Free vibrations of circular cylindrical shells with a small added concentrated mass

The effect of a small added mass on the frequency and shape of free vibrations of a thin shell are studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial bending vibrations. The interaction of shape-forming waves is studied using modal equations obtained by the Bubnov–Galerkin method. Splitting of the bending frequency spectrum is found which is caused not only by the added mass, but also shell wave-formation parameters. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of bending and radial vibrations can be ignored.