Free Vibration Analysis of Rhombic Plate with Central Crack

In this paper, free vibration analysis of rhombic plate with pre-existing central crack has been done using the finite element method. The Mindlin theory of plate has been used in the process of investigation. The following six boundary conditions at the edges of the plate have been considered. They are simply supported at all edges (SSSS), clamped at all edges (CCCC), free at all edges (FFFF), clamped-simply supported (CSSC), clamped-free (CFFC), and clamped-free-simply supported (CSFS). Effects of crack length on natural frequencies of rhombic plate with different skew angles i.e. 15 degrees, 30 degrees, 45 degrees, 60 degrees have been studied. It is observed that percentage drop in fundamental frequency due to presence of central crack in the rhombic plate increases with an increase in skew angle for CCCC, SSSS, and CSSC edge conditions at a given crack ratio (non-dimensional crack length). Under the CFFC, CSFS, and FFFF edge conditions, percentage drop in natural frequency of rhombic plate is very small for crack ratio of 0.2 at different skew angles. In case of the CFFC edge condition of the rhombic plate, percentage drop in fundamental frequency is within 0.7% at all skew angles and with all crack ratios considered. Some of the results obtained by the present method have been compared with the published results. Most of the results obtained are novel for rhombic crack plate.