A generalization of the Donnell model for a thin shell of arbitrary shape, and with position-dependent elastic and geometric properties, is used to formulate a wave theory for quasi-straight-crested waves of constant frequency propagating over the shell’s surface. The principal restriction on the theory is that the wavenumber components must be large compared with the two principal curvatures. A simple method for including fluid loading in the model yields a finite local specific radiation impedance even when the waves on the surface are moving with the fluid’s sound speed. The overall model is then used to derive a general dispersion relation which connects frequency and wavenumber components for the fundamental waves of the fluid-shell system.

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