Methods to reduce non-linear mechanical systems for instability computation

Sinou, Jean-Jacques; Thouverez, Fabrice; Jézéquel, L.

doi:10.1007/bf02736228

Cited by 32 publications

(36 citation statements)

References 133 publications

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“…For a non-linear system, stability is investigated by calculating the eigenvalues of the linearized system at the equilibrium point X 0 [5] …”

Section: Stability Analysismentioning

confidence: 99%

“…So in order to undertake extensive parametric studies and to investigate the role of structural damping, non-linear methods can be applied to find the non-linear response of the dynamical system. Because the purpose of this section is to study the effect of damping on limit cycle amplitudes of the non-linear system, we refer the interested reader to the following references for an extensive overview of the various non-linear methods and approaches [5,12]. Before briefly describing the methodology of this non-linear modal approach that will be used in this paper, it may be observed that the principle of this method is based on the well-known technique of equivalent linearization of Krylov and Bogoliubov [13]: the idea is to replace the non-linear system by an equivalent linear system in which the difference between the two systems is minimized.…”

Section: Self-excited Oscillations and Stable Limit Cyclesmentioning

confidence: 99%

“…Though many researchers have examined the problem of friction-induced vibrations with experimental, analytical and numerical approaches [1][2][3][4][5], there are still no methods for completely eliminating or reducing instability. The addition of damping to one part of a mechanical system such as the pads for brake systems [1,6] is commonly undertaken to reduce or eliminate vibration.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The influence of damping on the limit cycles for a self-exciting mechanism

Sinou¹,

Jézéquel²

2007

Journal of Sound and Vibration

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“…For a non-linear system, stability is investigated by calculating the eigenvalues of the linearized system at the equilibrium point X 0 [5] …”

Section: Stability Analysismentioning

confidence: 99%

Section: Self-excited Oscillations and Stable Limit Cyclesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The influence of damping on the limit cycles for a self-exciting mechanism

Sinou¹,

Jézéquel²

2007

Journal of Sound and Vibration

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“…Referring to [25], a 2-DoF mechanical model is established in Figure 4. In the model, two pads are symmetrically arranged on two sides of the brake disc and have the same motion.…”

Section: -Dof Minimal Model For Brake Squealmentioning

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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“…In self-sustained systems, these mechanisms fall into two distinct categories. First, one can mention the instabilities that depend mainly on geometrical characteristics of the system, such as sprag-slip or modal coupling through friction [1][2][3][4]. Sprag-slip instabilities were first described by Spurr [5]: the instability of the stationary position arises from a kinematic coupling between the variation of normal and friction forces.…”

Section: Introductionmentioning

confidence: 99%

Friction-induced vibration of a lubricated mechanical system

Sinou

Cayer-Barrioz

Berro

2013

Tribology International

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In a lubricated interface, the local dynamic responses can be complex and depend on molecular effects in the confined lubricating films. In a mechanical system comprising one or more of such interfaces, the influence of the local interfacial behaviour on the total vibrational response remains largely unknown. In this work, we propose a numerical model that incorporates realistic laws of local friction issued from previous experimental results. The objective is to characterize the dynamics of a lubricated system and to study its complex global responses triggered by the local interfacial behaviour. Both the stability analysis and vibrational oscillations of the mechanical system will be investigated through various operating conditions.

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Methods to reduce non-linear mechanical systems for instability computation

Cited by 32 publications

References 133 publications

The influence of damping on the limit cycles for a self-exciting mechanism

The influence of damping on the limit cycles for a self-exciting mechanism

Parameter Determination of a Minimal Model for Brake Squeal

Friction-induced vibration of a lubricated mechanical system

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