Solitons in Cyclic and Symmetric Structures

Abstract

This research focuses on localised states arising from modulationally unstable plane waves in non-conservative cyclic and symmetric structures. The main application is on vibrations of bladed-disks of aircraft engines experiencing non-linear effects, such as large displacements, friction dissipation, and/or complex fluid-structure interactions. The investigation is based on a minimal model composed of a chain of linearly damped Duffing oscillators under external travelling wave excitation. The computed results are based on two strategies: (1) a Non-Linear Schrodinger Equation (NLSE) approximation; and (2) the periodic and quasi-periodic Harmonic Balance Methods (HBM). In both cases, the results show that unstable plane waves may self-modulate, leading to stable and unstable single and multiple solitons configurations.