Approximate solution of limit angular speed for externally loaded rotating solid disk

The present work proposes a numerical method to investigate the stress and deformation states of rotating disks using variational method taking the radial displacement field as unknown variable. Assuming a series approximation following Galerkin's principle, the solution of the governing partial differential equation is obtained. The analysis is carried out for various disk geometries and the effect of geometry and loading parameters on the stress and deformation states is investigated. Limit angular speed of the disks is also calculated for various system parameters and reported in dimensionless form. The results are validated with those of other researchers for appropriate values of the system parameters and very good agreement is observed. It is observed that the present methodology is quite robust, stable and realistic and the documented tables and curves may be used by the practicing engineers as design monograms.