Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space

Semi-analytical Solution for the Dynamic Response of a Cylindrical Structure Embedded in a Homogeneous Half-Space

“…(56)-(57)), the wave potentials and the expressions for the displacements and stresses can be derived in terms of the complex variables  and  . The expressions are not given in this paper for brevity, they are similar to those presented in the papers on the two-dimensional problems [10,11]. The derivatives of the cylindrical wave potentials with respect to the complex variables are given by Liu et al in [18].…”

“…3 and 4, the results are in good agreement with those presented by Luco and de Barros [3] for the two-dimensional case and by de Barros and Luco [4,5] for the three-dimensional case, which confirms the accuracy of the proposed method. There are some benefits of using different numbers of circumferential modes for the waves directly scattered by the tunnel and for the secondary reflected waves compared with the case of using the same number of modes for both waves as done in [10,11]. The size and condition number of the coefficient matrix in Eq.…”

“…In this paper, a semi-analytical method is proposed to calculate the scattering of elastic waves by an infinitely long cylindrical structure of circular cross-section embedded in an linearly elastic, isotropic and homogeneous half-space. The method can be considered to be a straightforward extension of the method used to solve the two-dimensional scattering problems of P, SV, Rayleigh waves [10] and SH waves [11].…”

Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

“…Wave propagation in bimaterials can be considered as an elementary case in inhomogeneous media. Liu et al [8] considered the scattering problem of a circular cavity in two bonded half-spaces subjected to a SH wave. Because one half of the medium was homogeneous and the other half was exponentially graded, an auxiliary function was applied to normalize the Helmholtz equation.…”

Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM

“…Later, Liang et al [17,18] represented an analytical solution on scattering of in-plane P waves around a cavity and implemented several numerical examples in poroelastic medium. Moreover, Liu et al [19,20] presented an analytical solution for scattering of plane harmonic P, SV, SH and Rayleigh Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/soildyn waves by a shallow lined circular tunnel in an elastic half-space. This solution was developed based on the plane complex variable theory and the image technique.…”