Vibration behaviour of stators of electrical machines, part I: Theoretical study

Abstract A general analytical method for free vibrations of thick cylindrical shells is presented in this paper. The problems associated with thick cylindrical shells are of considerable engineering importance in numerous applications. One important application of such shells is the stator of electrical machines, where the thick stator-core with teeth and windings is encased by a thin frame provided with cooling ribs. In order to design a quiet electrical machine, the accurate determination of resonant frequencies and vibrational characteristics of the stator is essential. The well known energy method is used in the analysis presented for the derivation of the frequency equation of the stator. As a first step, the analysis is applied to a simple and smooth model of thick circular cylindrical shell having substantial axial length as used in actual stators. The analysis delivers information on resonant frequencies and associated mode shapes. The method of analysis and the theoretical results obtained for the model are presented. The experimental verification of the analysis is reported in a companion paper.