Elasticity formulation for motion equations of couple stress based micro-rotating disks with varying speeds

The elasticity formulation for equations of motion of micro-rotating disks in the presence of angular acceleration as well as the corresponding boundary conditions are developed based on the non-classical continuum theory of couple stress. The system of the boundary value problem is derived on the basis of the variational method. Analytical elasticity solutions to the system of equations are then provided. Based on the elasticity solution, the mechanical responses, including the displacement and stress fields, for varying-speed micro-rotating disks are studied. In a numerical case study, the effect of the couple stresses on the distribution of stress and displacement components are investigated.

Automated summary

The study develops an elasticity formulation for the equations of motion of micro-rotating disks based on the non-classical continuum theory of couple stress, and derives the boundary value problem system using the variational method. Analytical elasticity solutions are provided, and the effect of couple stresses on stress and displacement distributions is investigated through a numerical case study.