The integral-equation method is applied to study the diffraction of acoustic waves by rigid plane baffles, such as a circular disk and a ring. A set of six real Fredholm integral equations of the second kind is solved simultaneously to determine the velocity potentials on a circular disk. These equations are transformed into discrete forms by applying the Gauss-Legendre quadrature formula in the radial direction and the best possible numerical integration formula in the angular direction. The discrete equations are solved by the method of successive approximations, which is also called the direct integral-equation method. A new method is also developed to take care of integrations involving the Cauchy principal values, which occur when the moving point coincides with the fixed point. The accuracy of the present numerical approach has been tested by computing the excess-pressure ratio| p/p0| on the surfaces of a circular disk exposed to a plane wave and by comparing it with both analytical and experimental results. Our numerical results coincide with both results quite well, especially on the shadow side, where the diffraction field is not sensitive to the thickness of the circular disk. The effect of different parameters on the diffracted acoustic field about a circular disk due to a monochromatic acoustic source is systematically studied and compared. These parameters include the location of the acoustic source, the wave number, and the disk thickness. Some interesting results are obtained. As the wave number increases, the excess-pressure ratio approaches two on the “illuminated” side and zero on the “shadow” side of the disk, which indicates that KirchhofFs approximation is appropriate at higher wave numbers. As the acoustic source moves away from the symmetric axis toward one side, the bright spot on the shadow side moves toward the opposite side and has the same peak value. Finally, following the same approach as that for a circular disk, the diffraction of acoustic waves by a rigid ring is studied. Instead of six, a set of eight real Fredholm integral equations is solved simultaneously. The effect of different parameters on the diffraction field is also systematically studied and compared.
All Science Journal Classification (ASJC) codes
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics