Model reduction of nonlinear cyclic structures based on their cyclic symmetric properties

Abstract

Displacement control of bladed-disks is of primary stake for turbo-engineers. Such structures present cyclic symmetric properties that allow some specific reduction techniques. For linear problems, the equation of motion projected on spectral components, also called nodal diameters, gives a system of equations in which the unknowns are uncoupled. Each nodal diameter can therefore be considered independently. However in real applications, the presence of nonlinear terms couples the different nodal diameters and makes the spectral equation of motion more complex to handle.This paper deals with this difficulty and presents two main results. It first gives an analytical derivation to determine which nodal diameters get coupled by friction nonlinearities. Such procedure reduces the size of the model but also the number of unknowns in the system by considering only the interacting nodal diameters. This method is general and allows to tackle a wide range of industrial problems. However this may not be sufficient for an efficient resolution of the nonlinear system since the nonlinear forces must first be evaluated in the physical domain, and, a priori, for all the sectors of the cyclic system before being computed in the spectral domain. The second main originality of the paper is the development of different strategies on this matter. One is analytical, valid for any excitation and is straightforward to implement, while the others are based on specific assumptions on the deformed shape but offer further reduction.The new methodologies are validated on a simplified bladed-disk with different excitation forces and different friction’s laws. They show very good accuracy and a substantial computation time reduction.