A new series solution method for two-dimensional elastic wave scattering along a canyon in half-space. Issue 89 (October 2016)

• Record Type: Journal Article
• Authors: Yao, Yu; Liu, Tianyun; Zhang, Jian-min
• Is Part Of: Soil dynamics and earthquake engineering. Issue 89(2016:Oct.)
• Page Start: 128
• Page End: 135
• Publication Date: 2016-10
• Subjects: Series solutions -- Lamb's solution -- Wave functions -- Elastic waves -- Scattering problem; Soil dynamics -- Periodicals; Earthquake engineering -- Periodicals; Sols -- Dynamique -- Périodiques; Génie parasismique -- Périodiques; 624.176205
• DOI: 10.1016/j.soildyn.2016.07.006
• Languages: English
• ISSNs: 0267-7261

Abstract

Abstract: 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. Highlights: Wave functions combined with the Lamb solutions for zero tractions on the scattering boundary of half-space. A rigorous analysis method for investigating the elastic scattering problems of two-dimensional half space. Constructed scattering fields automatically satisfying the Navier equations as well as all boundary conditions. Solution method is of numerical stability, but less computational effort.