The Scattering of a Vertical Transverse Isotropic Cylindrical Canyon Subjected to Time-Harmonic Elastic Wave
Date Issued
2015
Date
2015
Author(s)
Hung-Liang-Tseng
Abstract
The objective of this research is to study the scattering of a vertically transversely isotropic cylindrical canyon subjected to the incidence of time harmonic plane elastic wave. The total displacement field of either the anti-plane or in-plane scattering problem can be decomposed into two parts, namely, free field as well as scattering filed part. The known free field part can be further separated into incident wave and reflected wave in order to satisfy the ground surface condition. While the unknown scattering field part is expanded into a series of n-th order outgoing singular solutions of Lamb’s problem with unknown amplitude which can be determined by boundary condition of canyon itself. The displacement field and stress field of each n-th order outgoing singular solutions of Lamb’s problem can only be expressed into a form of horizontal wave-number integral which can be evaluated efficiently in complex wave-number domain by using the so called steepest descend-stationary phase method. For in-plane scattering problem, the outgoing scattering field contains two kinds of wave field, namely, P wave and S wave, only two sheets of the four Riemann Surface are sufficient to describe the outgoing scattering field. In order to ensure the single value of a multi-value radical function in each Riemann sheet, the branch points and the associated branch cuts are carefully chosen according to the material considered. Least Square method is employed to solve the unknown coefficients of the expansion series of the scattering field. Once the coefficients are determined, the complete displacement field and stress field can be obtained.
Subjects
transversely isotropic
scattering problem
Lamb problem
steepest descent-stationary phase method.
Type
thesis
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