Investigating the effect of angular acceleration of the rotating disk having variable thickness and density function on shear stress and tangential displacement

  • Mortaza Salehian
  • Behrooz Shahriari
  • Masood Yousefi
Technical Paper


The present paper aims at exploring numerical and exact analytical procedures for evaluating the shear stress and tangential displacement in variable thickness rotating disks having angular accelerations solid or annular and density alterations along their radius. Galerkin method, a subset of weighted residual techniques, is applied for the numerical part. The procedure reduces a continuous equilibrium problem into an approximately equivalent equilibrium problem having many degrees of freedom, making it a powerful tool for solving any kind of profiles of arbitrary thicknesses and density functions. However, other numerical and analytical methods used in previous researches are applied in profiles having certain thickness functions evaluating only normal stresses and strains. Consequently, an attempt is made to fill the gap between the two utilizing comprehensive approaches which take all the circumstances into account. To verify both the numerical and the analytical methods, a few set examples of rotating disks of angular accelerations having various thicknesses and density functions were solved and compared. A good concordance was observed between the numerical and the analytical solutions, and finally, the distributions of the tangential displacement and shear stress are obtained appropriate comparisons and discussions being provided under the same environmental conditions. Also, the best thickness function having optimum and minimum shear stress and tangential displacement is selected.


Shear stress Tangential displacement Galerkin method Angular acceleration 


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Mortaza Salehian
    • 1
  • Behrooz Shahriari
    • 2
  • Masood Yousefi
    • 3
  1. 1.Department of Aerospace EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Mechanical EngineeringMalek Ashtar University of TechnologyIsfahanIran
  3. 3.Department of Aerospace EngineeringSharif University of TechnologyTehranIran

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