Splitting of quality factors for micro-ring with arbitrary point masses

A ring resonator model with mass imperfections can be represented by a circular ring with irregularly distributed point masses. In this paper, in-plane vibration of the micro-ring is to be investigated. Also, the ThermoElastic Damping (TED) effect is considered in the structures. In order to get the temperature profile for the thermal flow, one-dimensional heat conduction equation is employed. Using the assumed mode shapes for the inextensional vibration of the imperfect micro-ring with TED, analytical expressions for the natural frequencies with concentrated masses are determined by the equations of motion. Then, the split of the natural frequencies are determined according to the effect of distributed point masses. Finally, imperfect micro-ring with TED is presented with the variations of Quality-factors (Q-factors) for lower and higher modes. Based on the verification of the present work, more parametric studies are performed for the ring with mass imperfections.