1. Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches
- Author
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Arthur Givois, Mathieu Colin, Olivier Thomas, Claude-Henri Lamarque, Alireza Ture Savadkoohi, Vinciane Guillot, Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS), Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), Conservatoire National des Arts et Métiers [CNAM] (CNAM), and ANR-10-LABX-0060,CeLyA,Lyon Acoustics Centre(2010)
- Subjects
Acoustics ,vibration control ,Bimorph ,Aerospace Engineering ,02 engineering and technology ,01 natural sciences ,Mécanique: Vibrations [Sciences de l'ingénieur] ,Harmonic balance ,0203 mechanical engineering ,Normal mode ,0103 physical sciences ,Unimorph ,internal resonance ,General Materials Science ,[NLIN]Nonlinear Sciences [physics] ,010301 acoustics ,Nonlinear beam ,Physics ,[PHYS]Physics [physics] ,[PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] ,Vibration control ,Mechanical Engineering ,Modal energy exchange ,modal energy exchange ,experiments ,[PHYS.MECA]Physics [physics]/Mechanics [physics] ,[PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph] ,Vibration ,020303 mechanical engineering & transports ,Internal resonance ,Mechanics of Materials ,Harmonics ,Automotive Engineering ,Harmonic ,piezoelectric ,Piezoelectric ,Experiments ,Beam (structure) - Abstract
International audience; 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.
- Published
- 2020
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