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Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

Article dans une revue avec comité de lecture
Author
DENIS, V.
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
JOSSIC, M.
541882 Institut Jean Le Rond d'Alembert [DALEMBERT]
CHOMETTE, B.
541882 Institut Jean Le Rond d'Alembert [DALEMBERT]
RENAULT, A.
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
ccTHOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
ccGIRAUD-AUDINE, Christophe
13338 Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697 [L2EP]

URI
http://hdl.handle.net/10985/15358
DOI
10.1016/j.ymssp.2018.01.014
Date
2018
Journal
Mechanical Systems and Signal Processing

Abstract

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabiliz the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

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