Lumped parameter modelling of turbine blade packets for analysis of modal characteristics and identification of damage induced mistuning

Turbine blade vibration of packeted blade-disk system is generally studied on the assumption that all the blades are identical and tuned together geometrically as well as structurally. However in practice, blade to blade variations exist and sometimes the variation may be introduced by the onset of a local damage or a crack. It has been shown that even a small mistuning can lead to stress build up through mode localisation under forced vibration. There have been many analytical and FEM based studies for response prediction and stress localisation under mistuned conditions but few have attempted identification of damage from the blade-disk vibration response. Present work has two parts; in the first part tuned blade packet is analysed using lumped parameter model and eigen value problem is formulated involving special Jacobi matrices. Modal spectrum is characterised as a function of number of blades in the packet and lacing wire to blade stiffness ratio and it is demonstrated that the ratio can be estimated from the modal spectrum. In the second part mistuning in the blade packet is considered due to both blade damage and lacing wire damage and representative modal characteristics are investigated. It is mathematically shown that in case of lacing wire damage, fundamental submodal natural frequency does not change, whereas it changes for the blade damage. This fact is exploited for the damage identification and further investigations are made for determination of possible location of the damage from the measured modal spectrum.