Analysis of a reduced-order nonlinear model of a multi-physics beam

Guillot, Vinciane; Savadkoohi, Alireza Ture; Lamarque, Claude‐Henri

doi:10.1007/s11071-019-05054-x

Cited by 7 publications

(15 citation statements)

References 32 publications

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“…Moreover, we assume a linear PZT constitutive law, mostly because no available numerical values for those parameters are available in the literature. As shown in the Appendix 1 section and in Guillot et al (2019), the axial/bending coupling due to an asymmetry of the lamination of the beam (this is the case for the unimorph configuration (Ducarne et al, 2012)) is exactly canceled by the inextensibility property.…”

Section: Theoretical Modelingmentioning

confidence: 86%

“…The governing electromechanical equations of the system, involving the transverse displacement v ( x , t ), where t is the time, and the voltage V ( t ) across the PZT patches, can be written aswhere [v′]x1x2=v′(x2)−v′(x1) as observed in Ducarne et al (2012) and Guillot et al (2019).…”

Section: Theoretical Modelingmentioning

confidence: 99%

“…The linear part of the governing equation (2) is now considered in short circuit ( V = 0)and the associated eigenmodes of the stepped beams (the mass and stiffness addition of the PZT patches are included) are computed, as explained in Ducarne et al (2012) and Guillot et al (2019). To be rigorous, in the case of the unimorph configuration, which has a nonsymmetric lamination, the linear axial/bending coupling, not present in equation (4) because of the inextensibility condition, is included in those computations, as explained in Ducarne et al (2012).…”

Section: Theoretical Modelingmentioning

confidence: 99%

“…Modal linear damping terms of coefficients μ 1 and μ 2 have been added in the aforementioned equations. Moreover, the analytical expressions of all the N i , M i , i = 2, …, 12 coefficients can be found in Guillot et al (2019). They are here computed according to the geometrical and material parameters of the systems under study.…”

Section: Theoretical Modelingmentioning

confidence: 99%

See 3 more Smart Citations

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

Guillot

Givois

Thomas

et al. 2020

Journal of Vibration and Control

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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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Section: Theoretical Modelingmentioning

confidence: 86%

Section: Theoretical Modelingmentioning

confidence: 99%

Section: Theoretical Modelingmentioning

confidence: 99%

Section: Theoretical Modelingmentioning

confidence: 99%

See 2 more Smart Citations

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

Guillot

Givois

Thomas

et al. 2020

Journal of Vibration and Control

Self Cite

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show abstract

“…It should be mentioned that in this study we did not take into account possible internal resonances (Nayfeh and Balachandran, 1989) or multimodal interactions of the system (Abdelkefi et al, 2012; Garg and Dwivedy, 2019; Guillot et al, 2019, 2020; Lee et al, 2008). Moreover, the effects of inherent nonlinearities of the piezoelectric patch (Guyomar et al, 1997; Mam et al, 2016; Parashar and Wagner, 2004; Stanton et al, 2010) which follow the large deflection of the beam are also ignored.…”

Section: Discussionmentioning

confidence: 99%

Study of an electromechanical nonlinear vibration absorber: Design via analytical approach

Guillot

Savadkoohi

Lamarque

2020

Journal of Intelligent Material Systems and Structures

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This article deals with the behavior and design of a homogeneous beam linked to an electrical absorber, via a piezoelectric material patched on the beam. The beam presents a cubic nonlinearity, which is consistent with geometrical nonlinearities for clamped-free beams. A cubic nonlinearity is added to the electrical circuit for similarity purposes. The coupled electromechanical equations are reduced to a two degrees of freedom system. The equation representing the mechanical response of the system is seen as the main system, whereas the equation coming from the electrical circuit would represent a nonlinear absorber. An analytical treatment at different time scales is endowed to identify electrical coefficients allowing the design of the electromechanical vibration absorber behavior. The equilibrium and singular points are identified, allowing the definition of ranges of forcing amplitudes leading to periodic and modulated regimes. The analytical results are compared with those obtained from direct numerical integration of the two degree of freedom system.

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Tuning inter-modal energy exchanges of a nonlinear electromechanical beam by a nonlinear circuit

2022

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A model of a nonlinear beam with a piezoelectric patch linked to a nonlinear circuit is considered. The physical and mechanical parameters of the system are such that it presents a 1:3 internal resonance. The aim is to study, for different time scales, the effect of the nonlinearity of the electrical circuit on energy exchanges between the resonant modes. In fact, we would like to master energy channelling between two internally resonant modes of a composite beam via a nonlinear circuit. The investigations are carried out on the projected system equations on its internally resonant modes. The system behaviours at different scales of time are studied by coupled methods of complexification and multiple scale. Analytical developments permit to reveal different system dynamics characterized by periodic and/or non periodic regimes. Finally, the paper is accompanied by comparisons between systems equipped with a resonant circuit (linear) and a nonlinear one.

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Analysis of a reduced-order nonlinear model of a multi-physics beam

Cited by 7 publications

References 32 publications

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

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

Study of an electromechanical nonlinear vibration absorber: Design via analytical approach

Tuning inter-modal energy exchanges of a nonlinear electromechanical beam by a nonlinear circuit

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