Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Papangelo, Antonio; Grolet, Aurélien; Salles, Loïc; Hoffmann, Norbert; Ciavarella, M.

doi:10.1016/j.cnsns.2016.08.004

Cited by 27 publications

(20 citation statements)

References 32 publications

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“…Here, perhaps with an eye to the classical Stribeck curve, for the MB model we propose an exponentially weakening and linearly strengthening friction law. We show that this friction model yields to bistability thus vibration localization phenomena are expected as in Papangelo et al [24] if those oscillators were coupled together.…”

Section: Introductionmentioning

confidence: 76%

“…Recently, Papangelo et al [24] have found localized vibration states in a self-excited chain of mechanical oscillators weakly elastically coupled, which lead to the so-called snaking bifurcations in the bifurcation diagram. A key feature of the system was that, if isolated from the structure, each nonlinear oscillator experiences a subcritical Hopf bifurcation in a certain range of the control parameter (yielding bistability 1 ).…”

Section: Introductionmentioning

confidence: 99%

“…A key feature of the system was that, if isolated from the structure, each nonlinear oscillator experiences a subcritical Hopf bifurcation in a certain range of the control parameter (yielding bistability 1 ). However, Papangelo et al [24], adopted a polynomial nonlinearity quite remote from a real friction law. Here, perhaps with an eye to the classical Stribeck curve, for the MB model we propose an exponentially weakening and linearly strengthening friction law.…”

Section: Introductionmentioning

confidence: 99%

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Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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The dynamical behavior of a single-degreeof-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a subcritical Hopf bifurcation, using a velocity weakening-strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocity (v lw ) at which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick-slip vibrations exist. Together the two boundaries [v lw , v up ] define the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick-slip limit cycle. The model is used to fit recent experimental observations.

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Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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“…qualitative changes in system dynamics (see e.g. [19][20][21][22][23][24][25][26][27][28]). Nonlinear localization has been shown to appear not only in conservative systems [19] but also in friction-excited chains of weakly coupled oscillators [20,21], where the authors showed that the localization phenomenon is strongly related to the bistable behaviour of the single oscillator in the chain.…”

Section: Introductionmentioning

confidence: 99%

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Papangelo

Fontanela

Grolet

et al. 2019

Journal of Sound and Vibration

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Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.

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“…We refer interested readers to Papangelo et al [29] for detailed deductions. Lumped models in [29,30] illustrates a bistable zone where steady sliding and stick-slip limit cycle coexists in a certain range of the control parameter.…”

Section: X)mentioning

confidence: 99%

Parameter Determination of a Minimal Model for Brake Squeal

Chu

Zheng

Liang³

et al. 2018

Applied Sciences

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Abstract:In the research into the mechanism of brake squeal, minimal models with two degrees of freedom (DoFs) are widely used. Compared with the finite element method, the minimal model is more concise and efficient, making it easier to analyze the effect of parameters. However, how to accurately determine its kinetic parameters is rarely reported in the literature. In this paper, firstly, the finite element model of a disc brake is established and the complex eigenvalue analysis (CEA) is carried out to obtain unstable modes of the brake. Then, an unstable mode with seven nodal diameters predicted by CEA is taken as an example to establish the 2-DoF model. In order that the natural frequency, Hopf bifurcation point and real parts of eigenvalues of the minimal model coincide with that of the unstable mode with seven nodal diameters, the response surface method (RSM) is applied to determine the kinetic parameters of the minimal model. Finally, the parameter-optimized minimal model is achieved. Furthermore, the negative slope of friction-velocity characteristic is introduced into the model, and transient analysis (TA) is used to study the effect of braking velocity on stability of the brake system. The results show that the brake system becomes unstable when braking velocity is lower than a critical value. The lower the velocity is, the worse the stability appears, and the higher the brake squeal propensity is.

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Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Cited by 27 publications

References 32 publications

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Parameter Determination of a Minimal Model for Brake Squeal

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