Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect

Shami, Zein Alabidin; Shen, Yichang; Giraud-Audine, Christophe; Touzé, Cyril; Thomas, Olivier

doi:10.1007/s11012-022-01566-w

Cited by 14 publications

(13 citation statements)

References 55 publications

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“…Recently, a new semi-passive absorber, introduced in [19] and realized experimentally in [20], exploited a two-toone (2:1) internal resonance and a saturation phenomenon by adding a quadratic nonlinear component in a classical RL-shunt. This concept was improved to correct an unwanted detuning by adding a cubic component, as shown theoretically in [21] and experimentally in [22].…”

Section: Introductionmentioning

confidence: 99%

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

2023

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In this article, we propose a new concept for tuning a resonant piezoelectric shunt absorber thanks to the use of a nonsmooth electronic component. It consists in adding in the resonant shunt circuit a voltage source which is a bilinear function of the voltage across the piezoelectric patch. The main advantage is the ability to change the electrical resonance frequency with the bilinear component gain, enabling a tuning as well as a possible reduction of the required inductance value. Because of the intrinsic nonlinear nature of the bilinear component, a multi-harmonic response is at hand, leading to a nonlinear coupling between the mechanical and electrical modes. Two particular tunings between the electrical and the mechanical resonance frequencies are tested. The first one is one-to-one, for which the electrical resonance is tuned close to the mechanical one. It is proved to be similar to a classical linear resonant shunt, with the additional tuning ability. The second case consists in tuning the electrical circuit at half the mechanical resonance, leading to a two-to-one (2:1) internal resonance. The obtained response is also found to be similar to a classical resonant shunt near the main resonance. In either case, the shunt performances are analytically and numerically studied, leading to optimal values of the design parameters as well as an estimation of the amplitude reduction provided by the shunt. Finally, experimental validation is proposed, targeting the damping of the twisting mode of a hydrofoil structure, in which the bilinear component is realized with a diode.

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Section: Introductionmentioning

confidence: 99%

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

2023

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“…This saturation effect has been shown to be helpful in various fields of application and is a known to be related to subharmonic solutions (see e.g. [32][33][34] and references therein).…”

Section: Introductionmentioning

confidence: 99%

On the stability of pairs of subharmonic centrifugal pendulum vibration absorbers allowing a rotational mobility

MAHE

Renault

Grolet

et al. 2023

Preprint

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Centrifugal pendulum vibration absorbers (CPVAs) are passive devices used to reduce torsional vibrations in rotating machines. Previous works showed that a CPVA configuration with two pendulums oscillating in phase-opposition and at half the excitation frequency is efficient in reducing the rotor's vibrations. This paper deals with a new generation of CPVAs, in which the pendulums admit a rotational motion relative to the rotor in addition to the traditional translational motion. The aim of this study is to assess the dynamic stability of a particular subharmonic solution of CPVAs composed of several pairs of pendulum. To do so, a new method based on an analytical perturbation technique is proposed. It leads to more general conclusions than previous studies as the results are derived for CPVAs with any even number of pendulums. The validity of the analytical model is confirmed through a comparison with a numerical resolution of the system's dynamics, and new design guidelines are proposed.

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“…The effect of the unwanted nonlinear quadratic coupling terms was recently investigated in theory in [41]. It was proven using the normal form theory that they are equivalent to cubic nonlinearities and that their effect is equivalent to the hardening/softening effect brought by the cubic nonlinear term of a classical Duffing oscillator.…”

Section: Introductionmentioning

confidence: 99%

“…The present article is specifically devoted to the experimental proof of concept of this idea. We first recall in section 2 the main ideas of the underlying theory, already exposed in detail in [18,41]. Then, section 3 is devoted to the experimental proof of concept.…”

Section: Introductionmentioning

confidence: 99%

Saturation correction for a piezoelectric shunt absorber based on 2:1 internal resonance using a cubic nonlinearity

Shami

Giraud-Audine

Thomas

2023

Smart Mater. Struct.

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In this study, we present a theoretical and experimental analysis of an antiresonance detuning correction for a nonlinear piezoelectric shunt absorber based on a two-to-one internal resonance. Thanks to this purely nonlinear feature, the oscillations of the primary system become independent of the forcing at a particular antiresonance frequency, thus creating an eﬃcient reduction of the vibration. Past works of the literature present the design of the piezoelectric shunt and show that it is subjected to a softening behavior that detunes the antiresonance frequency as a function of the amplitude and thus degrades the performance. It is also shown that this softening behavior is caused by some non-resonant terms present in the equations, linked to the piezoelectric coupling. To counteract this undesired eﬀect, we propose in this work to add a cubic nonlinearity in the shunt circuit, in addition to the quadratic one already present. Its tuning is based on a normal form analysis already published, which shows how cubic nonlinearities can cancel the eﬀect of quadratic non-resonant terms. The present article focuses on the experimental proof of concept of this antiresonance detuning correction as well as the analysis of its range of validity. It is applied to the damping of the ﬁrst bending mode of a hydrodynamic foil structure.

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Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect

Cited by 14 publications

References 55 publications

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

On the stability of pairs of subharmonic centrifugal pendulum vibration absorbers allowing a rotational mobility

Saturation correction for a piezoelectric shunt absorber based on 2:1 internal resonance using a cubic nonlinearity

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