Effects of the rigid disk attached to the edges of the cylindrical shells on the natural frequencies of different modes

The vibration of cylindrical shells with rigid disks attached at the edges is investigated and the results are compared by those obtained under the common simplifying assumption that the edges are clamped at points attached to the rigid disk. The shell is modeled using Sanders-Koiter shell theory, including the transverse shear deformation. The effect of the rigid disk on the edges displacements is also determined in a systematic manner by using the kinematic relations of the disk. To solve the problem, the semi-analytical finite element method is used and the stiffness and mass matrices of the element attached to the disks are completely determined for the first time. The reason that the disk affects the stiffness matrix is that some constraints appear between the displacement components of the shell edges due to the attached rigid disk. Numerous numerical studies are performed to investigate the effect of mass properties of the rigid disks on different shell natural frequencies and mode shapes. Results show that the rigid disk can significantly change the natural frequencies of the modes with zero and one circumferential wave number. It is also shown that by increasing the rigid disk mass, the mode with the smallest frequency would change from a mode with a high circumferential wave-number to a beam-like bending mode.