Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

Fontanela, F; Grolet, A; Salles, Loïc; Hoffmann, N

doi:10.1016/j.jsv.2018.09.002

Article (Scientific journals)

Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

Fontanela, F; Grolet, A; Salles, Loïc et al.

2019 • In Journal of Sound and Vibration, 438, p. 54 - 65

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/334006

DOI
10.1016/j.jsv.2018.09.002

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Keywords :

Energy localisation; Harmonic balance methods; Cyclic structures; Quasi-periodic vibrations

Abstract :

[en] In this paper we develop a fully numerical approach to compute quasi-periodic vibrations bifurcating from nonlinear periodic states in cyclic and symmetric structures. The focus is on localised oscillations arising from modulationally unstable travelling waves induced by strong external excitations. The computational strategy is based on the periodic and quasi-periodic harmonic balance methods together with an arc-length continuation scheme. Due to the presence of multiple localised states, a new method to switch from periodic to quasi-periodic states is proposed. The algorithm is applied to two different minimal models for bladed disks vibrating in large amplitudes regimes. In the first case, each sector of the bladed disk is modelled by a single degree of freedom, while in the second application a second degree of freedom is included to account for the disk inertia. In both cases the algorithm has identified and tracked multiple quasi-periodic localised states travelling around the structure in the form of dissipative solitons.

Disciplines :

Mechanical engineering

Author, co-author :

Fontanela, F

Grolet, A

Salles, Loïc ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M) ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Vibration of Turbomachines ; Imperial College London > Mechanical Engineering > Vibration University Technology Center

Hoffmann, N

Language :

English

Title :

Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

Publication date :

2019

Journal title :

Journal of Sound and Vibration

ISSN :

0022-460X

eISSN :

1095-8568

Volume :

438

Pages :

54 - 65

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 06 July 2025

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