Mass imperfections in a toroidal micro-ring model with thermoelastic damping

Abstract

• Thermoelastic dissipation is discussed for a toroidal micro ring with mass distributions. • A three-dimensional heat conduction equation is used for more accurate estimation. • The temperature profile is obtained in terms of Bessel functions in the cylindrical coordinate system . • The modified quality factor is estimated by use of the eigenfrequency of an imperfect ring. • Deviations of the temperature profile due to the imperfections are graphically observed as a function of the radial component . This work estimates the difference in quality factors (Q-factors) resulting from the effect of thermoelastic damping on toroidal solid micro rings with point mass distributions. The imperfections are irregularities in the angular locations with concentrated masses. On the basis of the modeling, eigenfrequencies are obtained as the in-plane vibration of the ring with an inextensional assumption. To evaluate the thermal expansion in the strains of the structure, a three-dimensional heat conduction equation is used for more accurate estimation. The temperature profile is obtained in terms of Bessel functions in the cylindrical coordinate system. Finally, the modified Q-factors are evaluated as the the ratio of the maximum strain energy of the model to the energy loss due to the thermoelastic damping. To check the validity of the study, the results obtained are compared with results in the literature for a uniform micro-ring model. The Q-factors for an imperfect toroidal micro ring are discussed on the basis of the sizes of the imperfections and the eigenmodes of the ring. Also, deviations of the temperature profile due to the imperfections are graphically observed as a function of the radial component.