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Dynamic Green's Function for SH-Wave in Multi-Dipping Layers Embedded in a Half-Space

Published online by Cambridge University Press:  05 May 2011

Tsung-Jen Teng,
Juin-Fu Chai and
Chau-Shioung Yeh
Tsung-Jen Teng*
Affiliation:
National Center for Research on Earthquake Engineering, Taipei, Taiwan 10617, R.O.C.
Juin-Fu Chai*
Affiliation:
National Center for Research on Earthquake Engineering, Taipei, Taiwan 10617, R.O.C.
Chau-Shioung Yeh*
Affiliation:
Department of Civil Engineering, and Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Associate Research Fellow
*Associate Research Fellow
**Professor
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Abstract

In this paper, the recursive T-matrix formalism is developed to determine the dynamic Green's function for SH-wave in the multi-dipping layers with arbitrary shape embedded in a half-space. In each layer, the wave field generated by a harmonic line load can be separated into two parts: the source term and the complementary part. The source term is exactly the Green's function for SH-wave in two-dimensional half-space, and the complementary part which causes the SH-wave to satisfy the boundary conditions at the interface is determined by the wave function expansion method. Using the polar coordinates, the basis functions are constructed by Bessel typed cylindrical functions, and their orthogonality conditions at the corresponding interfaces can be derived by means of Betti's third identity. Applying the conditions of continuity at the interface, the recursive T-matrix formalism is developed for determining the expansion coefficients of the complementary part from the associated source dependent constants.

Keywords

Dynamic Green's functionMulti-dipping layersWave function expansionRecursive T-matrix formalism

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Type
Articles
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Journal of Mechanics , Volume 14 , Issue 4 , December 1998, pp. 161 - 172
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1998

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