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Stability and bifurcation analysis of a Van der Pol–Duffing oscillator with a nonlinear tuned vibration absorber
Habib, Giuseppe; Kerschen, Gaëtan
20148th European Nonlinear Dynamics Conference
 

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Abstract :
[en] The Van der Pol (VdP) oscillator is a paradigmatic model for description of self-excited oscillations, which are of practical interest in many engineering applications. In this paper the dynamics of a VdP-Duffing (VdPD) oscillator with an attached nonlinear tuned vibration absorber (NLTVA) is considered; the NLTVA has both linear and nonlinear restoring force terms. In the first part of this work, the stability of the trivial solution of the system is investigated, following results of previous works. The analysis allows to define an optimal tuning rule for the linear parameters of the absorber, which substantially enlarges the domain of safe operation of the primary system. In this case, the system loses stability through a double Hopf bifurcation. In the second part of this work, the bifurcations occurring at the loss of stability are analytically investigated, using the technique of the center manifold reduction and transformation to normal form. The obtained results show the effects of the nonlinear parameter of the absorber, which, in turn, allows to define its optimal value in order to avoid subcriticality and reduce the amplitude of self-excited oscillations.
Research center :
Structural Dynamics Research Group
Disciplines :
Mechanical engineering
Author, co-author :
Habib, Giuseppe ;  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 :
Stability and bifurcation analysis of a Van der Pol–Duffing oscillator with a nonlinear tuned vibration absorber
Publication date :
July 2014
Event name :
8th European Nonlinear Dynamics Conference
Event place :
Vienna, Austria
Event date :
from 06-07-2014 to 11-07-2014
Audience :
International
Funders :
ERC Starting Grant NoVib-307265
Available on ORBi :
since 13 May 2014

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