A nonlinear piezoelectric shunt absorber with a 2:1 internal resonance: Theory

Shami, Zein Alabidin; Giraud-Audine, Christophe; Thomas, Olivier

doi:10.1016/j.ymssp.2021.108768

Cited by 27 publications

(67 citation statements)

References 72 publications

(115 reference statements)

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“…In this section, a summary of the main equations that govern the electromechanical system is illustrated. The full theoretical model with numerical and analytical results is outlined in our previous paper [1], and only the main points are recalled here. We consider an arbitrary elastic structure subjected to an external excitation and connected to a nonlinear shunt circuit via a piezoelectric (PE) patch as shown in figure 1.…”

Section: Governing Equationsmentioning

confidence: 99%

“…V nl = βQ 2 ). As shown in [1], this latter choice would lead to a huge value of β (of the order of 10 15 V/C 2 ) to achieve the absorber's design conditions, unrealistic in practice. One has thus:…”

Section: Governing Equationsmentioning

confidence: 99%

“…This could lead to large amounts of stress, fatigue, and noise, especially for lightweight structures, reducing their life cycle and the comfort of their users. This article proposes the experimental proof of concept of an original nonlinear piezoelectric shunt vibration absorber, theoretically introduced in [1], and based on an intentional * Author to whom any correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

“…ω k /ω l ≃ n/m with n, m ∈ N * ), a strong coupling between the two corresponding modes is likely to occur, enabling to transfer energy from one mode to the other. As explained in [1], the present article focus on the intentional use of a 2:1 internal resonance, that is activated by the presence of quadratic nonlinearities in the system, leading to an energy transfer from the driven mode (of natural frequency ω 2 ), to a mode tuned at half this frequency (of natural frequency ω 1 ≃ ω 2 /2). This leads to two important features:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

Shami

Giraud-Audine

Thomas

2022

Smart Mater. Struct.

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An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

Shami

Giraud-Audine

Thomas

2022

Smart Mater. Struct.

Self Cite

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“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [66,137,251], piezoelectric material nonlinearities [60,138,299], non-local models for nanostructures [239,240], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,268] with applications to blades [77,225,227,272], large strain elastic nonlinear constitutive laws [188], fluid-structure interaction [105,166] and coupling with nonlinear aeroelastic forces [46]; or thermal effects [97,220], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization could be also used with such tools [63,292,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Touzé,

Vizzaccaro,

Thomas

2021

Preprint

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This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes (NNMs) and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations (PDE). They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then the specific case of structures discretized with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models (ROMs) relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

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Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method

Raze,

Volvert,

Kerschen

2023

Numerical Meth Engineering

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This work proposes a novel efficient method to track the evolution of amplitude extrema featured by frequency responses of nonlinear systems using the harmonic balance method. Means to compute the amplitude of a Fourier series are first outlined, and a set of equations characterizing a local extremum of a nonlinear frequency response amplitude curve is derived. Efficient numerical procedures are used to evaluate these equations and their derivatives (including second‐order ones) to embed them in a predictor‐corrector continuation framework. The proposed approach is illustrated on three examples of increasing complexity, namely a Helmholtz–Duffing oscillator, a two‐degree‐of‐freedom system with a modal interaction, and a doubly clamped von Kàrmàn beam with a nonlinear tuned vibration absorber.

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A nonlinear piezoelectric shunt absorber with a 2:1 internal resonance: Theory

Cited by 27 publications

References 72 publications

A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method

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