Dissipative solitons in forced cyclic and symmetric structures

Abstract

The emergence of localised vibrations in cyclic and symmetric rotating struc-tures, such as bladed disks of aircraft engines, has challenged engineers in thepast few decades. In the linear regime, localised states may arise due to alack of symmetry, as for example induced by inhomogeneities. However, whenstructures deviate from the linear behaviour, e.g. due to material nonlinearities,geometric nonlinearities like large deformations, or other nonlinear elements likejoints or friction interfaces, localised states may arise even in perfectly symmet-ric structures. In this paper, a system consisting of coupled Duffing oscillatorswith linear viscous damping is subjected to external travelling wave forcing.The system may be considered a minimal model for bladed disks in turboma-chinery operating in the nonlinear regime, where such excitation may arise dueto imbalance or aerodynamic excitation. We demonstrate that near the reso-nance, in this non-conservative regime, localised vibration states bifurcate fromthe travelling waves. Complex bifurcation diagrams result, comprising stableand unstable dissipative solitons. The localised solutions can also be continuednumerically to a conservative limit, where solitons bifurcate from the backbonecurves of the travelling waves at finite amplitudes.