The frequency domain response of arbitrary closed shells of revolution immersed in an infinite acoustic medium is considered. A reduction in dimensionality of the problem is achieved through a decomposition of motion into circumferential harmonics. The acoustic relation is thus represented as an integral equation defined along the shell meridian. This relation, derived on the basis of a Green's function technique featuring toroidal wavefunctions, is applicable to surfaces having arbitrary meridianal shape, including corners. In order to assure uniqueness of solution, interior equations are appended to the set of surface integral equations. The concept of an acoustic element is introduced with meridianal pressure variation determined by the response at a number of surface pressure nodes. The structure is represented in terms of an assemblage of conical frustum shell elements having either two or three nodal rings. The fluid‐structure interaction relation is consistently developed on the basis of modal degrees of freedom. The final product is an accurate, efficient scheme to predict structural response, and surface and exterior pressure fields. Examples considered include: spherical and toroidal substitute problems, a truncated cylinder having specified radial motion, and response of a spherical elastic shell excited by a harmonic point load.

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