Vibrational modes of slotted cylinders

The vibrational behaviour of clamped-free slotted tubes has been investigated to determine the influence of slot length upon their characteristic normal modes. FEM simulations were performed for a series of aluminium tubes consisting of a complete cylindrical shell through a series of cases, identical apart from having slots of different lengths but constant equal widths, running parallel to their symmetry axes. The lower frequency region of the spectrum was dominated by transverse and other flexural modes. Further classes, such as longitudinal and torsional modes, appeared progressively as frequency increased. ESPI was utilised to view the tubes while exciting them acoustically, providing good agreement with FEM predictions. Where modes occurred in degenerate pairs, the splitting increased with slot length. FEM simulations predicted a previously unreported modal form, which has been verified experimentally using ESPI. These "modes" appeared in families, but only in cylinders with longer slots, and had non-zero amplitudes only close to the edges of the slot.