A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Discs

Abstract

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disc using a periodic sector model without any loss of accuracy in calculations and modelling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disc forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disc model: (i) using sector finite element matrices; (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disc with shrouds have demonstrated the high efficiency of the method.