Analytical study of micro-rotating disks with angular acceleration on the basis of the strain gradient elasticity

The small-scale effects on the mechanical responses of micro-rotating disks with angular acceleration are investigated based on the strain gradient theory, as one of the powerful non-classical continuum theories which have been developed to justify the empirical observations of mechanical behavior in small-scale structures and components. The differential equations governing motion of the micro-disk elements in radial and circumferential direction together with the corresponding boundary conditions are derived. Then, an analytical solution is presented for the components of the displacement field which can be used as a base for determination of the components of the stress field. In a numerical case study, the distribution of stress components as well as of the displacement components is investigated, and the obtained results are compared with those of the classical continuum theories.