| Summary: | 碩士 === 中華科技大學 === 機電光工程研究所碩士班 === 99 === Abstract
In this thesis, the collocation multipole method is presented to solve the problem of the acoustic scattering of a plane sound wave by multiple elliptical cylinders. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions. The boundary conditions are satisfied by uniformly collocating points on the boundaries. The acoustic pressure at each boundary point is directly calculated in each elliptical coordinate system through the coordinate transformation. In different coordinate systems, the normal derivative of the acoustic pressure is calculated by using the appropriate directional derivative, an alternative to the addition theorem. By truncating the multipole expansion, a finite linear algebraic system is derived and then the scattered field can be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with those of analytical solution. The scattered fields by two and three elliptical-cylindrical scatterers are critically compared with those provided by the BEM to verify the validity of the present method. Finally, the effects of the convexity of an elliptical scatter, the space among scatterers and the incident wave number and angle on the scattered fields are investigated.
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