Tangential Displacement and Shear Stress Distribution in Non-Uniform Rotating Disk under Angular Acceleration by Semi-Exact Methods

In this paper, semi-exact methods are introduced for estimating the distribution of tangential displacement and shear stress in nonuniform rotating disks. At high variable angular velocities, the effect of shear stress on Von Mises stress is important and must be considered in calculations. Therefore, He’s homotopic perturbation method (HPM) and Adomian’s decomposition method (ADM) is implemented for solving equilibrium equation of rotating disk in tangential direction under variable mechanical loading. The results obtained by these methods are then verified by the exact solution and finite difference method. The comparison among HPM and ADM results shows that although the numerical results are the same approximately but HPM is much easier, straighter and efficient than ADM. Numerical calculations for different ranges of thickness parameters, boundary conditions and angular accelerations are carried out. It is shown that with considering disk profile variable, level of displacement and stress in tangential direction are not always reduced and type of changing the thickness along the radius of disk and boundary condition are an important factor in this case. Finally, the optimum disk profile is selected based on the tangential displacement-shear stress distribution. The presented algorithm is useful for the analysis of rotating disk with any arbitrary function form of thickness and density that it is impossible to find exact solutions.