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1.
Weighted residual method for diffraction of plane P-waves in a 2-D elastic half-space III: on an almost circular arbitrary-shaped alluvial valley 
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下载免费PDF全文 Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong motion seismologists for over forty years. The case of out-of-plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV-waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by Lee and Liu. This paper uses their technique of defining these stress-free scattered waves, which Brandow and Lee previously used to solve the problem of the scattering and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape, to the study of the scattering and diffraction of these in-plane waves on an almost circular arbitrary-shaped alluvial valley. 相似文献
2.
Weighted residual method for diffraction of plane P-waves in a 2-D elastic half-space Ⅲ: on an almost circular arbitrary-shaped alluvial valley 下载免费PDF全文
下载免费PDF全文 Scattering and diffraction of elastic in-plane P-and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong motion seismologists for over forty years. The case of out-ofplane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P-and SV-waves on the same circular canyon is a much more complicated problem because the in-plane P-and SV-scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by Lee and Liu. This paper uses their technique of defining these stress-free scattered waves, which Brandow and Lee previously used to solve the problem of the scattering and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape, to the study of the scattering and diffraction of these in-plane waves on an almost circular arbitrary-shaped alluvial valley. 相似文献
3.
A well-defined boundary-valued problem of wave scattering and diffraction in elastic half-space should have closed-form analytic solutions. This two-dimensional (2-D) scattering around a semi-circular canyon in elastic half-space subjected to seismic plane and cylindrical waves has long been a challenging boundary-value problem. In all cases, the diffracted waves will consist of both longitudinal (P-) and shear (S-) rotational waves. Together at the half-space surface, these in-plane longitudinal P- and shear SV-waves are not orthogonal over the infinite half-space flat-plane boundary. Thus, to simultaneously satisfy both the zero normal and shear stresses at the flat-plane boundary, some approximation of the geometry and/or wave functions often has to be made, or in some cases, relaxed (disregarded). This paper re-examines this two-dimensional (2-D) boundary-value problem from an applied mathematics points of view and redefines the proper form of the orthogonal cylindrical-wave functions for both the longitudinal P- and shear SV-waves so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite-canyon surface are then comparatively less complicated to solve. This is now a closed-form analytic solution of the 2-D boundary-valued problem satisfying the half-space zero-stress boundary conditions exactly. 相似文献
4.
The three-dimensional scattering by a hemi-spherical canyon in an elastic half-space subjected to seismic plane and spherical waves has long been a challenging boundary-value problem. It has been studied by earthquake engineers and strong-motion seismologists to understand the amplification effects caused by surface topography. The scattered and diffracted waves will, in all cases, consist of both longitudinal (P-) and shear (S-) shear waves. Together, at the half-space surface, these waves are not orthogonal over the infinite plane boundary of the half-space. Thus, to simultaneously satisfy both zero normal and shear stresses on the plane boundary numerical approximation of the geometry and/or wave functions were required, or in some cases, relaxed (disregarded). This paper re-examines this boundary-value problem from the applied mathematics point of view, and aims to redefine the proper form of the orthogonal spherical-wave functions for both the longitudinal and shear waves, so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite canyon surface will be easy to satisfy. 相似文献
5.
Scattering of elastic waves by three-dimensional canyons embedded within an elastic half-space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non-axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress-free boundary conditions at the half-space surface. The boundary conditions are imposed locally in the least-squares sense at several points on the surface of the canyon and the half-space. Through a comparative study the validity and limitations of two-dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three-dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two-dimensional models. These results emphasize the need for three-dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering. 相似文献
6.
An indirect boundary-method formulation to obtain the three-dimensional response of an infinitely long canyon of uniform but arbitrary cross-section cut in a layered viscoelastic half-space is presented. Seismic excitation in the form of plane elastic waves acting at an arbitrary angle with respect to the axis of the canyon is considered. Numerical results for SH-, SV- and P-wave excitation of a circular canyon and of a canyon with a topography similar to that in the vicinity of Pacoima Dam are discussed in some detail. 相似文献
7.
Diffraction of obliquely incident waves by a cylindrical cavity embedded in a layered viscoelastic half-space 总被引：1，自引：0，他引：1
The three-dimensional harmonic response in the vicinity of an infinitely long, cylindrical cavity of circular cross-section buried in a layered, viscoelastic half-space is obtained when the half-space is subjected to homogeneous plane waves and surface waves impinging at an oblique angle with respect to the axis of the cavity. The solution is obtained by an indirect boundary integral method based on the use of moving Green's functions for the viscoelastic half-space. Numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity are presented for obliquely incident P-, SV-, SH- and Rayleigh waves with different horizontal angles of incidence. 相似文献
8.
Foundation soil interaction is studied using an analytical two-dimensional model, for circular foundations embedded in a homogeneous elastic half-space and for incident plane P- and SV- and for surface Rayleigh waves. The scattered waves are expanded in complete series of cyclindrical wave functions. A detailed analysis is presented of the foundation response to unit amplitude incident waves as a function of the type of incident waves and angle of incidence, the depth of the embedment and the foundation mass per unit length.It is shown that free-field translations and point rotation approximate well the foundation input motion only for very long incident waves. For shorter incident waves, those in general overestimate the foundation input motion. Neglecting the rotation of the foundation input motion (which is usually done in practice) may eliminate a major contribution to the base excitation of buildings and may cause nonconservative estimates of the forces in these buildings. Incident waves appear as ‘longer’ to a shallow foundation than to a deeper foundation. Therefore, deeper foundations are more effective in reflecting and scattering the short incident waves. 相似文献
9.
Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation 下载免费PDF全文
下载免费PDF全文 This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green's functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot's theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method. 相似文献
10.
This paper presents a semi-analytical method for studying the two-dimensional problem of elastic wave scattering by surface irregularities in a half-space. The new method makes use of the member of a c-completeness family of wave functions to construct the scattering fields, and then applies equal but opposite tractions to those of the foregoing constructed scattering fields on the horizontal surface of the half-space to produce additional scattering fields. These additional scattering fields are a series of Lamb's solutions. Thus the whole scattering field constructed in the series automatically satisfies the Navier equations, the condition of zero traction on the half-space surface, and the radiation boundary conditions at infinity. Using the traction-free conditions along the canyon surface, the coefficients of the series solutions are determined via a least-squares method. For incident P, SV, and Rayleigh waves, the numerical results are presented for the scattering displacements in the vicinity of a semi-circular canyon in the half-space. 相似文献