Time period of tapered parallelogram-shaped plate with exponential profile in Young’s modulus

The current study estimates the time period of frequency (four modes) of parallelogram shaped plate having circular density and thickness in one and two dimensions, in respect, along with exponential profile in Young's modulus for two different edge conditions. The two different edge conditions of the plate are CCSS and CSSS. The Rayleigh-Ritz method is implemented to solve the frequency equation for the system mentioned above. The major conclusion made from the study is that we can optimise the time period for the system by choosing the circular profile in density and thickness for such plates. To validate our findings, we compare our results with previously published data and show in tabular form.