Abstract: The ring-shaped periodic structure (RSPS) with variable cross-section features is widely used in engineering practice. Due to the asymmetric variable cross-section features, the natural frequencies can split. Based on the static equilibrium relation, a general dynamic model of an RSPS with variable cross-section features is established by using Hamilton’s principle. Taking the through holes as an example, a dynamic model of the RSPS with cyclically symmetric through holes is derived, and the closed-form expressions of natural frequencies are obtained according to the classical vibration theory. The specific rules for eliminating frequency splitting are proposed based on a grouping pattern. The effects of the parameters of the through hole such as diameter, count, and angular position on natural frequencies and splitting behaviors are investigated. Splitting or non-splitting of natural frequencies is verified by the experiment with a test rig. The results show that the through holes can reduce the mass and stiffness, and then change the natural frequency; larger diameter and count of through holes decrease the repeated frequencies but increase the differences between the split frequencies. Remaining identical and symmetric through holes can eliminate the split. The research method and conclusion can be employed to study the dynamics of similar periodic structures and guide structural design.

Key words: ring-shaped periodic structure, variable cross-section feature, natural frequency splitting behavior, grouping pattern, elimination rule