Effects on thermo-elastic damping of micro-ring structure with arbitrarily attached masses

Abstract

In this paper, thermo-elastic damping of ring structure with random attached point masses is investigated. This work applies the thermo-elastic ring model with in-plane vibration of uniform rings. The model is assumed to have rectangular cross-section. And, attached point masses represent imperfections such as unbalanced mass distribution. Analysis is used to derive analytical expressions for natural frequency. Analytical model for circular ring is introduced using the vibration mode shapes. Extensional, bending and inextensional assumptions for the ring model are considered and discussed. In order to determine natural frequency of ring, equations of energy for the ring are used. As energy equations, Rayleigh-Ritz energy method is adopted. Also, equations of motion are derived for the rotating ring. For rotating model, extensional and inextensional assumptions are applied and discussed. Micro-ring with random point masses are represented by arbitrarily located point masses on the ring models in the formulation. Moreover, using heat conduction equations, effects of thermo-elastic damping are investigated. In order to obtain improved understanding of damping effects, concept of Quality factor(Q-factor) is used. Additionally, the influences of attached point masses are presented by the split of natural frequencies of the model. Q-factor and natural frequencies can be expressed as explicit functions of mode number for the ring. Moreover, various case studies are performed for further physical investigation of the models.