Probabilistic collocation for period-1 limit cycle oscillations

To cite this version:Lyes Nechak, Sébastien Berger, Evelyne Aubry. A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems. Abstract-This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and nonintrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic method such as parametric studies and Monte Carlo based techniques.

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“…The same problem is dealt with in other studies (Millman et al, 2003;Pettit and Beran, 2006;Witteveen et. al, 2007).…”

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confidence: 83%

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

Nechak

Berger²,

Aubry³

2011

European Journal of Mechanics - A/Solids

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“…This integral can be evaluated by the Probabilistic Collocation (PC) method using a Gauss quadrature [1] such as…”

Section: Alternate Frequency-time Methods With Probabilistic Collocatimentioning

confidence: 99%

“…This non-intrusive in a stochastic sense method can easily be done, however, the convergence of the method needs a high number of samples that means a high CPU time. One possibility to reduce this CPU time is to associate one non-intrusive method called the Probabilistic Collocation (PC) [1] method and consisting in calculating the deterministic problem on the collocation points, points Gaussian quadrature, alone, of number smaller than that for the classical MC approach. Besides, the Monte Carlo simulations, the perturbation methods are based on the development of the random quantities in Taylor series [2] or Neumann series [3,4].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties

Didier

Sinou

Faverjon

2013

Communications in Nonlinear Science and Numerical Simulation

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“…However, such approaches become impractical when each sample realization results from high-fidelity computational fluid and structural dynamics tools. Probabilistic collocation methodologies are promising candidates to get more insights into physical mechanisms of flutter and LCO [1,2] with affordable computational cost [3][4][5]. These studies are generally based on the use of ad hoc inviscid linear aerodynamics, and the stochastic response of the system is governed by the uncertainties associated with the nonlinear structural stiffness coefficients [5,6].…”

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confidence: 99%

Stochastic Investigation of Flows About Airfoils at Transonic Speeds

Chassaing

Lucor

2010

AIAA Journal

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In this study, a deterministic compressible solver is coupled to a nonintrusive stochastic spectral projection method to propagate several aerodynamic uncertainties through a transonic steady flow around a NACA0012 airfoil. The stochastic model is solved in a generalized polynomial chaos framework. This approach combines the advantage of not modifying the existing deterministic solver while maintaining accurate representations of the stochastic solution and its statistics. The major difficulty of this work is to deal with deterministic transonic flows for which aerodynamics nonlinearities are reported in the uncertain probabilistic space. The efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestream Mach number. An error analysis is carried out in order to determine appropriate physical and stochastic discretization levels. Different stochastic flow regimes are analyzed in details by means of various postprocessing procedures, including error bars, probabilistic density function of the aerodynamic field, and Sobol's coefficients.

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Probabilistic collocation for period-1 limit cycle oscillations

Cited by 42 publications

References 23 publications

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties

Stochastic Investigation of Flows About Airfoils at Transonic Speeds

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