Small-scale oriented elasticity modeling of functionally graded rotating micro-disks with varying angular velocity in the context of the strain gradient theory

During the varying angular speed timespans of the start or shutdown of rotating machinery, the machinery components may be subjected to intense mechanical loadings which should be taken into account by its fabricator in the designing processes. In the microscale rotating systems, where the angular velocity is typically very high, the importance of this issue is much higher. In this paper, a comprehensive strain-gradient elasticity formulation is presented for functionally graded rotating micro-disks under the effects of varying angular velocity. The gradation of the constituent material along the radial direction can be a helpful option to mitigate the stresses in rotating micro-disks under high mechanical loadings. The material properties and the thickness of the disk can arbitrarily vary along the radial direction. The effects of the material gradient index and the thickness profile of rotating micro-disks on the distribution of classical and higher-order stresses are examined. Moreover, the differences between the predicted responses from the strain gradient elasticity and from the classical continuum mechanics are highlighted and discussed.