Travelling and standing envelope solitons in discrete non-linear cyclic structures

Aurelien Grolet (1) , Norbert Hoffmann (1) , Fabrice Thouverez (2) , Christoph Schwingshackl (1)

1 Department of Mechanical Engineering [Imperial College London]
2 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.

Mots clés: Multiple scales; Non-linear dynamics; Envelope soliton; Cyclic system; Travelling waves

Domaines: Vibrations [physics.class-ph]

Aurelien Grolet, Norbert Hoffmann, Fabrice Thouverez, Christoph Schwingshackl. Travelling and standing envelope solitons in discrete non-linear cyclic structures. Mechanical Systems and Signal Processing, 2016, 81, pp.75-87. ⟨10.1016/j.ymssp.2016.02.062⟩. ⟨hal-02121462⟩