An Axisymmetric Integral Equation Formulation for Free Space Non-Axisymmetric Radiation and Scattering of a Known Incident Wave
✍ Scribed by P. Juhl
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 309 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
This paper gives a brief account of the formulation of the Helmholtz integral equation specialized to the case of an axisymmetric body in free space. In this case the surface integral of the Helmholtz integral equation may be reduced to a combination of a line integral and an integral over the angle of revolution; only the former integral needs to be discretized, and thus the dimension of the problem is reduced to one. In order to allow for non-axisymmetric boundary conditions the sound field is expanded in a cosine series over the angle of revolution. This expansion is as general as a full Fourier expansion but more efficient. The singularities in the Green function and its normal derivative are integrated analytically over the angle of revolution and expressed as sums of elliptic integrals. The formulation is tested for scattering and radiation problems.