Topology optimization for cyclic periodic structures with frequency objectives of nodal diameter modes

The evaluation of dynamic reliability in disc structures relies on the frequency of nodal diameter modes, which can be determined through calculations on cyclic periodic structures. There is a pressing need for a topology optimization approach that can effectively optimize the structural frequency. This article proposes a topology optimization framework specifically designed for optimizing the frequency of nodal diameter modes in cyclic periodic structures. The framework enables the specific frequency of nodal diameter modes, as well as the gaps between multiple specific frequencies, to be adjusted. Furthermore, a universal optimization strategy is introduced for the frequency optimization design of cyclic periodic structures. This optimization strategy is applied to the maximization optimization process of the fundamental frequency and frequency gaps to control multiple frequencies across various nodal diameters. The effectiveness of the frequency topology optimization framework for cyclic periodic structures is demonstrated through case studies involving different sector angles and frequencies.