A two-harmonic homotopy method to connect a primary resonance to its secondary resonances

Raze, Ghislain; Kerschen, Gaëtan

doi:10.1098/rspa.2024.0875

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A two-harmonic homotopy method to connect a primary resonance to its secondary resonances

Raze, Ghislain; Kerschen, Gaëtan

2025 • In Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, 481 (2312), p. 20240875

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https://hdl.handle.net/2268/330717

DOI
10.1098/rspa.2024.0875

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Keywords :

Nonlinear vibrations; Secondary resonance; Two-harmonic forcing; Simultaneous resonance; Isola; Homotopy

Abstract :

[en] Besides the well-known primary resonances, forced nonlinear systems can exhibit secondary (namely superharmonic, subharmonic and ultrasubharmonic) resonances whose frequencies are rationally related to the forcing frequency. Some of these secondary resonances can appear as isolated branches of solutions, challenging their characterization. This work leverages two-harmonic forcing to transition from a primary resonance to a specific secondary resonance. A homotopy problem is formulated, whose limit cases correspond to these resonances. The proposed method is shown to be able to uncover isolated responses in a deterministic and reliable way. It is illustrated on a Duffing oscillator, a two-degree-of-freedom system and a beam with contact.

Disciplines :

Aerospace & aeronautics engineering
Mechanical engineering

Author, co-author :

Raze, Ghislain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

A two-harmonic homotopy method to connect a primary resonance to its secondary resonances

Publication date :

16 May 2025

Journal title :

Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences

ISSN :

1364-5021

eISSN :

1471-2946

Publisher :

The Royal Society, United Kingdom

Volume :

481

Issue :

2312

Pages :

20240875

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://royalsocietypublishing.org/doi/10.1098/rspa.2024.0875

Funding text :

Ghislain Raze is a Postdoctoral Researcher of the Fonds de la Recherche Scientifique - FNRS which is gratefully acknowledged.

Available on ORBi :

since 15 April 2025

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