Papers by Keyword: SH-Wave Scattering

Abstract: In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. Sometimes the surface of the structure is fixed, and it could be seen as a rigid line. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities and the fixed surface, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with fixed surface and multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the displacement boundary condition of the fixed surface, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space with fixed surface can be investigated further.

Abstract: An anti-plane Green function is formulated for steady state solution of a circular lining impacted by a vertical interfacial point source in an elastic quarter space. Series forms of scattering and stationary wave of the circular lining are constructed with Fourier wave function expansion method. Basic solution of the anti-plane point source is employed to represent displacement fields of incident wave. Stress-free conditions on the quarter bounds are satisfied by using image method. Displacement and stress continuity conditions of the lining are expanded as Fourier series to determine definite equations of unknown coefficients of wave function series.

Abstract: The shear wave scattering due to an elliptical cavity in an infinitely long strip of orthotropic graded saturated porous (OGSP) media is studied with the boundary element method (BEM). The shear modulus and the mass density of the OGSP are assumed to have exponential forms. Using Biot's theory, the governing equations are developed for OGSP. The fundamental function is obtained by separating variables in terms of the Dirac delta function. A system of linear equations describing the displacement on the ellipse is obtained by applying the linear BEM. The numerical results for the normalized boundary surface displacements in the scattering field are presented with different OGSP coefficients. The effects of many parameters are evaluated with numerical examples. These results are expected to have great technical interest for determining boundary stability when elastic waves interact with OGSP cavities.

Abstract: Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction. The scattering field produced by multiple circular inclusions determines the dynamic stress concentration factor around the circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated, because there are many factors influenced. Researchers solved these problems by analysis and numerical methods. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions. Based on this solution, the problem of interaction of multiple cylindrical inclusions and a linear crack in semi-space can be investigated further.

Abstract: The scattering of SH-waves by two scalene triangle hills and a semi-cylindrical canyon was surveyed here using the methods of wave function expansion, complex function and multi-polar coordinates. Based on “division”, we divided the analytical model into 3 parts, and constructed displacement solutions of wave fields that meet the boundary conditions in the three regions, respectively. The three domains were then conjoined to satisfy the “conjunction” condition to deduce a series of infinite algebraic equations about the problem combined with the boundary condition of semi-cylindrical canyon. Lastly, numerical examples were presented to investigate the influence of different parameters on the ground motion of the hills and the canyon.

Abstract: In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space can be investigated further.

Abstract: In mechanical engineering, earthquake engineering and modern municipal construction, semi-cylindrical gap and shallow-buried inclusion structure are used widely. In this paper, Green's Function is studied, which is the solution of displacement field for elastic semi-space with semi-cylindrical gap and multiple shallow-buried inclusions while bearing anti-plane harmonic line source force at any point. In the complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field impacted by semi-cylindrical gap and multiple cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition of the cylindrical inclusion in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. Green's function, that is, the total wave displacement field is the superposition of the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of semi-cylindrical gap , the cylindrical inclusions and the location of the line source force. Based on this solution, the problem of interaction of semi-cylindrical gap , multiple cylindrical inclusions and a linear crack in semi-space can be investigated further.

Abstract: The dynamic response problems of out-plane line loads by a shallow-embedded circular lining structure were investigated here by using the method of Green’s Function. Firstly a suitable Green’s function was constructed, which is an essential solution to the displacement field possessing a shallow-embedded circular lining structure while bearing out-plane harmonic line loads at an arbitrary point. Then we obtained a series of algebraic equations to solve this problem after constructing scattering waves that satisfied the zero-stress condition on the ground surface. Lastly, some numerical examples are given to show the effects that different parameters influence dynamic stress concentration factor (DSCF) by out-plane line source loads.

Abstract: In mechanical engineering and modern municipal construction, shallow-buried inclusion structure is used widely. In this paper, Green's Function is studied, which is the solution of displacement field for elastic semi-space with double shallow-buried inclusions while bearing anti-plane harmonic line source force at any point. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field impacted by the circle inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition of the circle inclusions in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. Green's function, that is, the total wave displacement field is the superposition of the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the circle inclusions and the location of the line source force. Based on this solution, the problem of interaction of double circular inclusions and a linear crack in semi-space can be investigated further.

Abstract: Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect composition, location and shape, so the research on the scattering far-field is important to the geological prospects, seismological investigation, non-destruction evaluation and the other fields. In the ocean acoustics, the scattering far-field of the acoustic wave is also used in the under-water survey, object distinguishing and so on. In theory, the scattering solution of elastic waves is one of the basic topics of reverse problems on elastic wave. On the basis of literature, few paper concentrates on the scattering far-field solution of SH-wave by a circular inclusion and a linear crack around the inclusion. In the paper a new model and a new method are presented in order to investigate deeply on this kind problem. The paper uses the Green’s function to study the scattering far-field of an elastic wave by a circular inclusion and a linear crack. The Green’s function should be a fundamental solution of displacement field for an elastic space possessing a circular inclusion while bearing out-of-plane harmonic line source force at any point. In terms of the solution of SH-wave’s scattering by an elastic space with a circular inclusion, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Then, the expressions of the displacement and stresses are given when the circular inclusion and linear crack exist at the same time. When the special Green’s function has been constructed and close field solution has been illustrated, the far field of scattered wave is studied. The displacement mode of scattered wave at far field and scattering cross-section are given. At last, an example is given and its numerical results are discussed.