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.
Highlights
Piezoelectric (PZT) materials constitute an efficient mean of coupling mechanical vibrations to an electrical circuit
The aim of this work was to investigate experimentally the behavior of an elastic homogeneous beam equipped with PZT patches presenting a 1:3 internal resonance between modes
Because we focus in this article on a 1:3 internal resonance between the second and third modes of the structure, with a direct driving of the lower mode, the frequency bandwidth is defined around the second natural frequency ω2
Summary
Piezoelectric (PZT) materials constitute an efficient mean of coupling mechanical vibrations to an electrical circuit. Several applications are usually targeted such as micro/nano electromechanical systems (Bhugra and Piazza, 2017; Brand et al, 2015), vibration control (Bricault et al, 2019; Collet et al, 2008; Preumont, 2011; Soltani and Kerschen, 2015), and energy harvesting (Erturk and Inman, 2011; Jacquelin et al, 2011; Mam et al, 2016) In most of those cases, even if linear systems are traditionally considered for their simplicity, taking advantage of nonlinearities is of the most interest (Cao et al, 2015). When a primary structure is nonlinear, fully passive PZT nonlinear tuned vibration absorbers, that follow its change of frequency with the increasing vibration amplitude, have been recently proposed (Lossouarn et al, 2018) Another concept, the nonlinear energy sink, for which the absorber is intrinsically nonlinear, has been realized with a PZT shunt (Silva et al, 2018; Zhou et al, 2014), thanks to nonlinear electrical circuits
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