Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink

Bergeot, Baptiste; Bellizzi, Sergio; Berger, Sébastien

doi:10.1016/j.cnsns.2020.105623

Cited by 20 publications

(11 citation statements)

References 36 publications

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“…, N ), related to the stable modes, tend to zero. When the coupling term (which is of the order of magnitude of ) is taken into account, the variables q n and q n do not vanish but their contributions are very small and can be neglected [12,23,24]. Consequently, all terms related to q n and q n (with n = 2, .…”

Section: Reduction Of the Dynamicsmentioning

confidence: 99%

“…The center manifold reduction technique (as presented for example in [30,31]) is used in this section to reduce the slow flow (24), in the vicinity of the left fold point (r LF , s LF , ∆ LF ), to the normal form of the dynamic saddle-node bifurcation which is then solve to deduce the nontrivial scaling law previously mentioned.…”

Section: Center Manifold Reduction Of the Slow Flow At The Left Fold Pointmentioning

confidence: 99%

“…First, a network of parallel NESs coupled to a Van der Pol oscillator has been analyzed in [22] and then the prediction of the steady-state regimes of a multi-DOF dynamical system having one unstable mode and coupled to a set of NESs has been performed in [23]. Finally, in a recent paper, the possibility of mitigating simultaneously two unstable modes of a linear multi-DOF primary system using a single NES has been investigated by Bergeot et al [24]. The asymptotic analysis proposed in the latter reference reveals that the NES attachment can produce several and complex mitigated responses which results from the presence of several stable solutions and from the competition between them.…”

Section: Introductionmentioning

confidence: 99%

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Scaling law for the slow flow of an unstable mechanical system coupled to a nonlinear energy sink

Bergeot

2021

Journal of Sound and Vibration

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In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the dynamic saddle-node bifurcation. This allows us to then obtain a scaling law for the slow flow dynamics and to improve the accuracy of the theoretical prediction of the mitigation limit of the NES previously obtained as part of a zeroth-order approximation. For that purpose, the governing equations of the coupled system are first simplified using a reduced-order model for the primary structure by keeping only its unstable modal coordinates. The slow flow is then derived by means of the complexificationaveraging method and, by the presence of a small perturbation parameter related to the mass ratio between the NES and the primary structure, it appears as a fast-slow system. The center manifold theorem is finally used to obtain the reduced form of the slow flow which is solved analytically leading to the scaling law. The latter reveals a nontrivial dependence with respect to the small perturbation parameter of the slow flow dynamics near the fold point, involving the fractional exponents 1/3 and 2/3. Finally, a new theoretical prediction of the mitigation limit is deduced from the scaling law. In the end, the proposed methodology is exemplified and validated numerically using an aeroelastic aircraft wing model coupled to one NES.

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Section: Reduction Of the Dynamicsmentioning

confidence: 99%

Section: Center Manifold Reduction Of the Slow Flow At The Left Fold Pointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scaling law for the slow flow of an unstable mechanical system coupled to a nonlinear energy sink

Bergeot

2021

Journal of Sound and Vibration

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“…This TET is usually achieved through single or cascade of resonance captures with the associated linear primary structure [1]. There are comprehensive reviews of state-of-the-art researches on NESs [4][5][6][7], monographs [8,9], and numerous articles on this problem [10][11][12][13]. Nonlinear energy sinks have attracted much attention because of their ability to achieve energy-targeted transfer under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Lizunov

Pogorelova

Postnikova

2022

OMTC

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The nonlinear energy sink (NES) is defined as a single-degree-of-freedom structural element with relatively small mass and weak dissipation, attached to a primary structure via essentially nonlinear coupling. It is a passive energy dissipation device designed to rapidly absorb vibration energy (due to shock, blast, earthquakes, etc.) from a primary structure and locally dissipate it. The article contains a mini-review of the works on NESs. Design schemes for single-sided and double-sided vibro-impact NESs (SSVI and DSVI NESs) are proposed on the basis of conceptual and design NES schemes that exist in the world scientific literature. The motion equations and the impact rule are given. The quasistatic Hertz contact law is adopted as the impact rule. Various representations of the impulsive loading on the primary structure are discussed. These are excitations by initial velocities only, periodic excitation, a shock in the half-sine form, single-sided periodic impulses of a rectangular shape,wind, seismic and broadband excitation. The Tables of some numerical parameters that can be accepted for VI NES are given. Using the presented data, the authors intend to investigate both the efficiency of SSVI and DSVI NESs under different types of impulsive load, and their dynamical behavior with the changing in their parameters.

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“…This kind of absorber with strong nonlinearity is called a nonlinear energy sink (NES). At present, the NES has been used in the mitigation of relaxation oscillation of moving belt systems [6], shock vibration of fluid-conveying pipes [7], transverse vibration of flexible bladed rotor systems [8], and stochastic vibration of two-story shear buildings [9].…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Bistable Nonlinear Energy Sink Based on Global Vibration Control

Wang

Ding

Chen

2021

Preprint

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Although a linear vibration absorber (LVA) or nonlinear energy sink (NES) can effectively mitigate the vibration of the main system in harmonic excitation, the amplitude of the absorber can be very large. Using the single-objective differential evolutionary (DE) algorithm, this paper pioneers the global control of the main system and a bistable NES to achieve decent vibration mitigation effects and decrease the global response of the system. Using the multi-objective DE algorithms and comparing the optimization results of the LVA, this paper proposes multi-objective and multi-parameter design criteria of a bistable NES. The mass ratio, the displacement amplitude, and the mechanical energy are optimization goals. The results show that the maximum amplitude of the main system and the absorber can be controlled at the same level, and the global control strategy does not change the resonance frequency of the main system. Compared with the LVA, the bistable NES has similar vibration mitigation effects with the variation of the mass ratio in the multi-objective optimization. However, the bistable NES can achieve better control over a larger spring stiffness range. Therefore, through single- and multi-objective optimization design, this paper proves the superiority of the bistable NES in the vibration mitigation. Meanwhile, this paper provides an optimization design method for global vibration control.

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Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink

Cited by 20 publications

References 36 publications

Scaling law for the slow flow of an unstable mechanical system coupled to a nonlinear energy sink

Scaling law for the slow flow of an unstable mechanical system coupled to a nonlinear energy sink

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Optimal Design of Bistable Nonlinear Energy Sink Based on Global Vibration Control

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