This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.
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ASME 2007 Pressure Vessels and Piping Conference
July 22–26, 2007
San Antonio, Texas, USA
Conference Sponsors:
- Pressure Vessels and Piping Division
ISBN:
0-7918-4286-X
PROCEEDINGS PAPER
The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space
Wen-I Liao,
Wen-I Liao
National University of Kaohsiung, Kaohsiung, Taiwan
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Tsung-Jen Teng,
Tsung-Jen Teng
National Center for Research on Earthquake Engineering, Taipei, Taiwan
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Shiang-Jung Wang
Shiang-Jung Wang
National Center for Research on Earthquake Engineering, Taipei, Taiwan
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Wen-I Liao
National University of Kaohsiung, Kaohsiung, Taiwan
Tsung-Jen Teng
National Center for Research on Earthquake Engineering, Taipei, Taiwan
Shiang-Jung Wang
National Center for Research on Earthquake Engineering, Taipei, Taiwan
Paper No:
PVP2007-26116, pp. 19-24; 6 pages
Published Online:
August 20, 2009
Citation
Liao, W, Teng, T, & Wang, S. "The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space." Proceedings of the ASME 2007 Pressure Vessels and Piping Conference. Volume 8: Seismic Engineering. San Antonio, Texas, USA. July 22–26, 2007. pp. 19-24. ASME. https://doi.org/10.1115/PVP2007-26116
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