Vibration of mistuned bladed disks supported by flexible continuous shafts

Abstract A simple structural model is presented to investigate the effect of blade mistuning on the dynamic characteristics of a non-rotating flexible blade-rigid disk-flexible shaft assembly, which resembles a fan stage of a modern gas turbine engine. Each blade is allowed both in-plane and out-of-plane deformations with respect to the disk hub, and the supporting shaft is free to bend in two planes. Lagrange's equation is used with the assumed mode method to derive the governing equations of motion. It is shown that blade mistuning strongly affects the interaction between flexible bladed disk (on rigid shaft) and rigid bladed disk (on flexible shaft) modes. This interaction affects the flexible bladed disk modes with all possible nodal diameters, and it is not restricted to the modes with one nodal diameter, as observed for the tuned bladed disks, supported by a flexible shaft. Results are presented for a mistuned seven-bladed disk attached at the free end of a cantilever shaft in one case, and a simply supported shaft with an overhang in another.

[1]  A. V. Srinivasan,et al.  Vibrations of Bladed-Disk Assemblies—A Selected Survey (Survey Paper) , 1984 .

[2]  D. J. Ewins.  A Study of Resonance Coincidence in Bladed Discs , 1970 .

[3]  J. S. Rao.  Tubomachine blade vibration , 1987 .

[4]  J. S. Rao,et al.  FEATURE ARTICLE: items of special interest, tutorials, and surveys: Turbomachine Blade Vibration , 1987 .

[5]  R. C. F. Dye,et al.  Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies , 1969 .

[6]  K. Hall,et al.  Optimization and mechanisms of mistuning in cascades , 1985 .

[7]  M. Lalanne,et al.  VIbration problems in jet engines , 1985 .

[8]  Christophe Pierre,et al.  Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part I: Free Vibrations , 1988 .

[9]  O. Bendiksen,et al.  Vibration Characteristics of Mistuned Shrouded Blade Assemblies , 1986 .

[10]  D. J. Ewins,et al.  Vibration Characteristics of Bladed Disc Assemblies , 1973 .

[11]  A. Srinivasan,et al.  Influence of Mistuning on Rotor-Blade Vibrations , 1975 .

[12]  J. S. Rao.  Turbomachine Blade Vibration , 1991 .

[13]  J. Dugundji,et al.  Flutter and forced response of mistuned rotors using standing wave analysis , 1983 .

[14]  Robert E. Kielb,et al.  Flutter of turbofan rotors with mistuned blades , 1984 .

[15]  R Ali,et al.  FINITE DIFFERENCE METHODS IN VIBRATION ANALYSIS , 1983 .

[16]  Robert G. Loewy,et al.  Blade mistuning coupled with shaft flexibility effects in rotor aeroelasticity , 1989 .