Performance and tuning of a chaotic bi-stable NES to mitigate transient vibrations

Dekemele, Kevin; Torre, Patrick Van; Loccufier, Mia

doi:10.1007/s11071-019-05291-0

Cited by 36 publications

(17 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If only one mode of the primary system is activated, the dynamics of the system can be approximately reduced to that of a single DoF with an attached NES. This case was extensively studied in the literature with similar techniques [13][14][15][16]18]; therefore, here we only recall its main features. Figure 1 illustrates the four different manifolds (which are actually sections of the SIM), each one represented in the a h , b h space, for a j = 0 if j = h (i.e., the other modes are assumed null).…”

Section: Study Of the Manifoldmentioning

confidence: 99%

“…In further recent studies [13,14], the RCC phenomenon was again addressed in order to guide NES design by identifying a tuning procedure and predicting the so-called cascading time. The latter studies hinge on the single-mode SIM which is derived for the general case of NES stiffness (odd) polynomial nonlinearity and small positive or negative linear part.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tracking modal interactions in nonlinear energy sink dynamics via high-dimensional invariant manifold

Habib

Romeo

2020

Nonlinear Dyn

View full text Add to dashboard Cite

A nonlinear energy sink (NES), conceived to mitigate the vibrations of a multi-degree-of-freedom host mechanical system, is considered. The high-dimensional slow invariant manifold (SIM) describing the high-amplitude slow dynamics of the system is derived and exploited to interpret its transient regimes caused by impulsive excitation. It is shown that algebraic expressions derived from the SIM formulation enable to identify the so-called interaction points, providing the conditions in which two modes of the primary system interact and share energy through the nonlinear absorber. Moreover, the mutual effect of differently activated host system modes on the NES energy dissipation mechanism is discussed. Through sections of the multidimensional SIM, modal interaction triggering resonance capture cascades (RCC) can be effectively explained. The dissipation capabilities are eventually assessed in order to evaluate the efficiency of the RCC regime.

show abstract

Section: Study Of the Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tracking modal interactions in nonlinear energy sink dynamics via high-dimensional invariant manifold

Habib

Romeo

2020

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…4). As shown in [35], this unstable part of the branch has a significant effect on the TET in the system. In addition, Fig.…”

Section: Fep Using Complexification Averaging Techniquementioning

confidence: 92%

Frequency-Energy Plots of Bistable Nonlinear Energy Sink

Shudeifat¹,

Saeed²

2021

Preprint

View full text Add to dashboard Cite

The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as Bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency-energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out of- phase backbone branches, especially at low energy levels. The wavelet transform is imposed into the FEP for variety of initial conditions and damping content and it is found that the FEP has backbone branches at low energy levels associated with the oscillation of the bistable attachments about one of its stable equilibrium positions where passage through the unstable equilibrium position does not occur.

show abstract

“…When investigating the vibration mitigation effect of the NES, the selection of performance measures is very important. In different excitation conditions, researchers adopted different or even multiple indexes, e.g., energy dissipation rate and energy decaying duration in impulsive excitation [28][29][30][31], amplitude of the main system, energy dissipation rate of the NES, energy of the entire system, and transmissibility in harmonic excitation [23,26,32,33], transition probability densities of transmissibility and input energy absorption percentage of the main system in combined harmonic and random excitation [34], and displacement, acceleration, and shear force of the main system in seismic excitation [9,35]. From these studies, the vibration mitigation effect of the NES in harmonic excitation is mainly judged by the absolute number and rate of amplitude and energy.…”

Section: Introductionmentioning

confidence: 99%

Performance evaluation and design criterion of a bistable nonlinear energy sink

Ding

Wang

Chen

2021

Preprint

View full text Add to dashboard Cite

In the evaluation of the vibration mitigation effect of a nonlinear energy sink (NES), the selection of performance measures is important. Based on a square root model, this paper aims to propose new reasonable performance measures and new design criteria of the NES in harmonic excitation. To broaden the application range of the slow invariant manifold, coordinate correction is carried out for the square root model of the bistable NES. Two original performance measures (the displacement amplitude of the main system and the energy dissipation rate of the NES) and two new performance measures (the mechanical energy and the input energy of the main system) are compared. The optimal geometric configuration and response form of the NES are found in different excitation conditions. The results show that the energy dissipation rate of the NES is not competent to evaluate the performance of the NES in harmonic excitation, while the two new performance measures show competence. By adjusting the geometry parameter, the nonlinear vibration absorber with positive linear stiffness and the bistable NES show optimal vibration mitigation effect in small and large excitation amplitudes, respectively. The optimal response form is the periodic response rather than the strongly modulated response.

show abstract

Performance and tuning of a chaotic bi-stable NES to mitigate transient vibrations

Cited by 36 publications

References 26 publications

Tracking modal interactions in nonlinear energy sink dynamics via high-dimensional invariant manifold

Tracking modal interactions in nonlinear energy sink dynamics via high-dimensional invariant manifold

Frequency-Energy Plots of Bistable Nonlinear Energy Sink

Performance evaluation and design criterion of a bistable nonlinear energy sink

Contact Info

Product

Resources

About