| Project/Area Number |
10650469
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
構造工学・地震工学
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| Research Institution | Science University of Tokyo |
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Principal Investigator |
TOUHEI Terumi Science Univ.of Tokyo, Dept.of Civil Engineering, Assoc.Prof., 理工学部, 助教授 (50246691)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Green's function / Spectral theory / scattering waves / スペクトル分解 / Hyperfunction |
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| Research Abstract |
This research deals with the spectral representation of Green's function for a layered medium and its application to the scattering problem. Regarding the layered scalar wave field, the procedure for obtaining the spectral representation is rather simple. On the other hand, as for a 3-D layered medium, the precedure of deriving Green's function is not very simple due to the inability of establishing the orthogonality relations of the Rayleigh wave modes. Nevertheless, the concept of the Hyperfunction is found to be applicable to derive the spectral representation of Green's function.
The boundary integral equation method as well as the spectral representation of Green's function are introduced to the scattering problem in that the scattering waves are caused by the interaction between a scattering object in a layered medium and a plane wave. The spectral representation of Green's function enables us to introduce a viewpoint of eigenvalue problems into the boundary integral equation method. The scattering waves are decomposed into oeigenfunctions for the point and continuous spectra via interchanging the order of the boundary integral and the spectral integral or summation. As a result, an understanding of scattering waves becomes possible by means of the eigenfunctions for a layered medium.
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