Dissipative solitons in forced cyclic and symmetric structures

TL;DR

This paper investigates how nonlinear effects and external forcing lead to localized vibration states, called dissipative solitons, in symmetric cyclic structures like bladed disks, with implications for turbomachinery stability.

Contribution

It introduces a minimal model using coupled Duffing oscillators to analyze the emergence of dissipative solitons in nonlinear, forced, symmetric structures.

Findings

Localized vibration states bifurcate from travelling waves near resonance.

Complex bifurcation diagrams include stable and unstable dissipative solitons.

Solitons can be continued to a conservative limit, bifurcating from backbone curves.

Abstract

The emergence of localised vibrations in cyclic and symmetric rotating structures, such as bladed disks of aircraft engines, has challenged engineers in the past few decades. In the linear regime, localised states may arise due to a lack of symmetry, as for example induced by inhomogeneities. However, when structures deviate from the linear behaviour, e.g. due to material nonlinearities, geometric nonlinearities like large deformations, or other nonlinear elements like joints or friction interfaces, localised states may arise even in perfectly symmetric structures. In this paper, a system consisting of coupled Duffing oscillators with linear viscous damping is subjected to external travelling wave forcing. The system may be considered a minimal model for bladed disks in turbomachinery operating in the nonlinear regime, where such excitation may arise due to imbalance or aerodynamic excitation. We demonstrate that near the resonance, in this non-conservative regime, localised vibration states bifurcate from the travelling waves. Complex bifurcation diagrams result, comprising stable and unstable dissipative solitons. The localised solutions can also be continued numerically to a conservative limit, where solitons bifurcate from the backbone curves of the travelling waves at finite amplitudes.