Research On Dynamics Of Rotationally Periodic Structures

There exist a large number of rotationally periodic structures in engineering. The relationships between the basic parameters and the dynamics of the structures should be studied to present the theoretical foundation for the dynamic design of the structures. This work is a part of the National Natural Science Foundation of China (Investigations on the mechanism of noise and vibration reduction of permanent machines based on phase tuning, Grant No. 50705062). Motivated by the magnetic motor stators, the thesis studied the dynamic response of the rotational periodic structures. And the main contents are:1. The general dynamic model of the annular-rotational-periodic structures (ARPS) was developed by the Hamilton's principle, in which the basic symmetric element can be point or area element. Two methods for the perturbation analysis of the mode properties were presented according to the mass and stiffness operators, and the application range of the two methods are also given.2. Closed-form solution to the ARPS with point element was presented. The relationships between the basic parameters and the modal properties are given. The simulation analysis was also carried out to verify the relationships. In addition, the random mistuning of this structure was investigated, and the statistical distribution and the closed-form statistics characteristics of the modal response were also obtained.3. The modal properties of the ARPS with area element modeled as unit step function were studied. The natural frequency splitting and the mode contamination were analyzed by using the perturbation analysis. And the relationship between the configuration of the area element and the modal response was investigated. Furthermore, the modal properties of the multi-rotationally periodic structures were also studied, and the corresponding relationship between the basic parameters, such as the element number and the position angle between two adjacent elements, and the dynamic response was presented.4. The closed-form solution to the forced vibration of the ARPS was obtained by using the perturbation method. The method for the wave vibration suppression was also given. The main results were verified by the experimental results given by existing literature. Finally, the basic principle of the slot/pole combination of the magnetic motors was presented based on the rotationally periodic structure dynamics.