Elastic Limit Angular Velocity and Acceleration Investigation in Non-‎Uniform Rotating Disk under Time-Dependent Mechanical Loading

An analytical effort is made to achieve cognition on the effect of time-dependent mechanical loading ‎on the stress fields of rotating disks with non-uniform thickness and density. At high variable angular ‎velocities and accelerations, evaluation of the effect of shear stress on the values of von Mises stress is ‎significant and it is excellent to consider shear stress in this equivalent stress calculation alongside the ‎radial and tangential stress. In the proposed analytical model, the Homotopy perturbation method (HPM) ‎solves the general structure of rotating disks equilibrium equations in both radial and tangential ‎directions. HPM is an efficient tool to solve linear and nonlinear equations, providing solutions in quick ‎converging series. The results obtained through this process are then confirmed using the finite ‎difference method and the exact solution in the literature. The effect of parameters in angular velocity ‎and acceleration functions with the parameter in the thickness function and the effect of boundary ‎conditions on the values of elastic limit angular velocity and acceleration are established by performing ‎numerical examples. Furthermore, the effect of shear stress on the maximum values of ‎von Mises stress is discussed. It is shown that shear stress has more influence on the distribution of ‎equivalent von Mises stress in the elastic region. It is shown the introduced analytical model is useful for ‎evaluating rotating disk with any arbitrary shape of thickness and density function, without using the ‎commercial finite element simulation software.