Experimental continuation in nonlinear dynamics: recent advances and future challenges

Experimental nonlinear dynamics; Control-based methods; Experimental continuation; Control-based continuation; Phase-locked loop; Response-controlled testing

Abstract :

[en] Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without feedback control. Such control-based methods thus allow the experimenter to directly and exhaustively explore the dynamics of the system without the need for a good mathematical model. The objective of this paper is twofold, namely (i) to review and present the state-of-the-art methods in a unified manner and (ii) to introduce a novel experimental derivative-free arclength continuation procedure, termed arclength control-based continuation. These methods are also demonstrated and compared on an electronic Duffing oscillator and a clamped thin plate featuring geometrical nonlinearity. Finally, the current state of the art is reflected upon, and the challenges lying ahead for this growing field are discussed.

Disciplines :

Mechanical engineering
Aerospace & aeronautics engineering
Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

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

Abeloos, Gaëtan ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

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

Language :

English

Title :

Experimental continuation in nonlinear dynamics: recent advances and future challenges

Publication date :

24 November 2024

Journal title :

Nonlinear Dynamics

ISSN :

0924-090X

eISSN :

1573-269X

Publisher :

Springer Science and Business Media LLC

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/s11071-024-10543-9.pdf

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding text :

Gaëtan Abeloos and Ghislain Raze are a FRIA Grantee and a Postdoctoral Researcher, respectively, of the Fonds de la Recherche Scientifique - FNRS, which is gratefully acknowledged.

Data Set :

Experimental data from “experimental continuation in nonlinear dynamics: recent advances and future challenges”

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