Axisymmetrical Vibrations of Underwater Hemispherical Shells

Free vibrations of an underwater elastic hemispherical thin shell with fixed edge have been investigated based on the bending theory. The solution of this fluid-solid interaction problem involves the differential equations of motion of underwater spherical shells, the velocity potential of the water field, the hydrodynamic pressure, and the continuity and boundary conditions. A transcedental frequency equation in terms of Legendre functions is derived and the normal and tangential mode shapes are found. Examples are given and results are plotted for natural frequencies and modes shapes.