Integral Equation Methods in Sound Radiation and Scattering from Arbitrary Surfaces
Research and development rept.
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD
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Integral equation methods are described for calculating the entire sound pressure field when either the distribution of velocity or sound pressure is specified on an arbitrary closed surface. The theory is based on determining an equivalent surface layer of either monopoles only, dipoles only, or both monopoles and dipoles. Appropriate integral equations are derived for the unknown surface monopole andor dipole density for each case and each boundary condition. Every closed surface has two infinite sequences of characteristic wave numbers at each of which there exist an associated characteristic internal standing wave and an associated characteristic external traveling wave which satisfy the homogeneous parts of these integral equations at one or the other of the two series of wave numbers. At these wave numbers, and for particular boundary conditions which are specifically derived, all the integral equations may have infinite or indeterminate solutions. The problems of sound radiation by a pulsating sphere is used to illustrate the solutions of all the different integral equations and to demonstrate the complications that occur at the characteristic wave numbers. Special and simple techniques are described for approximating each of the integral equations by a linear matrix equation with finite elements and for the numerical solution of the matrix equation. Special methods are described to eliminate the indeterminacy in the solution to the matrix equation near the characteristic wave numbers.