Vibrations of orthotropic annular plates subjected to non-uniform boundary conditions over different sections of the inner and outer circumferences

The free vibrational response of homogeneous or symmetrically laminated polar orthotropic annular plates subjected to non-uniform boundary conditions on the inner and outer rims is scrutinized in detail, using a finite-difference method. Although the same sets of boundary conditions are considered, the angular location at which the altered boundary conditions are applied and the segments that they cover are allowed to be different on the inner and outer circumferences. The sensitivity of vibrational frequencies to the extent and relative location of the non-uniformities is investigated and shown to be strongly influenced by the material properties with the orthotropy ratio for the plate (defined here by Drr/DθθDrr/Dθθ) being the predominant parameter for indicating the sensitivity to non-uniformity. The behavior of higher modes of vibration is also discussed and the phenomenon of crossover, whereby two modes having the same frequency exist, is found to occur. Unlike the crossover previously reported in the literature, for which only higher modes of frequency were involved, in the current context, it was discovered that the phenomenon may also be associated with the lowest mode of vibration. The circumstances under which crossover transpires are dependent on the relative location of the boundary non-uniformities, the relative length over which the non-uniformities are applied and the orthotropy ratio.