This paper presents the equations for thin shell-of-revolution tanks containing an arbitrary level of fluid. The mass matrix can be used with any finite element or finite difference digital computer program that computes either the dynamic response or the natural frequencies and modes of a thin shell of revolution and that has provision for a nondiagonal mass matrix. The method does not require a numerical finite difference or finite element discretization of the fluid, but instead provides, in series form, a mass matrix that exactly satisfies the governing field equations for the fluid and satisfies the fluid-shell interface condition with a least-squares fit.

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