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

Abstract

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.

Keywords:

• Angular acceleration
• micro-rotating disks
• non-classical continuum theories
• the modified couple stress theory

Disclosure statement

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.