Impulsive vibration mitigation through a nonlinear tuned vibration absorber

Habib, Giuseppe; F, Kadar; Papp, Bálint

doi:10.1007/s11071-019-05312-y

“…As a last example, we consider a pitch-and-plunge wing profile with an attached nonlinear tuned vibration absorber, as the one studied in [10]. The pitch-and-plunge model considered, used to describe an airfoil motion, was implemented in various studies [49][50][51], while the nonlinear tuned vibration absorber is practically a tuned mass damper also encompassing a nonlinear restoring force [52][53][54]. Non-dimensional equations of motion governing the dynamics of the system are where…”

Section: Saddle-node Bifurcation Predictionmentioning

confidence: 99%

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Habib

¹

2023

Preprint

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This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories of a system obtained for parameters close to the saddle-node bifurcation present local minima of the logarithmic decrement trend in the vicinity of the bifurcation. By tracking the logarithmic decrement for these trajectories, the saddle-node bifurcation can be accurately predicted. The method does not strictly require any mathematical model of the system, but only a few time series, making it directly implementable for gray- and black-box models and experimental apparatus. The proposed algorithm is tested on various systems of different natures, including a single-degree-of-freedom system with nonlinear damping, the mass-on-moving-belt, a time-delayed inverted pendulum, and a pitch-and-plunge wing profile. Benefits, limitations, and future perspectives of the method are also discussed. The proposed method has potential applications in various fields, such as engineering, physics, and biology, where the identification of saddle-node bifurcations is crucial for understanding and controlling complex systems.

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“…As a last example, we consider a pitch-and-plunge wing profile with an attached nonlinear tuned vibration absorber, as the one studied in [10]. The pitch-andplunge model considered, used to describe an airfoil motion, was implemented in various studies [66][67][68], while the nonlinear tuned vibration absorber is practically a tuned mass damper also encompassing a nonlinear restoring force [69][70][71]. Non-dimensional equations of motion governing the dynamics of the system are…”

Section: Multi-dof System: Aeroelastic Fluttermentioning

confidence: 99%

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

Habib

2023

Nonlinear Dyn

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This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories of a system obtained for parameters close to the saddle-node bifurcation present local minima of the logarithmic decrement trend in the vicinity of the bifurcation. By tracking the logarithmic decrement for these trajectories, the saddle-node bifurcation can be accurately predicted. The method does not strictly require any mathematical model of the system, but only a few time series, making it directly implementable for gray- and black-box models and experimental apparatus. The proposed algorithm is tested on various systems of different natures, including a single-degree-of-freedom system with nonlinear damping, the mass-on-moving-belt, a time-delayed inverted pendulum, and a pitch-and-plunge wing profile. Benefits, limitations, and future perspectives of the method are also discussed. The proposed method has potential applications in various fields, such as engineering, physics, and biology, where the identification of saddle-node bifurcations is crucial for understanding and controlling complex systems.

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“…𝑏 2 [16,36]. As the dissipation power is proportional to the square of the relative NES amplitude of vibration, the SIM also expresses the performance of an NES.…”

Section: Dissipation Powermentioning

confidence: 99%

The periodically extended stiffness nonlinear energy sink

Dekemele

¹

,

Habib

²

,

Loccufier

³

2022

Mechanical Systems and Signal Processing

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Conventional nonlinear energy sinks (NES) are considered to be a more robust alternative to linear vibration absorbers such as the tuned-mass-damper (TMD). While the conventional NES has a larger efficient frequency bandwidth than the TMD, it is only really efficient for a small energy range. This implies a deterioration of the NES's mitigation properties if the primary system's amplitude varies. To overcome this issue, other researchers resort to increasing the complexity of the NES by adding degrees-of-freedom. Here, another line of thought is presented, by proposing an unconventional stiffness characteristic. To increase the energy bandwidth the NES in this paper features a non-smooth, periodically extended stiffness characteristic. This NES is attached to an uncertain primary system and its performance is compared with that of the conventional NES and of the TMD by deriving the slow invariant manifolds (SIMs) in transient 1:1 resonance. The SIMs are curves that relate the vibration amplitudes of the primary system and the NES, and serve as an easy and computationally efficient tool to analyze performance. The research in this paper will prove that the newly proposed NES can be both robust regarding energy and frequency uncertainty, by considering the novel periodically extended stiffness characteristic.

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Impulsive vibration mitigation through a nonlinear tuned vibration absorber

Cited by 15 publications

References 51 publications

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

The periodically extended stiffness nonlinear energy sink

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