Reduced models of multi-stage cyclic structures using cyclic symmetry reduction and component mode synthesis

Reduced models of multi-stage cyclic structures such as bladed-disk assemblies are developed by using the multi-stage cyclic symmetry reduction and/or component mode synthesis methods. The multi-stage cyclic symmetry reduction consists in writing the equations of the bladed disks, the inter-disk structures, the inter-disk constraints and the whole multi-stage coupled system in terms of the traveling wave coordinates for all the phase indexes of the reference sectors and for all the bladed disks. Several reduced coupled systems are then solved by selecting at each time only one or a few phase indexes for each bladed disk and by applying the cyclic symmetry boundary conditions. On the other hand, component mode synthesis methods are used either independently or in combination with the multi-stage cyclic symmetry reduction to obtain reduced models of the multi-stage structure. Two of them are particularly efficient, that are firstly component mode synthesis methods with interface modes applied on the bladed disks and secondly component mode synthesis methods with traveling wave coordinates applied on the reference sectors.