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.