Vibrational Analysis of Size-Dependent Rotating Micro-Rings

The size-dependent dynamic behavior and flexural vibration of rotating micro-rings are investigated in this paper. Using the modified couple stress theory and Hamilton's principle, the governing equations of motion of the rotating micro-ring are derived. The natural frequencies for both extensional and inextensional micro-rings are obtained in closed form along with the forward and backward traveling waves derived. The results indicate that the natural frequencies of the rotating micro-ring are clearly size dependent, but the size dependency decreases as the speed of rotation of the ring increases, while it decreases when the radius-to-thickness ratio of the ring increases. A comparison between the natural frequencies of the extensional and inextensional micro-rings is performed. Moreover, the effect of the radius-to-thickness ratio of the ring on the behavior of the micro-ring is investigated. Good agreement is found between the natural frequencies obtained and the experimental results reported in the literature.