An exact frequency analysis of annular plates with small core having elastically restrained outer edge and sliding inner edge

• Exact frequency analysis of annular plates with small core with elastic edge.
• Frequencies for the first six modes of annular plate presented.
• The fundamental frequency is governed by asymmetric mode for small core radius.
• The core radius and fundamental frequency at transition found quite sensitive to elastic restraint.
• The percentage decreases in frequency parameter with elastic edge support presented.

The present study deals with an exact analysis of free transverse vibrations of annular plates having small core and sliding inner edge and the outer edge being elastically restrained based on classical plate theory. This study focuses mainly on the influence of variations in the elastic restraint parameters on the fundamental frequencies of plate vibration. The natural frequencies for the first six modes of annular plate vibrations are computed for different materials and varying values of the radius parameter and these natural frequencies may correspond to either axisymmetric and/or non-axisymmetric modes of plate vibration. The extensive data of values of fundamental frequency parameter presented in this paper is believed to be of use in the design of acoustic underwater transducers, ocean and naval structures, compressor and pump elements, offshore platforms. These results may serve as bench mark values for researchers to validate their results obtained using approximate numerical methods.