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.