Resonant phase lags
of nonlinear mechanical systems

Abstract

The concept of a resonance is central in structural dynamics, because the maximum amplitude at which a system vibrates occurs near resonance frequencies. Unlike linear systems, nonlinear systems can exhibit different types of resonances including primary and secondary (superharmonic, subharmonic, ultra-subharmonic) resonances. An effective theoretical framework to characterize nonlinear resonances is nonlinear modal analysis, which has been developed since more than half a century. In this context, primary resonances received the most attention whereas very little effort was devoted to the characterization of secondary resonances.

This thesis is an attempt to answer two key questions: (i) How to define the primary and secondary resonances of a nonlinear system? and (ii) How to characterize these resonances analytically, numerically and experimentally? To answer the former question, the concept of a resonant phase lag associated with the amplitude resonance of the  -th harmonic of the  :  resonance is proposed. For the latter question, a new definition of a nonlinear normal mode termed phase resonance nonlinear mode which corresponds to the structural deformation at the resonant phase lag is introduced. These novel concepts are introduced based on analytical investigations, validated numerically on single- and multiple-degree-of-freedom nonlinear systems and demonstrated experimentally on two beam structures thanks to phase-locked loop testing.

Jury members

• J-P. PONTHOT, Université de Liège, Président;
• G. KERSCHEN, Université de Liège, Promoteur;
• O. BRULS,  Université de Liège;
• L. SALLES, Université de Liège;
• O. THOMAS, ENSAM (France) ;
• C. TOUZE, ENSTA Paris (France) ;
• A. VAKAKIS, University of Illinois Urbana-Champaign (USA).

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