Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes

Eric Jacquelin (1) , Olivier Dessombz (2) , Jean-Jacques Sinou (2) , Sondipon Adhikari (3) , Michael I Friswell (3)

1 LBMC UMR T9406 - Laboratoire de Biomécanique et Mécanique des Chocs
2 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
3 College of Engineering [Swansea]

Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate model based on a polynomial chaos expansion (PCE) can be built as an alternative to MCS. However, some previous studies have shown poor convergence properties around the deterministic eigenfrequencies. In this study, an extended Pade approximant approach is proposed not only to accelerate the convergence of the PCE but also to have a better representation of the exact frequency response, which is a rational function of the uncertain parameters. A second approach is based on the random mode expansion of the response, which is widely used for deterministic dynamical systems. A PCE approach is used to calculate the random modes. Both approaches are tested on an example to check their efficiency.

Mots clés: MULTIVARIATE PADE APPROXIMANTS; POLYNOMIAL CHAOS EXPANSION; RANDOM DYNAMICAL SYSTEMS; RANDOM MODES

Domaines: Mécanique [physics.med-ph]

Eric Jacquelin, Olivier Dessombz, Jean-Jacques Sinou, Sondipon Adhikari, Michael I Friswell. Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes. Procedia Engineering, 2017, X International Conference on Structural Dynamics, EURODYN 2017, 199, pp.1104-1109. ⟨10.1016/j.proeng.2017.09.212⟩. ⟨hal-01589593⟩