Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches. (5th March 2020)

• Record Type: Journal Article
• Authors: Guillot, Vinciane; Givois, Arthur; Colin, Mathieu; Thomas, Olivier; Ture Savadkoohi, Alireza; Lamarque, Claude-Henri
• Other Names: Benjeddou Ayech guest-editor.; Mechbal Nazih guest-editor.; Deü Jean-François guest-editor.
• Is Part Of: Journal of vibration and control. Volume 26:Number 13/14(2020)
• Page Start: 1119
• Page End: 1132
• Publication Date: 2020-03-05
• Subjects: Nonlinear beam -- internal resonance -- vibration control -- piezoelectric -- modal energy exchange -- experiments; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546320910536
• Languages: English
• ISSNs: 1077-5463

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.