Numerical and analytical investigation of free vibrations of circular cylindrical shells with added mass linearly distributed along generatrix

The influence of an added mass linearly distributed along generatrix on the frequency and modes of free vibrations of a thin shell is studied in the framework of the shallow shell theory. We introduce a refined version of the mathematical model which assumes that the excitation of bending vibrations gives rise not only to a conjugate bending mode, but to the radial vibrations of the shell as well. The mechanism of interaction between the bending and radial vibrations is the light added mass. The boundary value problem is solved using the Bubnov-Galerkin method. The resulting system of dynamical equations shows that the added mass effect leads to the coupling of the low-frequency bending vibrations of the shell and its high-frequency radial vibrations. Radial vibrations act as an additional inertial coupling between the conjugate bending modes. It is shown that the splitting of the bending frequency spectrum becomes stronger, which is caused not only by the added mass, but also by the wave parameters characterizing the relative length and thickness of the shell. The analysis yielded the ranges of relative length and thickness of the shell in which the interaction between the bending and radial vibrations could be neglected. The theoretical results are compared with the numerical solution obtained using the finite element software code NASTRAN.