Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

This paper considers the RL shunt damping of rotationally periodic structures with an array of regularly spaced piezoelectric patches. The technique is targeted to the damping of a specific mode withnnodal diameters. For this particular case, one can take advantage of the shape of the targeted mode to organize the piezoelectric patches as a modal filter (in parallel loops) which reduces the demand on the inductors of the tuned inductive shunt. In the case of a perfectly rotationally periodic structure, it is possible to organize 4npiezoelectric transducers (PZT patches) in two parallel loops of 2npatches each. In this way, the demand on the inductors is reduced by4n2as compared to independent loops, which may allow a fully passive integration of the RL shunt in a turbomachinery application. The method is first illustrated experimentally on a circular plate; it is then applied to a prototype of an industrial bladed drum. The influence of blade mistuning is investigated.

Excitation of Rotationally Periodic Structures

A rotationally periodic structure consists of a finite number of identical substructures forming a closed ring. The vibrational behavior of such structures is considered, especially the forced response due to a rotating force. It is known that for a rotationally symmetric structure, excited by a rotating force, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ωn = nΩ, where Ω is the angular velocity of the force. This resonance condition also holds for a rotationally periodic structure. But then additional resonance possibilities exist, given by ωn = (kN ± n)Ω, where N is the number of substructures and k = 0, 1, 2,… These resonance conditions give a zigzag line in the nodal diameters versus frequency diagram, which here is introduced as the ZZENF diagram. The deformation patterns at the resonances are both forward and backward traveling waves.