Research Articles

Scattering of SH waves by an arc-shaped interface crack between a cylindrical magneto-electro-elastic inclusion and matrix with the symmetry of 6 mm

Investigated are the scattered field properties of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material in this paper. The debonding region is modeled as an arc-shaped interface crack with magneto-electrically permeable surfaces. By expressing the scattered fields as the wave function expansions with unknown coefficients, the mixed boundary value problem is first reduced to a set of dual series equations. Then the dislocation density function is introduced as an unknown to transform the dual series equations to a Cauchy singular integral equation of the first type, which can be solved numerically. Finally, the scattered field intensity factor, the scattered far field pattern and scattered cross section are obtained. The effects of incident direction, crack opening angle and material combination on the properties of both near fields and far fields are respectively examined graphically. The solution of this problem is relevant to ultrasonic nondestructive detection of the debonding between two dissimilar magneto-electro-elastic materials and is expected to have applications to the question of how dynamic loading can lead to growth of debonds.

Dynamic anti-plane characteristic on an infinite piezoelectric medium with a movable rigid cylindrical inclusion

Scattering and dynamic stress concentrations of time harmonic SH-wave in an infinite elastic piezoelectric medium with a movable rigid cylindrical inclusion are studied in this paper with the help of complex variable and wave function expansion method. The relations that a movable rigid cylindrical inclusion depends on intensity of incident wave and electric field are revealed. The expressions of dynamic stress at the edge of the inclusion are obtained. Numerical calculations are made with different wave numbers and different piezoelectric characteristic parameters. The calculating results show that dynamic stress concentrations at the edge of the inclusion have linear dependence on the incident electric field. And dynamic analyses are very important for an infinite piezoelectric medium with a movable rigid cylindrical inclusion at larger piezoelectric characteristic parameters.

Scattering of SH-wave by cracks originating at an elliptic hole and dynamic stress intensity factor

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

Scattering of plane SH waves by a circulararc hill with a circular tunnel

An analytical solution for scattering of incident SH waves by a circular-arc hill with a concentric circular tunnel was derived by Fourier-Bessel series expansion and auxiliary functions technique. The solution is reduced to solving a set of infinite linear algebraic equations finally. The accuracies of the numerical results are checked by the residual errors of boundary conditions with the truncation order increasing. The numerical results show that the existence and dimension of the tunnel have great effect on motion of the ground surface nearby and dynamic stress concentration of the tunnel.

Scattering of SH waves by an elastic thin-walled rigidly supported inclusion

Explicit forms of the first-order approximate boundary conditions are derived for a 2D problem of SH waves scattering by a thin, curvilinear, elastic, rigidly supported inclusion in a uniform background. The effects of varying elastic modulus and geometrical forms of the inclusion on the stress and strain states of the body near and far from the ends of the inhomogeneity are examined. The method of investigation is based on the matching of asymptotic expansions with the thickness-to-length ratio as the perturbation parameter.

Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface

An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Green's function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Green's function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Green's function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different medial upon DSIF and DSCF.

Scattering of SH-waves by an interface cavity

The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.

Scattering of SH wave by a crack terminating at the interface of a bimaterial

A general method for solving the scattering of plane SH wave by a crack terminating at the interface of a bimaterial is presented. The crack can terminate at the interface in an arbitrary angle. In order to solve the proposed problem, the Green’s function for a point harmonic force applied at an arbitrary point of the bimaterial is established by the Fourier transformation method. Using the obtained Green’s function and the Betti-Rayleigh reciprocal theorem, the total scattered field of the crack is constructed. The total scattered field of the crack is divided into a regular part and a singular part. The hypersingular integral equation of the crack is obtained in terms of the regular and singular scattered field as well as the free wave field. The stress singularity order and singular stress at the terminating point are analyzed by the hypersingular integral equation and the singular scattered field of the crack. The dynamic stress intensity factor (DSIF) at the terminating point is defined in terms of the singular stresses at the terminating point. Numerical solution of the hypersingular integral equation gives the DSIFs at the crack tips. Comparison of our results with known results confirms the proposed method. Some numerical results and corresponding analysis are given in the paper.

Scattering of SH Waves by an Arc-Shaped Crack between a Cylindrical Piezoelectric Inclusion and the Matrix: Near Fields

The scattered far field pattern(SFFP) and scattered cross section(SCS) are obtained based on the work of part I. Different from the near field case, the numerical results indicate that the resonance occurs at relatively high frequency, and on the whole keeps in a wake of decreasing resonance peaks.

Scattering of SH-wave by multiple circular cavities in half space

In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circular cavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave function and method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for case with two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

Scattering of plane SH-wave by a cylindrical hill of arbitrary shape

Scattering of plane SH-wave by a cylindrical hill of arbitrary shape

Scattering of SH Waves by Fixed-Rigid Nearly Circular Cylinder

A solution for the two-dimensional scattering and diffraction of plane SH waves by fixed-rigid cylinder of arbitrary shape in an elastic infinite medium is presented. The wave field for arbitary geometry in this paper is computed numericaly by the method weighted residues (moment method). Dynamic stress concentration factors around the arbitrary obstacles are obtained with respect to various dimensionless wave numbers. When the cavity is circular, results obtained from the analytical solutions are the same.

Scattering of SH waves from a partially debonded rigid elliptic cylinder

Scattering of SH waves by an embedded rigid elliptic cylinder of finite length, which is partially debonded from elastic soil is studied. The debonding regions are modeled as multiple elliptic arc-shaped interface cracks with non-contacting faces. The scattered wave field is expressed as a Mathieu function expansion with unknown coefficients. The mixed boundary conditions of the problem lead to a set of singular integral equations of the first type in terms of the dislocation density functions of the cracks. A quadrature method is used to solve these integral equations numerically. The results for dynamic stress intensity factors, far-field pattern of the displacement and scattering cross sections are presented. We particularly discuss the effects of the ratio of the short radius to long radius of the cylinder.

Scattering of SH Waves by an Arc-Shaped Crack between a Cylindrical Piezoelectric Inclusion and Matrix-II: Far Fields

The scattered far field pattern(SFFP) and scattered cross section(SCS) are obtained based on the work of part I. Different from the near field case, the numerical results indicate that the resonance occurs at relatively high frequency, and on the whole keeps in a wake of decreasing resonance peaks.

Scattering of plane SH-waves on semi-canyon topography of arbitrary shape with linging in anisotropic media

The purpose of this paper is to use the conforma mapping method[1] to analyze and evaluate the ground displacement and scattering of incident SH-waves, on the surface of semi-canyon topography of arbitrary shape with lining in anisotropic media. The problem to be solved can be reduced to the solution of an infinite algebraic equation set by using the method of full-space expansion of Fourier progression. Using the mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitrary shape into a cylindrical canyon in full-space. Moreover, it is far practical in engineering practice. From the computational examples, it is obvious that the variation of displacement amplitudes on the surface near the lining and the canyon topography is rather sharp, especially when the freqencies of incident SH-waves increase.

Scattering of SH waves by cracks and delaminations in a cladded plate : Bratton, R.L.; Datta, S.K.; Shah, A.H. Proceedings of the 15th Annual Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (USA), 31 Jul – 5 Aug. 1988. Vol. 8B, pp. 1329–1335. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1989). ISBN 0-306-43209-9

Scattering of SH waves by cracks and delaminations in a cladded plate : Bratton, R.L.; Datta, S.K.; Shah, A.H. Proceedings of the 15th Annual Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (USA), 31 Jul – 5 Aug. 1988. Vol. 8B, pp. 1329–1335. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1989). ISBN 0-306-43209-9

Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section: Xiaoming Yuan & Zheng-Peng Liao, Earthquake Engineering & Structural Dynamics, 24(10), 1995, pp 1303–1313

Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section: Xiaoming Yuan & Zheng-Peng Liao, Earthquake Engineering & Structural Dynamics, 24(10), 1995, pp 1303–1313

Scattering of SH waves by flaws in sandwich plates and its use in flaw detection

The strip element method (SEM) is used to investigate SH wave scattering by rectangular flaws in sandwich plates. The plates containing flaws are divided by junctions into domains in which the SEM is applied. For each domain, SEM equations for anti-plane motion are derived. These equations give a relationship between the traction and displacement vector on the vertical boundaries. A set of equations which give a relationship between the traction and displacement vector on the junctions is then obtained by assembling the SEM equations for all the domains. This set of equations is solved by using the conditions on the junctions. Scattered SH wave fields in the frequency domain for sandwich plates with rectangular flaws are computed and discussed in comparison with results for corresponding plates without flaws. A technique for determining the length and the damage factor of a rectangular flaw in a sandwich plate is also presented.

Scattering of plane SH waves by a cylindrical alluvial valley of circular‐arc cross‐section

AbstractA closed‐form solution of two‐dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular‐arc cross‐section in a half‐space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth‐to‐width ratio of the alluvial valley on surface ground motion are finally illustrated.

Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases.