A study on the mode pair of a slightly asymmetric circular ring with multiple deviations

This paper theoretically investigates the effect of multiple local deviations on the property of mode pair of a circular ring. The Laplace transform method is applied to the asymmetric ring with multiple local deviations. Multiple heavy side step functions are used to model the local deviations by using distributed mass, stiffness and thickness elements. The effect of multiple deviations on the change of the frequency of the mode pair is investigated. Beat frequency and configuration of the mode pair are investigated according to the amount and the position of the deviation. This study aims to explain the deviation effect on the beats of rings and bell type structures. The proposed analytical method can be used to control the beat characteristics of bell type structures.