Free vibrations of cylindrical shells with non-axisymmetric mass distribution on elastic bed

The free vibrations of circular cylindrical shells partially loaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction, while they are considered to be uniformly distributed in longitudinal direction on the entire shell length. Therefore, the problem is not axisymmetric. The solution is obtained by using the development of the flexural mode shapes in a Fourier series, whose coefficients are determined by rendering the Rayleigh quotient stationary, so a Galerkin equation is obtained. The proposed method is independent of the boundary conditions at the shell ends. The results are satisfactorily compared to FEM results. Finally the influence of the mass-load and of the bed stiffness on the natural frequencies and mode shapes of a simply supported shell is shown and discussed.