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Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches

Article dans une revue avec comité de lecture
Author
GUILLOT, Vinciane
698 Laboratoire de Tribologie et Dynamique des Systèmes [LTDS]
GIVOIS, Arthur
12568 Laboratoire de Mécanique des Structures et des Systèmes Couplés [LMSSC]
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
COLIN, Mathieu
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
THOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
TURE SAVADKOOHI, Alireza
698 Laboratoire de Tribologie et Dynamique des Systèmes [LTDS]
79190 École Nationale des Travaux Publics de l'État [ENTPE]
217773 Laboratoire Génie Civil et Bâtiment [LGCB]
300365 École Nationale des Travaux Publics de l'État [ENTPE]
301088 Université de Lyon
LAMARQUE, Claude-Henri
698 Laboratoire de Tribologie et Dynamique des Systèmes [LTDS]
1386 Département génie civil et batiment [DGCB]
33137 Laboratoire Géomatériaux [DGCB-LGM]
79190 École Nationale des Travaux Publics de l'État [ENTPE]
217773 Laboratoire Génie Civil et Bâtiment [LGCB]
300365 École Nationale des Travaux Publics de l'État [ENTPE]
301088 Université de Lyon

URI
http://hdl.handle.net/10985/22676
DOI
10.1177/1077546320910536
Date
2020-03
Journal
Journal of Vibration and Control

Abstract

Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.

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