Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Bergeot, Baptiste; Bellizzi, Sergio

doi:10.1016/j.ymssp.2019.05.045

Cited by 22 publications

(21 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Set of NESs were recently proposed for passive mitigation of dynamic instability in discrete systems [10,11]. Nonlinear SDOF and MDOF primary systems were considered, respectively, providing the socalled mitigation limit of the NESs, i.e., the value of a chosen bifurcation parameter which separates harmful situations from harmless situations.…”

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

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: 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

“…tend to zero). When the coupling term f (q, v,v), which is of the order of magnitude of , is taken into account, the variables q 3 , q * 3 , q 4 and q * 4 do not vanish but their contributions remain minimal and can be neglected [9,22]. Consequently, all the terms related to q 3 , q * 3 , q 4 and q * 4 will be omitted in the following developments.…”

Section: The Reduced Modelmentioning

confidence: 99%

“…A network of parallel NES coupled to a Van der Pol oscillator has been considered in [21]. The prediction of the steady-state regimes of a multi-degree-of-freedom dynamical system having one unstable mode coupled to a set of NES has been performed in [22].…”

Section: Introductionmentioning

confidence: 99%

“…As for the primary system, the retained model, a simple 4-DOF friction system involving two unstable modes, has been introduced in [32] and used in [33] to illustrate different stability behaviors characterized by mode coupling having coalescence patterns. Based on the procedure presented in [22], we provide an analytic framework for characterizing the response regimes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Bergeot

Bellizzi²,

Berger³

2021

Communications in Nonlinear Science and Numerical Simulation

Self Cite

View full text Add to dashboard Cite

This paper investigates a problem of passive mitigation of vibratory instabilities caused by two unstable modes by means of a single nonlinear energy sink (NES). For this purpose, a linear four-degree-of-freedom (DOF) primary structure having two unstable modes (reproducing the typical dynamic behavior of a friction system) and undergoing, as it is linear, unbounded motions when it is unstable, is coupled to a NES. In this work, the NES involves an essentially cubic restoring force and a linear damping force. We are interested in characterizing analytically the response regimes resulting from the coupling of the two unstable linear modes of the primary structure and the nonlinear mode of the NES. To this end, from a suitable rescaling of the governing equations of the coupled system in which the dynamics of the primary structure is reduced to its unstable modal coordinates, the complexification-averaging method is applied. The resulting averaged system appears to be a fast-slow system with four fast variables and two slow ones related to the two unstable modes of the primary structure. The critical manifold of the averaged dynamics is obtained through the geometric singular perturbation theory and appears as a two-dimensional parametric surface (with respect to two of the four fast variables) which evolves in the whole six-dimensional variable space. The asymptotic analysis reveals that the NES attachment can produce some bounded responses and suggests that the system may have simultaneous stable attractors. Numerical simulations complement the study, highlighting a possible competition between stable attractors and allowing us to investigate their basins of attraction. In each considered situation, a good agreement has been observed between theoretical results and numerical simulations, which validates the proposed asymptotic analysis.

show abstract

“…Again the regimes described above have been observed and authors proposed analytical approach which allows to explain and predict some them. The difficulties encountered to differentiate, in the parameters space, mitigated situations from unmitigated situations have been solved in Bergeot and Bellizzi (2019). It has been shown that the transition from mitigated regimes to unmitigated regimes with respect to a parameter variation can involve a discontinuity in the steady-state amplitude profiles.…”

Section: Introductionmentioning

confidence: 99%

Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach

Snoun

Bergeot

Berger

2020

European Journal of Mechanics - A/Solids

Self Cite

View full text Add to dashboard Cite

In this paper, a friction system with uncertain parameters and coupled to two Nonlinear Energy Sinks (NESs) is studied. The dispersion of some physical parameters due to their uncertain nature may generate a dynamic instability which leads to a Limit Cycle Oscillations (LCO) causing a propensity of squeal. The concept of Targeted Energy Transfer (TET) by means of NESs to mitigate this squealing noise is proposed. In this kind of unstable dynamical system coupled to NES, the transition from harmless regimes (i.e. the LCO is mitigated) to harmful regimes (i.e. the LCO is not mitigated) as a function of the uncertain parameters implies a discontinuity in the steady-state amplitude profiles. In this context, a Multi-Element generalized Polynomial Chaos (ME-gPC) based method is proposed to locate this discontinuity (called mitigation limit) and therefore to predict the Propensity of the system to undergo an Harmless Steady-State Regime (PHSSR). The results obtained with this original method lead to a good compromise between computational cost and accuracy in comparison with a reference method.

show abstract

Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Cited by 22 publications

References 39 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

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

Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach

Contact Info

Product

Resources

About