### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3aSA7. A unique boundary integral approach for acoustic radiation of
axisymmetric bodies with arbitrary boundary conditions.

**W. Wang
**

**
N. Atalla
**

**
J. Nicolas
**

**
**
*G.A.U.S., Dept. of Mech. Eng., Univ. of Sherbrooke, Sherbrooke, PQ J1K 2R1,
Canada
*

*
*
A boundary integral method for solving the exterior acoustic radiation
problem of axisymmetric bodies with arbitrary boundary conditions has been
developed. The new formulation derives from the method proposed by Burton and
Miller, which uses a linear combination of the Helmholtz integral equation and
its normal derivative to ensure the uniqueness of the numerical solution at all
frequencies. By taking advantage of the properties of axisymmetric geometry, and
using the expansion of the boundary conditions and the surface distribution
functions in Fourier series with respect to the angle of revolution, the surface
integral is reduced to a line integral along the generator of the body, and
Fourier integrals of the Green's function and its derivatives over the
circumferential angle. A main feature of this formulation is that new recurrence
formulas of the Fourier coefficients have been developed to evaluate accurately
the Fourier integrals with the singular kernels in terms of the complete
elliptic integrals. In order to demonstrate the validity and accuracy of the
method, numerical results with quadratic isoparametric curvilinear elements are
presented for radiation problems of a pulsating sphere, an oscillating sphere,
and a finite cylinder with various boundary conditions.